House edge of every bet
The share of each bet a casino keeps on average over a long run. Every figure has its source: a published table we quote, or a pay table we work out exactly, card by card and roll by roll. It is an average cost, not a forecast of one evening.
Blackjack
Blackjack’s edge depends on the rules at the table: the payout for a blackjack, the number of decks and what the dealer does on soft 17. Played at 89 casinos we list.
| Bet | House edge |
|---|---|
| Pays 3:2, six decks, dealer hits soft 17All four blackjack rows use the rules of the source’s table by number of decks: the dealer peeks for blackjack, you may double on any two cards and after splitting, re-split any pair, aces too, up to three times, no surrender, and the cards are shuffled after every hand by a continuous shuffler. | 0.551% Source
Pays 3:2, six decks, dealer hits soft 17 Dealer hits soft 17. … Blackjack pays 3 to 2. … Dealer peeks for blackjack with a ten or ace up. … Player may double on any two cards. … Player may not surrender. … Player may double after splitting. … Player may re-split any pair (including aces) up to three times. … Continuous shuffler used (cards shuffled after every hand). … Player uses basic strategy. Table “Blackjack House Edge by Decks”, row “6”, column “House Edge”: 0.551% Wizard of Odds · Why the number of decks matters in blackjack · read |
| Pays 3:2, six decks, dealer stands on soft 17 | ≈ 0.33%worked out Source
Pays 3:2, six decks, dealer stands on soft 17 Worked out: 0.551% (dealer hits soft 17) minus 0.22%, what hitting soft 17 costs the player. Dealer hits soft 17. … Blackjack pays 3 to 2. … Dealer peeks for blackjack with a ten or ace up. … Player may double on any two cards. … Player may not surrender. … Player may double after splitting. … Player may re-split any pair (including aces) up to three times. … Continuous shuffler used (cards shuffled after every hand). … Player uses basic strategy. Table “Blackjack House Edge by Decks”, row “6”, column “House Edge”: 0.551% Wizard of Odds · Why the number of decks matters in blackjack · read These changes are relative to the following rules: eight decks, dealer stands on soft 17 Table “Blackjack Rule Variations”, row “Dealer hits on soft 17”, column “Effect”: -0.22% |
| Pays 6:5, six decks, dealer hits soft 17 | ≈ 1.94%worked out Source
Pays 6:5, six decks, dealer hits soft 17 Worked out: 0.551% (pays 3:2) plus 1.39%, what the 6:5 payout costs the player. Dealer hits soft 17. … Blackjack pays 3 to 2. … Dealer peeks for blackjack with a ten or ace up. … Player may double on any two cards. … Player may not surrender. … Player may double after splitting. … Player may re-split any pair (including aces) up to three times. … Continuous shuffler used (cards shuffled after every hand). … Player uses basic strategy. Table “Blackjack House Edge by Decks”, row “6”, column “House Edge”: 0.551% Wizard of Odds · Why the number of decks matters in blackjack · read These changes are relative to the following rules: eight decks, dealer stands on soft 17 Table “Blackjack Rule Variations”, row “Blackjack pays 6-5”, column “Effect”: -1.39% |
| Pays 6:5, six decks, dealer stands on soft 17 | ≈ 1.72%worked out Source
Pays 6:5, six decks, dealer stands on soft 17 Worked out: 0.551% minus 0.22% (dealer stands on soft 17) plus 1.39% (6:5 payout). Dealer hits soft 17. … Blackjack pays 3 to 2. … Dealer peeks for blackjack with a ten or ace up. … Player may double on any two cards. … Player may not surrender. … Player may double after splitting. … Player may re-split any pair (including aces) up to three times. … Continuous shuffler used (cards shuffled after every hand). … Player uses basic strategy. Table “Blackjack House Edge by Decks”, row “6”, column “House Edge”: 0.551% Wizard of Odds · Why the number of decks matters in blackjack · read These changes are relative to the following rules: eight decks, dealer stands on soft 17 Table “Blackjack Rule Variations”, row “Dealer hits on soft 17 / Blackjack pays 6-5”, column “Effect”: -0.22% / -1.39% |
| Free Bet Blackjack: free doubles on 9, 10 and 11, free splits, dealer’s 22 pushesMeasured against the first bet. Rules of the source’s table: six decks, dealer hits soft 17, re-split to four hands, aces too, no surrender.Played at 35 casinos we list | 1.04% Source
Free Bet Blackjack: free doubles on 9, 10 and 11, free splits, dealer’s 22 pushes It is my understand that the rules below are now the norm. … Six decks … Dealer hits soft 17's … Blackjacks pay 3 to 2 … Double after split allowed … Double on two cards only … Re-split pairs up to four hands, including aces … No surrender … The house edge under the standard rules above is 1.04%. |
| Spanish 21: dealer stands on soft 17Before the Super Bonus, which lowers it by a few hundredths of a percent.Played at 8 casinos we list | 0.40% Source
Spanish 21: dealer stands on soft 17 Following is the house edge under various common rules, before considering the Super Bonus. … Dealer stands on soft 17: 0.40% Wizard of Odds · Spanish 21 · read |
| Spanish 21: dealer hits on soft 17, redoubling allowedPlayed at 8 casinos we list | 0.42% Source
Spanish 21: dealer hits on soft 17, redoubling allowed Following is the house edge under various common rules, before considering the Super Bonus. … Dealer hits on soft 17, redoubling allowed: 0.42% Wizard of Odds · Spanish 21 · read |
| Spanish 21: dealer hits on soft 17, redoubling not allowedPlayed at 8 casinos we list | 0.76% Source
Spanish 21: dealer hits on soft 17, redoubling not allowed Following is the house edge under various common rules, before considering the Super Bonus. … Dealer hits on soft 17, redoubling not allowed: 0.76% Wizard of Odds · Spanish 21 · read |
| Insurance, pays 2 to 1A side bet that the dealer’s hidden card is a ten when the up card is an ace. Worked out without your own two cards. | 7.40%worked out Source
Insurance, pays 2 to 1 Worked out: pays 2 to 1; with six decks and the dealer’s ace showing, 96 of the 311 unseen cards are tens: 1 − 3 × 96/311 = 7.40%; with eight decks, 1 − 3 × 128/415 = 7.47%. Rules published by BCLC for B.C. casinos, 1.0 Basic Blackjack, 4.6.2. In our words: Insurance pays 2 to 1 when the dealer turns out to have a blackjack. BCLC · BCLC Rules of Play for Table Games - Blackjack · read Rules published by Loto-Québec for its casinos, The player options. If the house draws a blackjack, the insurance bet pays 2 to 1. Rules Fallsview Casino Resort and Casino Niagara publish for their tables, Blackjack terms: Insurance. All winning insurance wagers pay 2 to 1. Fallsview Casino Resort and Casino Niagara · Playing Blackjack · read |
- 6 decksSource
B.C. (BCLC): 6 decks
Rules published by BCLC for B.C. casinos, 1.0 Basic Blackjack, 1.1.
In our words: The dealer deals from a shoe holding six ordinary decks.
BCLC · BCLC Rules of Play for Table Games - Blackjack · read
- Blackjack pays 3 to 2Source
B.C. (BCLC): Blackjack pays 3 to 2
Rules published by BCLC for B.C. casinos, 1.0 Basic Blackjack, 7.1.1.
In our words: A blackjack pays 3 to 2.
BCLC · BCLC Rules of Play for Table Games - Blackjack · read
- Dealer hits soft 17Source
B.C. (BCLC): Dealer hits soft 17
Rules published by BCLC for B.C. casinos, 1.0 Basic Blackjack, 8.8.
In our words: draw on 16 or less, and on soft 17; and stop drawing at hard 17.
BCLC · BCLC Rules of Play for Table Games - Blackjack · read
- Double on any two cardsSource
B.C. (BCLC): Double on any two cards
Rules published by BCLC for B.C. casinos, 1.0 Basic Blackjack, 4.3.
In our words: you may double on any first two cards by adding a second bet.
BCLC · BCLC Rules of Play for Table Games - Blackjack · read
- Double after splittingSource
B.C. (BCLC): Double after splitting
Rules published by BCLC for B.C. casinos, 1.0 Basic Blackjack, 4.4.6.
