How the game works
In a typical video poker game you are dealt five cards, choose which to keep, and the rest are replaced from the same deck. The final five-card hand is paid according to a fixed pay table. There is no dealer and no opponent. The game is a puzzle of one decision per hand, with random cards on both sides of it.
The most common version is Jacks or Better. A pair of jacks or higher is the lowest paying hand, and a pay table lists what each ranked hand pays, for example for a one-coin bet.
Counting five-card hands
The starting point is a count of all possible five-card hands from a 52-card deck, a straightforward use of combinations: C(52, 5) = 2,598,960. Here is how many of those hands are each type:
| Hand | Number of hands | Share of all hands |
|---|---|---|
| Royal flush | 4 | 1 in 649,740 |
| Straight flush (not royal) | 36 | about 0.0014% |
| Four of a kind | 624 | about 0.024% |
| Full house | 3,744 | about 0.14% |
| Flush (not straight flush) | 5,108 | about 0.20% |
| Straight (not straight flush) | 10,200 | about 0.39% |
| Three of a kind | 54,912 | about 2.11% |
| Two pair | 123,552 | about 4.75% |
| One pair | 1,098,240 | about 42.26% |
| No pair | 1,302,540 | about 50.12% |
The counts sum to 2,598,960. These are the frequencies of hands dealt at random. In video poker the player draws to improve, so the frequencies of final hands differ from this table, but it shows the underlying scarcity: a flush is rarer than a straight, a full house is rarer than both, and so on. It is a good introduction to the permutations and combinations used to count card hands.
Why the pay table is the whole story
The return of a video poker game is set by combining two things: how often each final hand occurs under best play, and what each pays. If a pay table pays a full house 9 coins and a flush 6 coins on a one-coin bet, the game is called “9/6”. A weaker table that pays 8 and 5 is “8/5”.
Commonly published figures, assuming perfect play, are roughly:
- 9/6 Jacks or Better: about 99.54% return.
- 8/5 Jacks or Better: about 97.30% return.
These figures are widely cited; check the specific paytable and source rather than assuming a number. The point is that the difference is about 2.24 percentage points of return. Cutting one coin from the full house and one from the flush looks minor, but these hands come up often enough that the lost payouts add up to more than two percentage points of return.
Put differently, a casino can leave the screen and the rules looking identical and quietly change the game’s cost by altering a few numbers. Reading the pay table is the single most useful check on any machine.
The role of the royal flush
A large share of the return comes from rare, large payouts. The royal flush, which pays 800 coins for a five-coin bet on a standard table (250 on one coin), occurs roughly once in 40,000 or so hands under correct play. Because it contributes a meaningful piece of the long-run return in a very small number of rounds, a session that never hits it will typically return noticeably less than the published figure. This is why short-run results can differ so widely from the average and why the volatility of video poker is high even when the edge is small.
Hold decisions and expected value
For every deal there are 32 ways to choose which cards to hold, since each of the five cards is either kept or discarded (2 x 2 x 2 x 2 x 2 = 32). Optimal play computes the expected value of each of those 32 options, based on which cards remain in the deck, and picks the highest.
For example, holding a pair of low cards gives a decent chance to improve to two pair, three of a kind or better, while discarding it to chase a four-card flush draw gives a lower chance of a bigger payout. Which is better depends on the pay table: a table that pays flushes less makes draws to flushes less valuable. Strategy charts for video poker are therefore specific to a pay table, in the same way blackjack charts depend on rules. The published return assumes you follow the right chart every time. Mistakes lower the return, and most players do not play perfectly.
What the numbers do not give you
- A 99.5% return still means a 0.5% edge for the machine over the long run. It is not a break-even or winning game.
- Bonus promotions or loyalty offers, when they exist, may change the effective cost, but they come with terms that vary and are outside the scope of this article.
- Each hand is independent. A machine does not become more likely to pay a big hand because it has not paid one for a while. Believing it does is the gamblers fallacy.
Video poker rewards correct decisions and punishes bad ones, but even perfect play cannot remove the uncertainty of the deal. Outcomes vary, and money wagered can be lost.