Video Poker

One hand is four decisions long. Choose a bet of one to five coins, press Deal, and five cards come off a freshly shuffled deck. Hold any subset of them — none, all five, or anything between — and press Draw. Every card you did not hold is replaced from the same deck, so the cards you threw away are gone rather than shuffled back. The five cards you end up with are paid on the table below, and nothing else about the hand matters: there is no opponent, no bluff and no second betting round.

Because the deal and the draw both come off one shuffle that is fixed before you touch anything, the cards available to you are decided the instant you press Deal. What you decide is which of the 32 possible holds to take, and that is worth real points: on the suited hand worked through further down, the best hold is worth three times the obvious one.

"9/6" names two rows and nothing else: nine per coin for a full house, six per coin for a flush. The shorter tables you will have seen elsewhere — 8/5, 7/5, 6/5 — cut exactly those two rows and leave the other seven alone, so comparing two Jacks or Better tables is a matter of reading two numbers.

Every row except one is simply the per-coin figure multiplied by the coins bet. The royal flush is the exception, and it is the whole reason the maximum bet exists: 250 per coin at one to four coins, 800 per coin at five. Four coins into a royal pays 1,000; the fifth coin turns that into 4,000. That single step is worth more than everything else on the table put together.

There are 2,598,960 distinct five-card hands in a 52-card deck, and the counts below are every one of them sorted by what this pay table pays. They are the hands as dealt, before any draw — the draw is what you do about them.

Those add up to 536,100 hands, so 20.6% of deals already pay before you draw — about one in five. The other four are the interesting ones. Note how much of the paying total is the smallest prize: 337,920 of the 536,100 are a single high pair returning one per coin, which is a push, not a win. Video poker is a game about turning the 79.4% into something, not about the 20.6%.

A dealt royal flush is one hand in 649,740. You will draw many more royals than you are dealt, which is the point of the draw.

The honest answer is: whichever of the 32 holds has the highest expected value, and that is a calculation rather than a feeling. The Hint button here does it exactly — for each hold it walks every possible replacement out of the 47 unseen cards, categorises the resulting hand and averages the payout. Across all 32 holds that is 2,598,960 draws examined, which is the same figure as the number of dealt hands, and not a coincidence: every draw from a five-card hold is one of the C(52,5) ways five cards come off the deck.

The single most instructive hand is a suited nine-Jack-Queen-King-Ace. That is a made flush, worth exactly 30 points at five coins, guaranteed. Throw the nine away and the four remaining cards are worth 92.13 points on average — because one of the 47 unseen cards makes the royal flush for 4,000, seven more make another flush, three make an Ace-high straight, and twelve pair a high card. Keeping a certain 30 over an expected 92 is the commonest beginner mistake in the game.

• Break a made flush for four to the royal. 92.13 against 30, as above.
• Do not break a made straight for four to an ordinary straight flush. At five coins that trade is 20 against 17.23 — the straight flush draw is not worth a sure straight.
• A high pair beats three to a royal, but barely: 7.68 against 7.44. Three cards is one card too few.
• Four to a flush beats a low pair: 6.06 against 4.12. The pair looks like something and the flush draw is worth half as much again.

No. There is no money in this game in either direction. The points are a score kept in your own browser, they arrive free, they reset free, they cannot be bought, sold, cashed out or transferred, and running out of them costs nothing but a click. There are no in-app purchases anywhere on this site, no accounts, no deposits and no links to anywhere that takes a deposit. What is being simulated is the arithmetic of a draw-poker pay table, which is a genuinely interesting piece of applied probability and is the reason the page exists.

If you want the same card-handling with an opponent on the other side of it, try gin rummy or cribbage; if you want the same one-decision-at-a-time arithmetic, blackjack is next door.