In our words: Doubling is allowed on hands that came from a split.
BCLC · BCLC Rules of Play for Table Games - Blackjack · read
- Pairs may be re-splitSource
B.C. (BCLC): Pairs may be re-split
Rules published by BCLC for B.C. casinos, 1.0 Basic Blackjack, 4.4.1.
In our words: A pair that turns up after a split can be split again.
BCLC · BCLC Rules of Play for Table Games - Blackjack · read
- Aces split once, one card eachSource
B.C. (BCLC): Aces split once, one card each
Rules published by BCLC for B.C. casinos, 1.0 Basic Blackjack, 4.4.2.
In our words: A pair of aces can be split one time, and each ace then gets just one card.
BCLC · BCLC Rules of Play for Table Games - Blackjack · read
- Late surrenderSource
B.C. (BCLC): Late surrender
Rules published by BCLC for B.C. casinos, 1.0 Basic Blackjack, 4.5.
In our words: after your first two cards and before you act, you may surrender. Surrender is not available when the dealer holds a blackjack.
BCLC · BCLC Rules of Play for Table Games - Blackjack · read
- No hole card; a dealer blackjack takes only your original betSource
B.C. (BCLC): No hole card; a dealer blackjack takes only your original bet
Rules published by BCLC for B.C. casinos, 1.0 Basic Blackjack, 8.2.2, 4.3.4.a, 4.4.8.a.
In our words: then deals the dealer’s own card face up, in front of the chip rack; If the dealer has a blackjack, a doubled hand loses only its first bet; the extra chips come back. If the dealer has a blackjack, a split hand loses only its first bet; the extra bet for the split comes back.
BCLC · BCLC Rules of Play for Table Games - Blackjack · read
- Insurance pays 2 to 1Source
B.C. (BCLC): Insurance pays 2 to 1
Rules published by BCLC for B.C. casinos, 1.0 Basic Blackjack, 4.6.2.
In our words: Insurance pays 2 to 1 when the dealer turns out to have a blackjack.
BCLC · BCLC Rules of Play for Table Games - Blackjack · read
- A 6:5 table opens only alongside a 3:2 tableSource
B.C. (BCLC): A 6:5 table opens only alongside a 3:2 table
Rules published by BCLC for B.C. casinos, 4.0 6 to 5 Blackjack, 1.6.
In our words: Whenever a 6 to 5 game is open, a game paying 3 to 2 for a blackjack has to be open as well.
BCLC · BCLC Rules of Play for Table Games - Blackjack · read
- Blackjack pays as posted at the tableSource
Fallsview and Casino Niagara: Blackjack pays as posted at the table
Rules Fallsview Casino Resort and Casino Niagara publish for their tables, Blackjack.
you have "Blackjack" and will be paid odds as marked on the layout (3 to 2 or 6 to 5).
Fallsview Casino Resort and Casino Niagara · Playing Blackjack · read
- Soft 17: as posted at the tableSource
Fallsview and Casino Niagara: Soft 17: as posted at the table
Rules Fallsview Casino Resort and Casino Niagara publish for their tables, Blackjack.
The Dealer must draw cards according to the rules posted on the table;
Fallsview Casino Resort and Casino Niagara · Playing Blackjack · read
- Split to 4 hands; aces split once, one card eachSource
Fallsview and Casino Niagara: Split to 4 hands; aces split once, one card each
Rules Fallsview Casino Resort and Casino Niagara publish for their tables, Blackjack terms: Splitting Pairs.
This may be done to a total of four hands except for Aces. Aces receive only one card and may be split only once.
Fallsview Casino Resort and Casino Niagara · Playing Blackjack · read
- Double after splitting, except split acesSource
Fallsview and Casino Niagara: Double after splitting, except split aces
Rules Fallsview Casino Resort and Casino Niagara publish for their tables, Blackjack terms: Splitting Pairs.
You may also "double down" on the first two cards of each hand after the split, except when splitting Aces.
Fallsview Casino Resort and Casino Niagara · Playing Blackjack · read
- Insurance pays 2 to 1Source
Fallsview and Casino Niagara: Insurance pays 2 to 1
Rules Fallsview Casino Resort and Casino Niagara publish for their tables, Blackjack terms: Insurance.
All winning insurance wagers pay 2 to 1.
Fallsview Casino Resort and Casino Niagara · Playing Blackjack · read
- 1 to 8 decksSource
Québec (Loto-Québec): 1 to 8 decks
Rules published by Loto-Québec for its casinos, The cards.
Blackjack is played with 1 to 8 decks of 52 cards.
- Soft 17: as posted at the tableSource
Québec (Loto-Québec): Soft 17: as posted at the table
Rules published by Loto-Québec for its casinos, The house strategy.
according to the house strategy indicated at the table which may either be: HIT on a count of soft 17 or less and STAND on a count of hard 17 or more, or HIT on a count of 16 or less and STAND on a count of (soft or hard) 17 or more.
- Blackjack pays as posted at the tableSource
Québec (Loto-Québec): Blackjack pays as posted at the table
Rules published by Loto-Québec for its casinos, The payouts; Variations.
If the player gets a blackjack, the bet is paid 3 to 2, except when the house's hand is also a blackjack. … If the player gets a blackjack, the payout is issued according to the payout indicated at the table.
- Split to 4 hands; aces split once, one card eachSource
Québec (Loto-Québec): Split to 4 hands; aces split once, one card each
Rules published by Loto-Québec for its casinos, The player options.
for a maximum of four hands. … In the case of a pair of aces, players can split only once and hit for only one additional card for each hand.
- Double after splitting, except split acesSource
Québec (Loto-Québec): Double after splitting, except split aces
Rules published by Loto-Québec for its casinos, The player options.
Players may also double down on each hand after SPLITTING two cards of the same value, except in the case of a pair of aces.
- Insurance pays 2 to 1Source
Québec (Loto-Québec): Insurance pays 2 to 1
Rules published by Loto-Québec for its casinos, The player options.
If the house draws a blackjack, the insurance bet pays 2 to 1.
The house edge for a given set of these rules is worked out in Blackjack strategy
Roulette
On a given wheel every bet costs the same, except the five-number bet on a double-zero wheel. Played at 85 casinos we list.
Roulette in B.C.
Rules published by BCLC for B.C. casinos, 1.0 Double Zero, 1.2.
The layout and wheel for a roulette game contain the numbers 1-36, 0 and 00.
Roulette in Québec
Rules published by Loto-Québec for its casinos, The wheel.
The wheel contains the numbers 0 to 36 (English roulette), or 00 and 0 to 36 (American roulette).
| Bet | Single zero Source
Roulette, single zero Worked out: every bet pays as if the wheel had 36 numbers, and the zeros are the difference: 1 − 36/37. What most call "European roulette" is roulette played on a 37-number wheel, with one zero only. The pays are the same as in American roulette. However, with one zero the house edge is cut to 1/37, or 2.70%, on all bets. Rules published by Loto-Québec for its casinos, The wheel. The wheel contains the numbers 0 to 36 (English roulette), or 00 and 0 to 36 (American roulette). | Double zero Source
Roulette, double zero Worked out: every bet pays as if the wheel had 36 numbers, and the zeros are the difference: 1 − 36/38. A U.S. roulette wheel consists of 38 numbered slots: numbers 1 to 36, a zero, and a double zero. … The house edge on all bets is 1/19, or 5.26%, except for the 0-00-1-2-3 combination, which carries a house edge of 7.89%. | Triple zero Source
Roulette, triple zero Worked out: every bet pays as if the wheel had 36 numbers, and the zeros are the difference: 1 − 36/39. Triple-Zero Roulette is roulette played on a 39-number wheel. … The house edge on every bet is 1/13 or 7.69%. |
|---|---|---|---|
| Straight upPays 35 to 1 · one number | 2.70%SD 5.84 | 5.26%SD 5.76 | 7.69%SD 5.69 |
| SplitPays 17 to 1 · two numbers | 2.70%SD 4.07 | 5.26%SD 4.02 | 7.69%SD 3.97 |
| StreetPays 11 to 1 · three numbers | 2.70%SD 3.28 | 5.26%SD 3.24 | 7.69%SD 3.20 |
| CornerPays 8 to 1 · four numbers | 2.70%SD 2.79 | 5.26%SD 2.76 | 7.69%SD 2.73 |
| Five-number betPays 6 to 1 · 0, 00, 1, 2, 3 | not on this wheel | 7.89%SD 2.37 | not on this wheel |
| Six linePays 5 to 1 · six numbers | 2.70%SD 2.21 | 5.26%SD 2.19 | 7.69%SD 2.16 |
| Dozen or columnPays 2 to 1 · 12 numbers | 2.70%SD 1.40 | 5.26%SD 1.39 | 7.69%SD 1.38 |
| Red or black, odd or even, 1–18 or 19–36Pays 1 to 1 · 18 numbers | 2.70%SD 1.00 | 5.26%SD 1.00 | 7.69%SD 1.00 |
Craps
Per bet resolved and per roll: a place bet waits several rolls for its decision, a proposition bet is settled on the next roll. Per roll is the fair way to compare them. Played at 39 casinos we list.
