Blackjack and Card Math

Video Poker Math: Pay Tables and Return

How a video poker pay table sets a machine's return, why machines that look alike can differ by several percentage points, and why strong play still carries a house edge.

On this page
  1. What kind of game this is
  2. How the game works
  3. The pay table sets the return
  4. Hypothetical cost of the difference
  5. What “perfect strategy” means
  6. Maximum coins and the top prize
  7. Bonus variants
  8. Putting it together

What kind of game this is

Video poker is a game of chance with a built-in casino advantage. Skill affects the size of that advantage, but no strategy, system, pattern or timing turns the game into one the player expects to win, and most players lose money over time. Results over a session are uncertain. Nobody should gamble money they cannot afford to lose, and anyone concerned about their gambling can contact local support services.

How the game works

A video poker machine deals five cards from a simulated 52-card deck. The player chooses which cards to hold, and the discarded cards are replaced once from the remaining deck. The final five-card hand is paid according to a pay table, which lists a payout for each hand rank, from the lowest paying hand up to a royal flush. There is no opponent and no dealer hand to beat. The machine just pays a fixed amount for the hand shown.

Behind the screen, random number generators decide the order of the cards, so each deal is independent of the previous one. The machine does not remember earlier hands, and a hand that failed to pay does not make the next one more likely to.

There are 2,598,960 possible five-card hands from a 52-card deck. Strong hands are rare: for example, about half of all dealt five-card hands are high card only, and about 42 percent hold a single pair. That rarity is what the pay table prices.

The pay table sets the return

The return of a machine, often called return to player, is the average share of all money wagered that is paid back over a very large number of hands. It is set by two things: how often each hand occurs, which is fixed by the cards, and how much each hand pays, which is the casino’s choice. Because the frequencies are fixed, the pay table is the lever.

A typical pay table lists values in coins for one coin wagered. A well-known family of machines pays, per coin bet, 1 for a pair of jacks or better, 2 for two pair, 3 for three of a kind, 4 for a straight, then values for a flush, a full house, four of a kind, a straight flush and a royal flush. Two machines in that family can share most of the table and differ only in the full house and flush lines. A “9/6” version pays 9 for a full house and 6 for a flush. An “8/5” version pays 8 and 5.

Commonly published figures, assuming a perfect strategy, put the 9/6 version near 99.5 percent return and the 8/5 version near 97.3 percent. The reduced lines each pay one coin less. Full houses and flushes each show up in somewhat more than one percent of hands. So removing one coin from each line costs a little over two percent of the amount wagered, which fits the gap between those figures. A change that looks small on the screen, one number on two lines, reduces the machine’s return by more than two percentage points.

This also explains why similar-looking machines are not interchangeable. The pay table is displayed on the screen, but the numbers are easy to miss, and the cabinet, the cards and the game name can be identical while the return differs. Reading the pay table is the only way to know which version is in front of you.

Hypothetical cost of the difference

Using the round figures above, and treating them as hypothetical: a player who wagers a total of $1,000 on a machine returning 99.5 percent would expect to get back about $995, an average loss of $5. On a machine returning 97.3 percent, the expected return is $973, an average loss of $27. Neither number predicts a session. Variance is large because the biggest prizes are rare: a royal flush occurs roughly once in 40,000 hands under strong play, so most of the return is made up of a mix of small and mid-sized wins, with the occasional large one carrying a big share of the average.

What “perfect strategy” means

The quoted returns assume the player makes the best hold-or-discard choice on every hand, which is the one with the highest average payout for that pay table. Those choices can be worked out by computer, and published strategy charts exist for popular tables. The charts differ by pay table, because a change in what a flush pays changes which draws are worth chasing.

Two things follow:

  • Mistakes lower the return, so the quoted figure is a ceiling for a given pay table. A casual player who does not follow the chart will usually do worse than the percentage shown.
  • Even perfect play leaves a return below 100 percent on most tables. Strong strategy reduces the cost of playing, much like basic strategy does at the blackjack table; it does not eliminate it.

This is where the question of skill versus chance becomes concrete. Decisions matter here more than in many casino games, but the skill is in minimizing a loss, not in overturning it.

Maximum coins and the top prize

Many machines are designed so that the royal flush pays disproportionately more when the maximum number of coins is bet. A published return figure is often calculated at the maximum coin level, because it includes that bonus. A player betting fewer coins faces a lower return, since the extra top-prize payout is out of reach. Reading the machine’s rules about what is paid at each coin level is part of understanding the cost.

Bonus variants

Some machines add features, such as extra pay for particular four-of-a-kind hands or multipliers that apply on later hands. These changes shift the pay table, and with it the return, sometimes by lowering the payout on common hands to fund bigger prizes on rare ones. The same principle applies: the numbers on the pay table, not the name or the excitement of the feature, determine the return.

Putting it together

The math of video poker is clear and published, which makes it a good case study for how a payout schedule works. A pay table sets the return, small changes to common-hand payouts move it noticeably, and strategy affects only how much of the theoretical return the player achieves. Treat any play as a paid form of entertainment, set limits first, and stop when they are reached.

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