What mistakes cost per 100 hands

You sit at a 9/6 Jacks or Better video poker machine and play 100 hands. What do those hands cost you?

Mayaformer floor supervisor · manners, money and breaks

I keep a notebook when I play video poker, and every page in it has two columns. The pay table fills in the first column before I sit down: that is the table’s price. Nobody prints the second column, so I fill it in myself: that is the price of my own holds.

The table’s price: the return assumes the hold worth most

The return of a video poker game is worked out for a player who, on every hand, keeps the cards that pay back the most on average. Any other hold lowers that return. At 9/6 Jacks or Better with five coins in, the return with optimal play is 99.54%.

The sliver is the lowest price a player can pay at this table: it holds only for the hold worth most on every hand.

In money, on an example bet that is not a suggested bet:

1. One hand$1.25five coins of $0.25, an example bet
2. A hundred hands$125bet through the machine
3. Kept by the table, on average$0.57the table’s price for a hundred hands

The last figure is an average over a very long run, not what any one hundred hands will do. Amounts are in Canadian dollars.

A mistake is a hold worth less than the hold worth most

Every deal gives you thirty-two ways to hold: any of the five cards, in any combination, or none of them. Each hold is worth the average of what all of its draws pay, counted over every card that could replace the cards you let go.

Leoformer dealer · rules and maths

I spent years explaining pay tables, and the thing I wish I had said sooner is this: the pay table on the glass is the same for everyone who sits at that machine, and the holds are not. Two people at the same machine pay the same table’s price and very different prices for the evening, and the difference is decided one hold at a time.

That gap is the price of the mistake. On one hand the eight can still pair up, but the gap is an average over every draw: a price over many hands, not a forecast of the next one.

A hundred hands, audited

Here are the same hundred hands played twice, dealt from a full deck shuffled before every hand. The first player keeps the hold worth most every time. The second player does the same, with one habit: whenever the hold worth most is a pair on its own, the second player keeps one more card beside the pair.

The table’s line is the same on both receipts, because the table and the bet are the same. The mistakes line is exact for these hundred hands: every hold made was compared with the hold worth most on that deal, and the gaps were added up. On these hundred hands the habit’s line is longer than the table’s own line.

Counted as a return, the second player plays this table at 94.21% instead of the 99.54% worked out with optimal play. The difference is what the kept kickers gave up, spread over the hundred hands.

Why the price is per hundred hands, and not per hour

Video poker is fast, and with a rapid pace of play, losses can add up quickly. Speed does not change the price of a hundred hands; speed changes how many hundreds an evening holds.

No document we could read gives a number of hands an hour for video poker, so every price here is for a hundred hands, the same way the video poker pay table tool counts it. Count your own hands, and let the hours follow.

The right-hand column assumes every hundred hands goes the way the hundred on the receipt went, and no hundred hands promises that.

Mayaformer floor supervisor · manners, money and breaks

Machines are fast. Put a time limit next to the money limit, and decide both limits before you sit down: the time limit is what stops a small price per hundred hands from turning into a large evening.

When either limit runs out, stop. Putting more money in to get a loss back only buys more hands.

Practice: hands from the receipt

Every hand in the practice run is one of the hundred hands on the receipt above, in the order the receipt played them: 10 hands in all. You choose a hold, and the answer shows what every offered hold pays back on average and what each other hold gives up against the hold worth most.

Nothing is scored, and nothing is bet. There is no strip of squares and no running total here: the practice walks through the hands one at a time, and the receipt above has already added the hundred up. Dealing a hundred hands at speed and adding your own holds into your own receipt is not part of this page.

Check yourself

Mayaformer floor supervisor · manners, money and breaks

Five quick ones. Pick an answer, then check it. No timer, no points: just whether it stuck.

Back to the question we opened with. A hundred hands at 9/6, on an example bet of $1.25, cost the table’s price of $0.57 plus whatever your holds gave up: nothing extra for a player whose every hold is worth most, and $6.67 extra for the player on the receipt who kept a kicker beside every pair.

Further reading

19+ (18+ in AB, MB, QC) · Play responsibly · the helplines are further up this page

Further reading

• Video Poker: how to play · OLG PlaySmartHow a hand goes, the hands that pay, and why only the pay table decides what a hand is worth.

How it’s worked out