| Bet | House edge | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Pass line or comePays 1 to 1 | 1.41%worked out Source
Pass line or come Worked out: come-out 7 or 11 wins, 2, 3 or 12 loses, a point wins if it comes before a 7: win 244/495, lose 251/495; the bet lasts 557/165 ≈ 3.376 rolls on average. Table “Pass”, row “Bet resolved / Roll”, column “House Edge”: 1.41% / 0.42% | ||||||||
| Don’t pass or don’t come, 12 pushesPays 1 to 1 | 1.36% per bet made · 1.40% resolvedworked out Source
Don’t pass or don’t come, 12 pushes Worked out: a 12 on the come-out is a push; per bet made the push stays in: 1.36%; per bet resolved it does not: 1.40%. A 12 is a push, except in Reno and Lake Tahoe, where a 2 is a push instead of the 12. Table “Don't Pass”, row “Bet made / Bet resolved / Roll”, column “House Edge”: 1.36% / 1.40% / 0.40% | ||||||||
| Odds behind the pass linePays true odds: 2 to 1 on 4 or 10, 3 to 2 on 5 or 9, 6 to 5 on 6 or 8 | 0% Source
Odds behind the pass line The odds on the Odds are exactly fair, which zero house edge. Rules published by BCLC for B.C. casinos, 1.0 Craps, 6.1.2. The Player's Odds wager may be up to a maximum of 3 times the amount of the Pass Line and Come wager if the point is 4 or 10; … The Player's Odds wager may be up to a maximum of 4 times the amount of the Pass Line and Come wager if the point is 5 or 9. … The Player's Odds wager may be up to a maximum of 5 times the amount of the Pass Line and Come wager if the point is either 6 or 8. | ||||||||
| Pass line with full 1× oddsMeasured against all money bet, pass line and odds together. | 0.848%worked out Source
Pass line with full 1× odds Worked out: the pass line loses 7/495 of the pass bet on average and the odds lose nothing, so the same loss is divided by everything bet: 1.414% ÷ (1 + 0.6667 average odds per pass bet). The following table shows the combined house edge on the pass or come bet, backed up by taking full odds according to the maximum odds allowed. Table “Combined House Edge on Pass/Come & Taking Full Odds”, row “1X”, column “Bet Made / Roll”: 0.00848 / 0.00251 | ||||||||
| Pass line with full 2× oddsMeasured against all money bet, pass line and odds together. | 0.606%worked out Source
Pass line with full 2× odds Worked out: the pass line loses 7/495 of the pass bet on average and the odds lose nothing, so the same loss is divided by everything bet: 1.414% ÷ (1 + 1.3333 average odds per pass bet). The following table shows the combined house edge on the pass or come bet, backed up by taking full odds according to the maximum odds allowed. Table “Combined House Edge on Pass/Come & Taking Full Odds”, row “2X”, column “Bet Made / Roll”: 0.00606 / 0.00180 | ||||||||
| Pass line with full 3-4-5× oddsMeasured against all money bet, pass line and odds together. Lower only because the free odds bet is counted in the total; in dollars an hour it costs the same as the pass line alone. | 0.374%worked out Source
Pass line with full 3-4-5× odds Worked out: the pass line loses 7/495 of the pass bet on average and the odds lose nothing, so the same loss is divided by everything bet: 1.414% ÷ (1 + 2.7778 average odds per pass bet). The following table shows the combined house edge on the pass or come bet, backed up by taking full odds according to the maximum odds allowed. Table “Combined House Edge on Pass/Come & Taking Full Odds”, row “3X-4X-5X”, column “Bet Made / Roll”: 0.00374 / 0.00111 Rules published by BCLC for B.C. casinos, 1.0 Craps, 6.1.2. The Player's Odds wager may be up to a maximum of 3 times the amount of the Pass Line and Come wager if the point is 4 or 10; … The Player's Odds wager may be up to a maximum of 4 times the amount of the Pass Line and Come wager if the point is 5 or 9. … The Player's Odds wager may be up to a maximum of 5 times the amount of the Pass Line and Come wager if the point is either 6 or 8. | ||||||||
| Pass line with full 5× oddsMeasured against all money bet, pass line and odds together. | 0.326%worked out Source
Pass line with full 5× odds Worked out: the pass line loses 7/495 of the pass bet on average and the odds lose nothing, so the same loss is divided by everything bet: 1.414% ÷ (1 + 3.3333 average odds per pass bet). The following table shows the combined house edge on the pass or come bet, backed up by taking full odds according to the maximum odds allowed. Table “Combined House Edge on Pass/Come & Taking Full Odds”, row “5X”, column “Bet Made / Roll”: 0.00326 / 0.00097 | ||||||||
| Pass line with full 10× oddsMeasured against all money bet, pass line and odds together. | 0.184%worked out Source
Pass line with full 10× odds Worked out: the pass line loses 7/495 of the pass bet on average and the odds lose nothing, so the same loss is divided by everything bet: 1.414% ÷ (1 + 6.6667 average odds per pass bet). The following table shows the combined house edge on the pass or come bet, backed up by taking full odds according to the maximum odds allowed. Table “Combined House Edge on Pass/Come & Taking Full Odds”, row “10X”, column “Bet Made / Roll”: 0.00184 / 0.00055 | ||||||||
| Place bet on 6 and 8Pays 7 to 6 | 1.52%worked out Source
Place bet on 6 and 8 Worked out: 6 before 7: 5 ways against 6, pays 7 to 6. To be specific, place bets on the 6 and 8 pay 7 to 6, the 5 and 9 pay 7 to 5, and the 4 and 10 pay 9 to 5. Table “Place 6 and 8”, row “Bet resolved / Roll”, column “House Edge”: 1.52% / 0.46% Rules published by BCLC for B.C. casinos. Table “PLACE BET WAGER”, 1.0 Craps, 6.3.5:
| ||||||||
| Place bet on 5 and 9Pays 7 to 5 | 4.00%worked out Source
