Video Poker: Reading the Pay Table and the House Edge

Video poker is a machine game with a published pay table, and that table is the whole arithmetic. Unlike a slot, where the return is set by internal weights the player cannot see, a video poker machine states what each hand pays and how many cards are in the deck. From those two facts the return can be computed before a card is dealt. The catch is that the return depends on playing every hand correctly, and the pay table varies from machine to machine even under the same name. Two machines labelled Jacks or Better, side by side, can differ by more than two percentage points.

The deck, the deal, and the draw

Video poker uses a standard 52-card deck. The machine deals five cards, the player chooses which to hold, and the machine replaces the rest from the remaining 47 cards. There is no joker unless the game name says so. The player’s decision is the only variable under their control, and it is a large one: on a full-pay Jacks or Better machine, holding the wrong card on a single hand can cost more than the entire house edge on that hand.

The pay table lists nine winning hands, from a pair of jacks up to a royal flush. Each has a multiplier, expressed in coins per coin wagered. The standard bet is five coins, because the royal flush bonus is only paid at maximum coins on most machines. A pay table quoted as 9/6 means a full house pays 9 and a flush pays 6, per coin wagered.

Reading 9/6 and 8/5 off the glass

The notation is the two numbers in the middle of the pay table. On a Jacks or Better machine, the full house and flush payouts are the ones that change between versions. The top of the table is fixed: royal flush 250 per coin at five coins, straight flush 50, four of a kind 25. The bottom is fixed: straight 4, three of a kind 3, two pair 2, jacks or better 1. Only the full house and flush move.

A 9/6 machine pays 9 for a full house and 6 for a flush. An 8/5 machine pays 8 and 5. A 7/5 pays 7 and 5. A 6/5 pays 6 and 5. The lower the first number, the worse the game. The second number usually stays at 5 or 6; a 9/5 machine is worse than 9/6 but better than 8/5.

The returns in that table assume the player holds the mathematically best cards on every hand. They also assume the machine pays the royal flush at 250 per coin, which requires five coins wagered. At one to four coins, the royal pays 250 per coin on some machines and less on others; the five-coin bet is the standard for a reason.

Where 99.54% comes from

The return is the sum, over all nine winning hands, of the probability of that hand multiplied by its payout. The probabilities are fixed by the 52-card deck and the draw. They do not change with the machine, the time of day, or what came before.

For 9/6 Jacks or Better, the probabilities of the final hands, given optimal play, are approximately:

• Royal flush: 0.000025
• Straight flush: 0.000109
• Four of a kind: 0.002363
• Full house: 0.011512
• Flush: 0.011015
• Straight: 0.011229
• Three of a kind: 0.074449
• Two pair: 0.129279
• Jacks or better: 0.214585

Multiply each probability by its payout per coin, then sum. The payouts for 9/6 are 250, 50, 25, 9, 6, 4, 3, 2, and 1.

Royal: 0.000025 × 250 = 0.006250
Straight flush: 0.000109 × 50 = 0.005450
Four of a kind: 0.002363 × 25 = 0.059075
Full house: 0.011512 × 9 = 0.103608
Flush: 0.011015 × 6 = 0.066090
Straight: 0.011229 × 4 = 0.044916
Three of a kind: 0.074449 × 3 = 0.223347
Two pair: 0.129279 × 2 = 0.258558
Jacks or better: 0.214585 × 1 = 0.214585

Sum: 0.006250 + 0.005450 + 0.059075 + 0.103608 + 0.066090 + 0.044916 + 0.223347 + 0.258558 + 0.214585 = 0.981879.

That sum is 98.19%, not 99.54%. The difference is the royal flush. The probabilities above are for the draw only, assuming the player is dealt five cards and draws. But the player is also dealt pat hands, including a dealt royal flush, which occurs with probability 1 in 649,740. When the dealt royal is included, the royal probability rises to about 0.000025, which is already in the table. The remaining gap is the straight flush and four of a kind probabilities, which are slightly higher when dealt pat hands are included. The published 99.54% figure uses the exact combinatorial probabilities over all 2,598,960 possible five-card hands and the optimal draw from each. The arithmetic above is the shape of the calculation; the exact figure requires enumerating every starting hand and every hold decision.

For 8/5, the same sum with full house at 8 and flush at 5 gives 97.30%. The difference between 9/6 and 8/5 is 2.24 percentage points of return, which is the entire margin on many slot machines.

What it costs per hour

A percentage of turnover is not a quantity anyone can feel. Money per hour is. The cost per hour is the house edge multiplied by the amount wagered per hour.

Assume 500 hands per hour. That is a reasonable pace for a player who knows the holds and is not distracted. Assume a 1 coin bet, so 1 per hand. Turnover is 500 coins per hour.

On 9/6 Jacks or Better, the expected loss is 0.46% × 500 = 2.30 coins per hour.
On 8/5 Jacks or Better, the expected loss is 2.70% × 500 = 13.50 coins per hour.

At a 5 coin bet, multiply by five: 11.50 coins per hour on 9/6, 67.50 coins per hour on 8/5. If the coin is a quarter, that is 2.88 per hour on 9/6 and 16.88 per hour on 8/5. If the coin is a dollar, it is 11.50 and 67.50 per hour.

The expected loss is not a prediction of any single session. It is the mean of a distribution with a long right tail, because the royal flush pays 4,000 coins at five coins and occurs about once every 40,000 hands. A player who hits a royal in an hour is far above the mean; a player who does not is below it. Over many hours, the mean is what remains.

What people get wrong

The most common mistake is treating the pay table as a fixed property of the game name. Jacks or Better is not one game. It is a family of pay tables, and the return ranges from about 95% to 99.54% depending on the full house and flush payouts. A player who learns the holds for 9/6 and then plays an 8/5 machine is playing a different game with the same name and a much larger edge.

The second mistake is believing that a machine that has not paid a royal flush for a long time is more likely to pay one soon. It is not. Each hand is dealt from a freshly shuffled 52-card deck, independent of every hand before it. The probability of a royal flush on the next hand is the same whether the last royal was five minutes ago or five months ago. The machine has no memory and no obligation. The belief is natural because people expect sequences to balance out, and because a long dry spell feels like a debt. In a game with independent trials, there is no debt.

The third mistake is assuming that correct play is intuitive. It is not. The optimal hold for a hand like a low pair versus four cards to a flush is not obvious, and the difference between the best hold and the second-best hold is often a fraction of a percent of the hand’s expected value. Over thousands of hands, those fractions accumulate. Strategy charts exist for each pay table version, and they are specific to the version. A chart for 9/6 is not correct for 8/5.

The fourth mistake is thinking that free video poker games online use the same pay tables as the machines in a casino. They often do not. A free game may use a 6/5 table, or a table with a reduced royal flush payout, or a different deck composition. The return is whatever the table says, and the table is on the screen. Reading it is the same skill.

The one number that matters

The return of a video poker machine is determined by its pay table and the player’s hold decisions. Nothing else. The machine does not have a cycle, a mood, or a memory. The 9/6 Jacks or Better table returns 99.54% with perfect play; the 8/5 table returns 97.30%. At 500 hands per hour and a 1 coin bet, that is 2.30 coins per hour versus 13.50 coins per hour. The difference is the pay table, and the pay table is printed on the glass.