7 Nov

# Odds of Drawing a Winning Video Poker Hand

Statisticians guide to video poker odds for every winning hand.

What’s the real deal on video poker, you ask? That’s a great question. Video poker isn’t the plain-Jane gambling mechanism so many people think it is. In fact, video poker can have the highest theoretical return to player (RTP) of any game on the virtual online casino floor – even higher than blackjack, depending on the rules and pay table.

Just knowing it’s a good option for the cost-conscious among us isn’t enough to assuage every gambler. Odds are, if you’re interested enough to know what games have the best payouts, you’d be equally interested in what makes the game tick. Is the 99.91% RTP of Microgaming’s All Aces Video Poker more likely to pay out smaller sums just often enough to keep you running about even on your bankroll, or is there a reasonable chance of winning the bigger payouts for Quad Aces, Straight Flush or the grand daddy of them all, the Royal Flush?

What about Jacks or Better? Everyone says the 9/6 Full Pay games are as good as it gets. With an RTP of 99.54%, it’s pretty close. All Aces is actually better, but JoB Full Pay is far more readily available. But again, what’s the chance you’ll hit a payout that’s really worth something? That’s exactly what we aim to answer in today’s write up.

## Video Poker Odds for Every Winning Hand

The chart below details the odds of being dealt any particularly hand, segmented by each possible winning hand, versus all losing hands – in a standard video poker game. The following table does not account for specialty games like Deuces Wild or Joker Poker, where extra cards and/or wilds are present.

Before I continue, I’ll briefly explain how this information was gathered. If you hate mathematics, feel free to skip ahead to the odds table. If you love mathematics, then check out this page to discover how I arrived at the answer to this first equation, because I have no desire to explain the theory behind binomial coefficients. You can learn how to write up and work the equation (52,5) for this next part here.

#### 5-Card Possibilities on Initial Deal

From a 52-card deck, there are exactly 2,598,960 ways to be dealt 5 cards. That’s 2,598,960 possible hands you can be randomly dealt the moment you insert money and press the “DRAW” button on a standard video poker machine. This is as far as most video poker hand calculations go in telling you the odds of being dealt any type of hand, win or lose.

#### 5-Card Possibilities after the Draw

Let’s remember, however, that you can “HOLD” any number of cards, discarding the rest for replacements – replacements that cannot mimic the held cards, or the discards you’re throwing away. If we calculate all of those possible combinations, we come to a grand total of 19,933,230,517,200 possible hands after the draw.

Wow, that’s a lot of combinations! Don’t believe me? Think a bout this. On the opening draw, there are only 4 ways to be dealt a Royal Flush. But when you base the possibilities on all hand combinations (2.5 million) that you can start with, accounting for the 32 different ways to discard, and another 1,533,939 possible replacement cards, it’s not so ridiculous to think there are 554,637,108 ways to draw to a Royal Flush.

Like I said, I’m not going to explain the math behind this because, if you aren’t familiar with binomial theorem, it won’t make sense anyway. With that being said, here is the chart depicting your odds of being dealt a paying video poker hand on the initial deal, as well as after the draw.

## Odds Of Being Dealt Winning Video Poker Hands

This chart adheres to the winning hands on a standard Jacks or Better pay table (Full Pay or otherwise); this being the most common game available at land-based and online casinos worldwide.

 WinningPoker Hand Combinationson the Deal Odds /% Chance PossibilitiesAfter Draw Odds /% Chance Royal Flush 4 1 in 649,7400.0002% 554,637,108 1 in 35,9390.0028% Straight Flush 40 1 in 64,9470.0015% 2,218,146,252 1 in 8,9860.0111% 4 of a Kind 624 1 in 4,1650.0240% 46,944,834,792 1 in 4250.2355% Full House 3,744 1 in 6940.1441% 228,938,634,648 1 in 87.11.1485% Flush 5,108 1 in 5090.1965% 221,687,899,200 1 in 89.91.1122% Straight 10,200 1 in 2543.9246% 225,414,163,536 1 in 88.41.1308% 3 of a Kind 54,912 1 in 47.32.1128% 1,478,350,617,468 1 in 13.57.4165% 2 Pair 123,552 1 in 21.04.7539% 2,569,778,781,732 1 in 7.812.892% Jacks or Better 337,920 1 in 7.6913.000% 4,240,539,117,972 1 in 4.721.273% Other (Lose) 2,062,856 1 in 1.2579.372% 10,918,803,684,492 1 in 1.854.777% Total (AllPossibilities) 2,598,960 1 in 1100% 19,933,230,517,200 1 in 1100%