Place bet on 5 and 9 Worked out: 5 before 7: 4 ways against 6, pays 7 to 5. To be specific, place bets on the 6 and 8 pay 7 to 6, the 5 and 9 pay 7 to 5, and the 4 and 10 pay 9 to 5. Table “Place 5 and 9”, row “Bet resolved / Roll”, column “House Edge”: 4.00% / 1.11% Rules published by BCLC for B.C. casinos. Table “PLACE BET WAGER”, 1.0 Craps, 6.3.5:
| ||||||||
| Place bet on 4 and 10Pays 9 to 5 | 6.67%worked out Source
Place bet on 4 and 10 Worked out: 4 before 7: 3 ways against 6, pays 9 to 5. To be specific, place bets on the 6 and 8 pay 7 to 6, the 5 and 9 pay 7 to 5, and the 4 and 10 pay 9 to 5. Table “Place 4 and 10”, row “Bet resolved / Roll”, column “House Edge”: 6.67% / 1.67% Rules published by BCLC for B.C. casinos. Table “PLACE BET WAGER”, 1.0 Craps, 6.3.5:
| ||||||||
| Big 6 or Big 8Pays 1 to 1 | 9.09%worked out Source
Big 6 or Big 8 Worked out: the same as a place bet on 6, but paid even money: 5 ways against 6. The Big 6 and 8 are exactly like the place bets on 6 and 8, respectively, except pay even money, instead of 7 to 6. Table “Big 6 and 8”, row “Bet resolved / Roll”, column “House Edge”: 9.09% / 2.78% Rules published by BCLC for B.C. casinos, 1.0 Craps, 6.10.4. Big 6 or Big 8 is won the wager will be paid even money. | ||||||||
| FieldOne roll: wins on 2, 3, 4, 9, 10, 11 or 12, loses on 5, 6, 7 or 8. | 2.78%worked out Source
Field Worked out: one roll: 3, 4, 9, 10, 11 pay even money (14 of 36), 2 pays 2 to 1, 12 pays 3 to 1, 5 to 8 lose (20 of 36). In Las Vegas most casinos pay 2 to 1 on the 2, and 3 to 1 on the 12. … The lower right cell shows a house edge of 2.78%. Source
Field (B.C.) Worked out: one roll: 3, 4, 9, 10, 11 pay even money (14 of 36), 2 pays 2 to 1, 12 pays 2 to 1, 5 to 8 lose (20 of 36). Rules published by BCLC for B.C. casinos. A Field bet is a one roll bet that wins if 2, 3, 4, 9, 10, 11 or 12 is rolled. Table “FIELD BET WAGER”, 1.0 Craps, 6.9:
pay only 2 to 1 on both the 2 and 12. This doubles the house edge to 5.56%. | ||||||||
| Hard 6 or 8Pays 9 to 1 | 9.09%worked out Source
Hard 6 or 8 Worked out: the pair on 6 (1 way) before a 7 or an easy 6 (10 ways), pays 9 to 1. In the U.S., and most other countries, the Hard 6 and 8 pays 9 to 1, and the Hard 4 and 10 pays 7 to 1. Table “Hard — 6 and 8”, row “Bet resolved / Roll”, column “U.S.”: 9.09% / 2.78% Rules published by BCLC for B.C. casinos. Table “HARDWAY WAGER”, 1.0 Craps, 6.7.5:
| ||||||||
| Hard 4 or 10Pays 7 to 1 | 11.11%worked out Source
Hard 4 or 10 Worked out: the pair on 4 (1 way) before a 7 or an easy 4 (8 ways), pays 7 to 1. In the U.S., and most other countries, the Hard 6 and 8 pays 9 to 1, and the Hard 4 and 10 pays 7 to 1. Table “Hard — 4 and 10”, row “Bet resolved / Roll”, column “U.S.”: 11.11% / 2.78% Rules published by BCLC for B.C. casinos. Table “HARDWAY WAGER”, 1.0 Craps, 6.7.5:
| ||||||||
| 2 or 12Pays 30 to 1, one roll | 13.89%worked out Source
2 or 12 Worked out: one way of 36 wins 30 to 1. Since all Proposition Bets resolve in one throw and never push the house edge is the same whether defined as per made, resolved, or per throw. Table “Proposition Bets”, row “2, 12, and all "hard" hop bets”, column “House Edge”: 13.89% Rules published by BCLC for B.C. casinos. Table “PROPOSITION BET WAGER”, 1.0 Craps, 6.6.4:
| ||||||||
| 3 or 11Pays 15 to 1, one roll | 11.11%worked out Source
3 or 11 Worked out: two ways of 36 win 15 to 1. Since all Proposition Bets resolve in one throw and never push the house edge is the same whether defined as per made, resolved, or per throw. Table “Proposition Bets”, row “3, 11, and all "easy" hop bets”, column “House Edge”: 11.11% Rules published by BCLC for B.C. casinos. Table “PROPOSITION BET WAGER”, 1.0 Craps, 6.6.4:
| ||||||||
| Any craps (2, 3 or 12)Pays 7 to 1, one roll | 11.11%worked out Source
Any craps (2, 3 or 12) Worked out: four ways of 36 win 7 to 1. Since all Proposition Bets resolve in one throw and never push the house edge is the same whether defined as per made, resolved, or per throw. Table “Proposition Bets”, row “Any craps (2, 3, or 12)”, column “House Edge”: 11.11% Rules published by BCLC for B.C. casinos. Table “PROPOSITION BET WAGER”, 1.0 Craps, 6.6.4:
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| Any sevenPays 4 to 1, one roll | 16.67%worked out Source
Any seven Worked out: six ways of 36 win 4 to 1. Since all Proposition Bets resolve in one throw and never push the house edge is the same whether defined as per made, resolved, or per throw. Table “Proposition Bets”, row “Any seven”, column “House Edge”: 16.67% Rules published by BCLC for B.C. casinos. Table “PROPOSITION BET WAGER”, 1.0 Craps, 6.6.4:
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| Hop bet on a pair (for example 3-3)Pays 30 to 1, one roll | 13.89%worked out Source
Hop bet on a pair (for example 3-3) Worked out: one way of 36 wins 30 to 1. Since all Proposition Bets resolve in one throw and never push the house edge is the same whether defined as per made, resolved, or per throw. Table “Proposition Bets”, row “2, 12, and all "hard" hop bets”, column “House Edge”: 13.89% Rules published by BCLC for B.C. casinos. Table “HOP BET WAGER”, 1.0 Craps, 6.8.5:
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| Hop bet on two different numbers (for example 1-4)Pays 15 to 1, one roll | 11.11%worked out Source
Hop bet on two different numbers (for example 1-4) Worked out: two ways of 36 win 15 to 1. Since all Proposition Bets resolve in one throw and never push the house edge is the same whether defined as per made, resolved, or per throw. Table “Proposition Bets”, row “3, 11, and all "easy" hop bets”, column “House Edge”: 11.11% Rules published by BCLC for B.C. casinos. Table “HOP BET WAGER”, 1.0 Craps, 6.8.5:
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Baccarat
Eight decks unless stated. Played at 68 casinos we list.
| Bet | House edge |
|---|---|
| Banker, 5% commissionPays 1 to 1, less 5% | 1.06%worked out Source
Banker, 5% commission Worked out: eight decks, every deal worked out card by card: player wins 44.6247%, banker wins 45.8597%, tie 9.5156%. As the lower right cells in each table show, the house edge is 1.06% on the banker bet, 1.24% on the player bet, and 14.36% on the tie. Rules published by BCLC for B.C. casinos, 1.0 Mini-Baccarat, 1.1. Mini-Baccarat is a card game played with six (6) to eight (8) standard decks of 52 playing cards dealt from a shoe Rules published by BCLC for B.C. casinos, 1.0 Mini-Baccarat, 5.1. A 5% commission shall be charged for winning banker bets. |
| PlayerPays 1 to 1 | 1.24%worked out Source
Player Worked out: eight decks, every deal worked out card by card: player wins 44.6247%, banker wins 45.8597%, tie 9.5156%. As the lower right cells in each table show, the house edge is 1.06% on the banker bet, 1.24% on the player bet, and 14.36% on the tie. Rules published by BCLC for B.C. casinos, 1.0 Mini-Baccarat, 1.1. Mini-Baccarat is a card game played with six (6) to eight (8) standard decks of 52 playing cards dealt from a shoe |
| Tie, paid 8 to 1Pays 8 to 1 | 14.36%worked out Source
Tie, paid 8 to 1 Worked out: a tie comes up 9.5156% of eight-deck hands. As the lower right cells in each table show, the house edge is 1.06% on the banker bet, 1.24% on the player bet, and 14.36% on the tie. Rules published by BCLC for B.C. casinos, 1.0 Mini-Baccarat, 1.1. Mini-Baccarat is a card game played with six (6) to eight (8) standard decks of 52 playing cards dealt from a shoe Rules published by BCLC for B.C. casinos, 1.0 Mini-Baccarat, 7.3. Winning bets on the tie are paid 8 to 1. |
| Tie, where it pays 9 to 1Pays 9 to 1 | 4.84%worked out Source
Tie, where it pays 9 to 1 Worked out: a tie comes up 9.5156% of eight-deck hands and pays 9 to 1. The Tie has been known to pay 9 to 1 at some casinos. … 8 decks: 4.844% |
| EZ Baccarat banker: no commission, a three-card banker 7 pushesPays 1 to 1At B.C. tables this game is called Ruyi Baccarat.Played at 15 casinos we list | 1.02%worked out Source
EZ Baccarat banker: no commission, a three-card banker 7 pushes Worked out: the banker wins with a three-card 7 in 2.2534% of eight-deck hands, and that win pushes. The rules followed standard baccarat except on the Banker bet: (1) all wins pay even money, and (2) if the banker wins with a three-card total of 7, then the banker bet will push. … The following table shows the possible outcomes of the Banker bet, based on eight decks. The lower right cell shows a house edge of 1.02% Wizard of Odds · EZ Baccarat · read Rules published by BCLC for B.C. casinos, 1.0 Mini-Baccarat, 1.1. Mini-Baccarat is a card game played with six (6) to eight (8) standard decks of 52 playing cards dealt from a shoe Rules published by BCLC for B.C. casinos, 7.0 Ruyi Baccarat, 1.1-1.3, 3.2.1. No commission is taken on winning Banker bets; … which pays 40 to 1 when the three card winning total of 7 occurs in the Banker hand … which pays 25 to 1 when the three card winning total of 8 occurs in the Player hand … A bet on the Banker hand is a push; |
| Dragon 7: the banker wins with a three-card 7 (at B.C. tables, Gold 7)Pays 40 to 1Played at 15 casinos we list | 7.61%worked out Source
Dragon 7: the banker wins with a three-card 7 (at B.C. tables, Gold 7) Worked out: 2.2534% of eight-deck hands, paid 40 to 1. The Dragon 7 bets wins on a Banker winning three-card total of seven. The following table shows the probability and return of each event, based on eight decks. The lower right cell shows a house edge of 7.61%. Wizard of Odds · EZ Baccarat · read Rules published by BCLC for B.C. casinos, 1.0 Mini-Baccarat, 1.1. Mini-Baccarat is a card game played with six (6) to eight (8) standard decks of 52 playing cards dealt from a shoe Rules published by BCLC for B.C. casinos, 7.0 Ruyi Baccarat, 1.1-1.3, 3.2.1. No commission is taken on winning Banker bets; … which pays 40 to 1 when the three card winning total of 7 occurs in the Banker hand … which pays 25 to 1 when the three card winning total of 8 occurs in the Player hand … A bet on the Banker hand is a push; |
| Panda 8: the player wins with a three-card 8 (at B.C. tables, Jade 8)Pays 25 to 1Played at 15 casinos we list | 10.19%worked out Source
Panda 8: the player wins with a three-card 8 (at B.C. tables, Jade 8) Worked out: 3.4543% of eight-deck hands, paid 25 to 1. The Panda 8 bets wins on a Player winning three-card total of eight. The following table shows the probability and return of each event, based on eight decks. The lower right cell shows a house edge of 10.19%. Wizard of Odds · EZ Baccarat · read Rules published by BCLC for B.C. casinos, 1.0 Mini-Baccarat, 1.1. Mini-Baccarat is a card game played with six (6) to eight (8) standard decks of 52 playing cards dealt from a shoe Rules published by BCLC for B.C. casinos, 7.0 Ruyi Baccarat, 1.1-1.3, 3.2.1. No commission is taken on winning Banker bets; … which pays 40 to 1 when the three card winning total of 7 occurs in the Banker hand … which pays 25 to 1 when the three card winning total of 8 occurs in the Player hand … A bet on the Banker hand is a push; |
| Player pair or banker pairPays 11 to 1 | 10.36%worked out Source
Player pair or banker pair Worked out: the first two cards of the hand share a rank: 13 × C(32,2) of C(416,2) two-card starts with eight decks (6,448 of 86,320). The Player Pair bet wins if the first two cards in the Player hand are of the same rank. All other outcomes lose. Table “Pair Bets — 8 Decks”, row “Pair”, column “Pays / Probability”: 11 / 0.074699 |
Sic Bo
Pays on the totals, doubles and triples differ between casinos; where they do, the range covers the pays Wizard of Odds lists, and your table’s sign decides. Played at 18 casinos we list.
| Bet | House edge |
|---|---|
| Small (4 to 10) or big (11 to 17), not a triplePays 1 to 1 | 2.78%worked out Source
Small (4 to 10) or big (11 to 17), not a triple Worked out: 105 of the 216 rolls of three dice win, 1 to 1. Small: Wins on total of 4-10, except for a three of a kind. Probability of winning is 48.61%. Pays 1 to 1. House edge is 2.78%. Wizard of Odds · Sic Bo · read |
| Total of 4 or 17Pays 50 to 1 (Macau), 60 to 1 (Atlantic City), 62 to 1 (Australia) | 12.50% to 29.17%worked out Source
Total of 4 or 17 Worked out: 3 of the 216 rolls of three dice win: at 50 to 1 (Macau) 29.17%, at 60 to 1 (Atlantic City) 15.28%, at 62 to 1 (Australia) 12.50%. Total of 4 and 17: Pays 50 to 1 in Macau, 60 to 1 in Atlantic City, and 62 to 1 in Australia. Wizard of Odds · Sic Bo · read |
| Total of 5 or 16Pays 18 to 1 (Macau), 30 to 1 (Atlantic City), 31 to 1 (Australia) | 11.11% to 47.22%worked out Source
Total of 5 or 16 Worked out: 6 of the 216 rolls of three dice win: at 18 to 1 (Macau) 47.22%, at 30 to 1 (Atlantic City) 13.89%, at 31 to 1 (Australia) 11.11%. Total of 5 and 16: Pays 18 to 1 in Macau, 30 to 1 in Atlantic City, and 31 to 1 in Australia. Wizard of Odds · Sic Bo · read |
| Total of 6 or 15Pays 14 to 1 (Macau), 17 to 1 (Atlantic City), 18 to 1 (Australia) | 12.04% to 30.56%worked out Source
Total of 6 or 15 Worked out: 10 of the 216 rolls of three dice win: at 14 to 1 (Macau) 30.56%, at 17 to 1 (Atlantic City) 16.67%, at 18 to 1 (Australia) 12.04%. Total of 6 and 15: Pays 14 to 1 in Macau, 17 to 1 in Atlantic City, and 18 to 1 in Australia. Wizard of Odds · Sic Bo · read |
| Total of 7 or 14Pays 12 to 1 | 9.72%worked out Source
Total of 7 or 14 Worked out: 15 of the 216 rolls of three dice win, 12 to 1. Total of 7 and 14: Pays 12 to 1 everywhere. Wizard of Odds · Sic Bo · read |
| Total of 8 or 13Pays 8 to 1 | 12.50%worked out Source
Total of 8 or 13 Worked out: 21 of the 216 rolls of three dice win, 8 to 1. Total of 8 and 13: Pays 8 to 1 everywhere. Wizard of Odds · Sic Bo · read |
| Total of 9 or 12Pays 6 to 1 (Macau and Atlantic City), 7 to 1 (Australia) | 7.41% to 18.98%worked out Source
Total of 9 or 12 Worked out: 25 of the 216 rolls of three dice win: at 6 to 1 (Macau and Atlantic City) 18.98%, at 7 to 1 (Australia) 7.41%. Total of 9 and 12: Pays 6 to 1 in Macau and Atlantic City. Pays 7 to 1 in Australia. Wizard of Odds · Sic Bo · read |
| Total of 10 or 11Pays 6 to 1 | 12.50%worked out Source
Total of 10 or 11 Worked out: 27 of the 216 rolls of three dice win, 6 to 1. Total of 10 and 11: Pays 6 to 1 everywhere. House edge of 12.50%. Wizard of Odds · Sic Bo · read |
| A given double (for example two 4s)Pays 8 to 1 (Macau), 10 to 1 (Atlantic City), 11 to 1 (Australia) | 11.11% to 33.33%worked out Source
A given double (for example two 4s) Worked out: 16 of the 216 rolls of three dice win: at 8 to 1 (Macau) 33.33%, at 10 to 1 (Atlantic City) 18.52%, at 11 to 1 (Australia) 11.11%. Double: Bet on any specific pair (for example two 1's). Player wins if at least 2 of the number chosen appears. Pays 8 to 1 in Macau, 10 to 1 in Atlantic City, and 11 to 1 in Australia. Wizard of Odds · Sic Bo · read |
| A given triple (for example three 4s)Pays 150 to 1 (Macau), 180 to 1 (Atlantic City) | 16.20% to 30.09%worked out Source
A given triple (for example three 4s) Worked out: 1 of the 216 rolls of three dice win: at 150 to 1 (Macau) 30.09%, at 180 to 1 (Atlantic City) 16.20%. Specific Triple: Player may bet on any specific trips (for example three 1's). Player wins if all 3 dice match the number chosen. Pays 150 to 1 in Macau and 180 to 1 in Atlantic City. Wizard of Odds · Sic Bo · read |
| Any triplePays 24 to 1 (Macau), 30 to 1 (Atlantic City) | 13.89% to 30.56%worked out Source
Any triple Worked out: 6 of the 216 rolls of three dice win: at 24 to 1 (Macau) 30.56%, at 30 to 1 (Atlantic City) 13.89%. Any Triple: Wins on any three of a kind. Pays 24 to 1 in Macau and 30 to 1 in Atlantic City. Wizard of Odds · Sic Bo · read |
| Two given numbers (for example 2 and 5)Pays 5 to 1 | 16.67%worked out Source
Two given numbers (for example 2 and 5) Worked out: 30 of the 216 rolls of three dice win, 5 to 1. The bet pays 5 to 1 if the roll contains both numbers. Wizard of Odds · Sic Bo · read |
| One number, paid by how many dice show itPays 1 to 1 for one, 2 to 1 for two, 3 to 1 for three | 7.87%worked out Source
One number, paid by how many dice show it Worked out: of the 216 rolls, 75 show the number once, 15 twice, 1 three times, 125 not at all. The house edge under the usual pay table is 7.87%. Wizard of Odds · Sic Bo · read |
Pai Gow Poker
Against the dealer, playing the house way. Played at 16 casinos we list.
| Bet | House edge |
|---|---|
| Against the dealer, house way, 5% commission | 2.72% Source
Against the dealer, house way, 5% commission If the player wins both comparisons, then the player will win even money on his bet, less a 5% commission. Table “House way Strategy — Dealer Banker”, row “Total”, column “Return”: -0.027212 |
Poker games against the house
These edges assume every decision is made the way that loses least; a guess costs more. Measured against the first bet, the Ante; element of risk divides the same loss by everything bet in the hand. Played at 80 casinos we list.
| Bet | House edge | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Three Card Poker: Ante and Play, ante bonus 5-4-1Measured against the Ante; the Play bet is not counted.Played at 33 casinos we list | 3.37% Source
Three Card Poker: Ante and Play, ante bonus 5-4-1 The vast majority of tables follow pay table #1. Table “Ante Bet Bonus”, row “House Edge”, column “Table 1”: 3.37% Rules published by BCLC for B.C. casinos. Table “ANTE BONUS PAY TABLE”, 6.0 Three Card Poker with Six Card Bonus Side Bet, 5.8:
Rules published by Loto-Québec for its casinos. Regardless of how the dealer's hand ranks, if the player raised and his hand is a straight flush, a three of a kind or a straight, his initial bet is also paid according to the following payout table: Table “INITIAL BET PAYOUT TABLE”, Bonus prize:
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| Ultimate Texas Hold’em: Ante and BlindMeasured against the Ante alone, although the Blind is bet too.Played at 65 casinos we list | 2.185% Source
Ultimate Texas Hold’em: Ante and Blind The lower right cell shows a house edge of 2.185% per ante bet. … So the element of risk would be 2.185%/4.152252 = 0.526%. The standard deviation, relative to the Ante bet, is 4.94. Rules published by BCLC for B.C. casinos. Table “BLIND PAYOUT SCHEDULE”, 11.0 Ultimate Texas Hold'em, 5.6:
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| Mississippi Stud, the standard pay tableMeasured against the Ante; raises are not counted.Played at 24 casinos we list | 4.91% Source
Mississippi Stud, the standard pay table The lower right cell shows a house edge of 4.91%. On average, the player will bet 3.59 units per hand. The ratio of the expected loss to total amount bet, what I call the "element of risk," is 4.91%/3.59 = 1.37%. | ||||||||||||||||||
| Let It Ride, the standard pay tableMeasured against one of the three bets.Played at 6 casinos we list | 3.51% Source
Let It Ride, the standard pay table The following is the standard pay table most casinos follow. … The lower right cell shows an expected loss of 3.51% of the minimum bet size. … This makes the element of risk, defined as the ratio of expected loss to total amount bet 3.51%/1.232 = 2.85%. … The standard deviation, relative to a single bet, is 5.17. Wizard of Odds · Let it Ride · read Rules published by BCLC for B.C. casinos. Table “5.3 Bets shall be paid according to each hand:”, 1.0 Let It Ride, 5.3:
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| Crazy 4 Poker: Ante, Super Bonus and PlayMeasured against the Ante.Played at 5 casinos we list | 3.42% Source
Crazy 4 Poker: Ante, Super Bonus and Play The bottom right cell of the table above shows a house edge of 3.42%. This is the ratio of the expected player loss to the Ante bet. … Thus, the element of risk of the game (ratio of expected loss to average total bet) is 3.42%/3.14 = 1.09%. … The standard deviation is 3.13, based on the Ante bet. |
Side bets
Side bets are where pay tables differ most. Each figure is worked out from the pay table named beside it; the check for your own table is below.
| Bet | House edge | ||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Pairplus (Three Card Poker)Pays on a pair or better in your three cardsPlayed at 33 casinos we list | 7.28%worked out Source
Pairplus (Three Card Poker) Worked out: 22,100 three-card hands: straight flush 48, three of a kind 52, straight 720, flush 1,096, pair 3,744; pays 40-30-6-3-1. The following table shows the probability and return for the most common pay table of the Pairplus bet. The lower right cell shows a house edge of 7.28%. Table “Pairplus Pay Tables — Without Mini Royal”, row “House edge”, column “Pay table 8”: 7.28% Source
Pairplus (Three Card Poker) (B.C.) Worked out: 22,100 three-card hands: straight flush 48, three of a kind 52, straight 720, flush 1,096, pair 3,744; pays 40-30-5-4-1. Rules published by BCLC for B.C. casinos. Table “PAIR PLUS PAY TABLE”, 6.0 Three Card Poker with Six Card Bonus Side Bet, 5.9:
Table “Pairplus Pay Tables — Without Mini Royal”, row “House edge”, column “Pay table 6”: 5.57% Source
Pairplus (Three Card Poker) (Québec) Worked out: 22,100 three-card hands: straight flush 48, three of a kind 52, straight 720, flush 1,096, pair 3,744; pays 40-30-6-4-1. Rules published by Loto-Québec for its casinos. Table “PAIR PLUS SIDE BET PAYOUT TABLE”, Pair Plus bet:
Table “Pairplus Pay Tables — Without Mini Royal”, row “House edge”, column “Pay table 1”: 2.32% | ||||||||||||||||||||
| 6 Card Bonus (Three Card Poker)Pays the highest five-card hand from your three cards and the dealer’s three | 8.56% to 15.28%worked out Source
6 Card Bonus (Three Card Poker) Worked out: the highest five-card hand from the player’s and the dealer’s six cards, over all 20,358,520 six-card deals: royal flush 188, straight flush 1,656, four of a kind 14,664, full house 165,984, flush 205,792, straight 361,620, three of a kind 732,160; across the four pay tables Wizard of Odds lists. The next table shows all four known pay tables and the house edge. Table “6 Card Bonus — Pay Table Summary”, row “House Edge”, column “Pay Table 1 / 2 / 3 / 4”: 8.56% / 14.36% / 15.28% / 10.22% Source
6 Card Bonus (Three Card Poker) (B.C.) Worked out: the highest five-card hand from the player’s and the dealer’s six cards, over all 20,358,520 six-card deals: royal flush 188, straight flush 1,656, four of a kind 14,664, full house 165,984, flush 205,792, straight 361,620, three of a kind 732,160. Rules published by BCLC for B.C. casinos. Combined maximum total Ante Bonus, Pair Plus and 6 Card Bonus payouts to all Players during any one round of play shall be an aggregate amount of $50,000.00. Table “SIX (6) CARD BONUS PAY TABLE”, 6.0 Three Card Poker with Six Card Bonus Side Bet, 5.10-5.11:
Table “6 Card Bonus — Pay Table Summary”, row “House Edge”, column “Pay Table 3”: 15.28% | ||||||||||||||||||||
| Trips (Ultimate Texas Hold’em)Pays three of a kind or better in your final handPlayed at 65 casinos we list | 0.90% to 6.18%worked out Source
Trips (Ultimate Texas Hold’em) Worked out: the highest five-card hand from the player’s two cards and the five on the board, over all 133,784,560 seven-card deals: royal flush 4,324, straight flush 37,260, four of a kind 224,848, full house 3,473,184, flush 4,047,644, straight 6,180,020, three of a kind 6,461,620; across the four pay tables Wizard of Odds lists. Shufflemaster literature mentions the following four possible pay tables on the Trips bet. Table “Trips Bet - Pay Table 1 / 2 / 3 / 4”, row “Total”, column “Return”: -0.009018 / -0.01904 / -0.034979 / -0.061808 Source
Trips (Ultimate Texas Hold’em) (B.C.) Worked out: the highest five-card hand from the player’s two cards and the five on the board, over all 133,784,560 seven-card deals: royal flush 4,324, straight flush 37,260, four of a kind 224,848, full house 3,473,184, flush 4,047,644, straight 6,180,020, three of a kind 6,461,620. Rules published by BCLC for B.C. casinos. The combined maximum total Blind and Trips Bonus payout to all Players during any one round of play shall be an aggregate amount of $50,000.00. Table “TRIPS BONUS PAYTABLE”, 11.0 Ultimate Texas Hold'em, 5.7-5.8:
Table “Trips Bet - Pay Table 2”, row “Total”, column “Return”: -0.01904 | ||||||||||||||||||||
| Perfect Pairs (blackjack), 25-12-6Pays perfect pair 25 to 1, coloured pair 12 to 1, mixed pair 6 to 1The pay table Fallsview Casino Resort and Casino Niagara publish in “Playing Blackjack”; the document does not say how many decks.Played at 6 casinos we list | 6.11%worked out Source
Perfect Pairs (blackjack), 25-12-6 Worked out: the player’s first two cards: with six decks 780 perfect pairs, 936 coloured and 1,872 mixed of 48,516 two-card starts; with eight decks 1,456, 1,664 and 3,328 of 86,320. It pays if the player's first two cards are a pair. Table “Perfect Pairs Expected Returns”, row “6 / 8 decks”, column “Pay Table A”: -0.061093 / -0.040964 Rules Fallsview Casino Resort and Casino Niagara publish for their tables. MIXED PAIR Pays 6 to 1 A pair with 1 red card and 1 black card. COLOURED PAIR Pays 12 to 1 A pair of the same colour but different suits. PERFECT PAIR Pays 25 to 1 An identical pair. Pay table, Blackjack side bets: Perfect Pairs:
Fallsview Casino Resort and Casino Niagara · Playing Blackjack · read | ||||||||||||||||||||
| 21+3 (blackjack), 9 to 1 on a flush, straight, straight flush or three of a kindPays your two cards and the dealer’s up card as a poker handVersion 1 in Wizard of Odds’ list; tables post their own pay table. | 3.24%worked out Source
21+3 (blackjack), 9 to 1 on a flush, straight, straight flush or three of a kind Worked out: the three cards over a six-deck shoe, 5,013,320 combinations: 1 deck 13.30%, 2 decks 7.26%, 4 decks 4.24%, 6 decks 3.24%, 8 decks 2.74%. If the three cards equal a flush, straight, straight flush, or three of a kind the side bet pays 9 to 1. … Following is the house edge for 4, 6, and 8 decks. … 1 deck — 13.30% … 2 decks — 7.26% … 4 decks — 4.24% … 6 decks — 3.24% … 8 decks — 2.74% Wizard of Odds · 21+3 · read | ||||||||||||||||||||
| Lucky Ladies (blackjack), pay tables A and BPays a first-two-card total of 20; the queen of hearts pair pays most | 17.64% (table B) to 24.71% (table A)worked out Source
Lucky Ladies (blackjack), pay tables A and B Worked out: six decks, the player’s two cards and the dealer’s two cards in order: 9,294,695,280 deals. The next table is an analysis of pay table A with six decks. The lower right cell shows a return of 75.29%, or a house edge of 24.71%. … The next table is an analysis of pay table B with six decks. The lower right cell shows a house edge of 17.64%. | ||||||||||||||||||||
| Fire Bet (craps): 4, 5 or 6 different points before the seven-outPays 24, 249 and 999 to 1 (at B.C. tables written 25, 250 and 1,000 for 1) | 20.76%worked out Source
Fire Bet (craps): 4, 5 or 6 different points before the seven-out Worked out: the chance of making 4, 5 or 6 different points before the shooter sevens out: 0.880%, 0.1640%, 0.01624%, worked out exactly over which points are already made. Pay Table 1 is the most common. Pays are indicated on a "to one" basis. Table “Fire Bet Pay Tables”, row “House edge”, column “Pay Table A”: 20.76% Wizard of Odds · Fire Bet · read Rules published by BCLC for B.C. casinos. The side bet shall be paid according to the number of individual points the Shooter successfully makes before rolling a `Seven Out'' … A `Fire Bet' wager may be a minimum of $1, up to a maximum of $5. Table “FIRE BET WAGER”, 2.0 Fire Bet, 5.2-5.4, 3.3:
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Slot machines
A slot machine’s edge is set by its program, and no casino publishes it per machine. What is published: the average return in B.C. and the lowest return Ontario allows.
| Bet | House edge |
|---|---|
| Returns 92% (average at B.C. casinos) | 8%worked out Source
Returns 92% (average at B.C. casinos) Worked out: 100% − 92% returned. The average return to player at B.C. casinos is 92 percent. |
| Returns 85% (lowest allowed in Ontario)A floor set by law, not an average: machines return this or more. | 15%worked out Source
Returns 85% (lowest allowed in Ontario) Worked out: 100% − 85% returned. 11.9.1 The minimum theoretical payout percentage of a Game is eighty-five (85.000) percent. |
Your table’s pay table
Side-bet pay tables differ from table to table, and the house edge changes with every line. Type the pays printed on the felt or the sign at your table. Where the pays alone decide the odds, the house edge is worked out exactly; where it also depends on how you play (Mississippi Stud, Let It Ride, the Blind), we only recognise the pay tables Wizard of Odds has analysed.
Decisions per hour
How many rounds an hour you play decides what an hour costs: the same bet at a full table costs a fraction of what it costs at an empty one. By number of players, from Kilby’s tables; for other games, the Las Vegas Strip rating table; for slot machines, as fast as the machine allows.
| Game | Rounds an hour | Source |
|---|---|---|
| Blackjack: hands an hourKilby, Casino Operations Management, via Wizard of Odds | 1 player 2092 players 1393 players 1054 players 845 players 706 players 607 players 52 | Source
Blackjack: hands an hour by players at the table The following tables show the number of hands/tosses per hour in blackjack, craps, and roulette. The source of the tables is Casino Operations Management by Jim Kilby. Table “Hands per Hour in Blackjack”, row “Players 1 / 2 / 3 / 4 / 5 / 6 / 7”, column “Hands per hour”: 209 / 139 / 105 / 84 / 70 / 60 / 52 Wizard of Odds · Table games FAQ (tables from Kilby, Casino Operations Management) · read |
| Roulette: spins an hourKilby, Casino Operations Management, via Wizard of Odds | 1 player 1122 players 763 players 604 players 555 players 486 players 35 | Source
Roulette: spins an hour by players at the table The following tables show the number of hands/tosses per hour in blackjack, craps, and roulette. The source of the tables is Casino Operations Management by Jim Kilby. Table “Spins per Hour in Roulette”, row “Players 1 / 2 / 3 / 4 / 5 / 6”, column “Spins per hour”: 112 / 76 / 60 / 55 / 48 / 35 Wizard of Odds · Table games FAQ (tables from Kilby, Casino Operations Management) · read |
| Craps: rolls an hourKilby, Casino Operations Management, via Wizard of Odds | 1 player 2493 players 2165 players 1447 players 1359 players 12311 players 102 | Source
Craps: rolls an hour by players at the table The following tables show the number of hands/tosses per hour in blackjack, craps, and roulette. The source of the tables is Casino Operations Management by Jim Kilby. Table “Rolls per Hour in Craps”, row “Players 1 / 3 / 5 / 7 / 9 / 11”, column “Rolls per hour”: 249 / 216 / 144 / 135 / 123 / 102 Wizard of Odds · Table games FAQ (tables from Kilby, Casino Operations Management) · read |
| Craps: pass-line decisions an hourOur reading: rolls an hour ÷ 557/165, the average rolls a line bet lasts | 1 player 743 players 645 players 437 players 409 players 3611 players 30 | Source
Craps: pass-line decisions by players at the table Worked out: rolls an hour ÷ 557/165 ≈ 3.376 rolls a decision: 1 player: 249 ÷ 3.376 ≈ 74; 3 players: 216 ÷ 3.376 ≈ 64; 5 players: 144 ÷ 3.376 ≈ 43; 7 players: 135 ÷ 3.376 ≈ 40; 9 players: 123 ÷ 3.376 ≈ 36; 11 players: 102 ÷ 3.376 ≈ 30. The following tables show the number of hands/tosses per hour in blackjack, craps, and roulette. The source of the tables is Casino Operations Management by Jim Kilby. Table “Rolls per Hour in Craps”, row “Players 1 / 3 / 5 / 7 / 9 / 11”, column “Rolls per hour”: 249 / 216 / 144 / 135 / 123 / 102 Wizard of Odds · Table games FAQ (tables from Kilby, Casino Operations Management) · read Adding it all up, the expected rolls to resolve a line bet is 1 + (1/6)*4 + (2/9)*3.6 + (5/18)*(36/11) = 557/165 =~ 3.375758 rolls. |
An empty table plays faster than a full one: 4.0 times as many hands at blackjack (209 against 52), 3.2 times as many spins at roulette, 2.4 times as many rolls at craps. At the same minimum, an hour alone at a table costs that many times more.
| Game | Pace | Source |
|---|---|---|
| BlackjackLas Vegas Strip rating table | 70 hands | Source
Pace: Blackjack The following table shows the average hands per hour and the house edge for comp purposes various games. … This table was given to me anonymously by an executive with a major Strip casino and is used for rating players. Table “Hands per Hour and Average House Edge”, row “Blackjack”, column “Hands/Hour”: 70 |
| BaccaratLas Vegas Strip rating table | 72 hands | Source
Pace: Baccarat The following table shows the average hands per hour and the house edge for comp purposes various games. … This table was given to me anonymously by an executive with a major Strip casino and is used for rating players. Table “Hands per Hour and Average House Edge”, row “Baccarat”, column “Hands/Hour”: 72 |
| CrapsPace casino rating systems are set toAbout 60 rolls an hour, the pace player-rating systems are set to; a line bet is settled once in about 3.4 rolls, so that is about 18 pass-line decisions. A busy table can roll faster: Kilby counts 102 to 249 rolls an hour, from a table of 11 players down to one. | 18 decisions | Source
Pace: Craps Worked out: 60 rolls an hour ÷ 557/165 ≈ 3.376 rolls a decision ≈ 18 pass-line decisions an hour. Most systems have been pre-programed to reflect sixty (60) rolls per hour. … the pass/come wager (either “do” or “don’t) is subject to a win/loss decision, not every roll, but every 3.4 rolls. … The correct number of decisions in the player tracking computer for craps wagering should be closer to 15 to 18 decisions per hour. Adding it all up, the expected rolls to resolve a line bet is 1 + (1/6)*4 + (2/9)*3.6 + (5/18)*(36/11) = 557/165 =~ 3.375758 rolls. The following tables show the number of hands/tosses per hour in blackjack, craps, and roulette. The source of the tables is Casino Operations Management by Jim Kilby. Table “Rolls per Hour in Craps”, row “Players 1 / Players 11”, column “Rolls per hour”: 249 / 102 Wizard of Odds · Table games FAQ (tables from Kilby, Casino Operations Management) · read |
| Roulette, double zeroLas Vegas Strip rating table | 38 spins | Source
Pace: Roulette, double zero The following table shows the average hands per hour and the house edge for comp purposes various games. … This table was given to me anonymously by an executive with a major Strip casino and is used for rating players. Table “Hands per Hour and Average House Edge”, row “Roulette”, column “Hands/Hour”: 38 |
| Roulette, single zeroLas Vegas Strip rating table | 35 spins | Source
Pace: Roulette, single zero The following table shows the average hands per hour and the house edge for comp purposes various games. … This table was given to me anonymously by an executive with a major Strip casino and is used for rating players. Table “Hands per Hour and Average House Edge”, row “Single 0 Roulette”, column “Hands/Hour”: 35 |
| Sic BoLas Vegas Strip rating table | 45 rounds | Source
Pace: Sic Bo The following table shows the average hands per hour and the house edge for comp purposes various games. … This table was given to me anonymously by an executive with a major Strip casino and is used for rating players. Table “Hands per Hour and Average House Edge”, row “Sic Bo”, column “Hands/Hour”: 45 |
| Pai Gow PokerLas Vegas Strip rating table | 34 hands | Source
Pace: Pai Gow Poker The following table shows the average hands per hour and the house edge for comp purposes various games. … This table was given to me anonymously by an executive with a major Strip casino and is used for rating players. Table “Hands per Hour and Average House Edge”, row “Pai Pow Poker”, column “Hands/Hour”: 34 |
| Poker games against the houseLas Vegas Strip rating tableThe table has no figure for this game; the figure for Caribbean Stud, another poker game played against the dealer, is used. | 50 hands | Source
Pace: Poker games against the house The following table shows the average hands per hour and the house edge for comp purposes various games. … This table was given to me anonymously by an executive with a major Strip casino and is used for rating players. Table “Hands per Hour and Average House Edge”, row “Car. Stud”, column “Hands/Hour”: 50 |
| Slot machinesAs fast as the machine allowsTimed on reel slots at an Ontario casino: about one spin every 6 seconds. Video slots in the same study allowed one about every 3 seconds, 1,200 an hour. This is the machine’s limit, not how fast people usually play. | 600 spins | Source
Pace: Slot machines We analyzed the PAR Sheets and played the four games for approximately 60 hr at an Ontario casino, Grand River Raceway, which has 200 slot machines. … We estimated the speed of play by using the second hand on a watch. … traditional mechanical reel slot machine games, the player can play approximately every 6 s, which is approximately 10 spins per minute, or 600 spins per hour. On the two video slots games, the player can play approximately every 3 s, which is 1,200 spins per hour. |
How it’s worked out
House edge is the average loss as a share of the bet. Over many rounds, what you lose tends towards it; over one evening, luck swings far wider in both directions.
Worked out means our own exact count: every roll of the dice, every card of the shoe, every poker hand. Pays come from the published table named beside the figure. Where Wizard of Odds prints the same figure, it is quoted next to ours, and the page is only built when the two agree to the last digit the source prints.
Quoted figures are those that depend on how the hand is played: blackjack, poker games against the house, pai gow. We quote Wizard of Odds’ figure for optimal play and do not work these out ourselves.
Pay tables of B.C. and Québec are taken from the rules BCLC and Loto-Québec publish for their casinos. They describe the games the operator runs, not a given casino’s table; a table may post a different sign, and the sign at your table decides.
SD is the standard deviation of one bet, in bets: how far one round usually lands from the average. Element of risk divides the average loss by everything bet in the hand, raises included.
What these figures leave out. Every win is assumed paid in full. BCLC caps what all players at a Three Card Poker or Ultimate Texas Hold’em table are paid in one round at $50,000 together; a single player reaches it only with a bet above $50 on a 1,000 to 1 hand. Progressive jackpots are not counted. Card counting is not considered.
If it stops being fun
If gambling stops being entertainment, help is available. 19+ in most of Canada; 18+ in Alberta, Manitoba and Quebec. More on responsible gaming.
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