Flush Probability A flush consists of five cards which are all of the same suit. We must remember that there are four suits each with a total of 13 cards. Thus a flush is a combination of five cards from a total of 13 of the same suit. Poker Hand Number of Combinations Probability Royal Straight Flush 4. Other Straight Flush 36.

For the 1 in 2,777 times that you'll be dealt four royal flush cards, you have 1 in 47 odds of grabbing video poker's largest payout. The reason why it's a 1-in-47 chance is because five cards have already been dealt, and one of the remaining 47 cards (standard 52-card deck) will net you the jackpot. Getting a royal flush = 1 in 649,740 odds Starting with 4 royal flush cards = 1 in 2,777 3 RFCs = 1 in 92 2 RFCs = 1 in 13 1 RFC = 1 in 6. Drawing to a Royal. We just discussed how players can receive certain parts of a royal flush and improve their opportunities of getting video poker's best hand. The odds of being dealt a Flush on the flop is only the tip of the iceberg. To view a wider range of odds and probabilities of being dealt different hands then check out our very own poker odds.

I have a feeling I'm making a mistake posting this without checking it through simulation first, but I get a probability of 1 in 274.564, assuming you always play a 'royal or nothing' strategy (for example, if you are dealt A-A-A-A-2, keep one of the aces and discard the other four cards; if you are dealt a suited J-10-9-8-7, keep the jack and 10; if you are dealt 9-9-9-9-6 or suited 9-8-7-6-5, discard all five cards).

High cards by suit	Number of hands
5	4
4	4 x 5 x 32
4-1	4 x 5 x 15
3	4 x 10 x (32 x 31 / 2)
3-1	4 x 10 x 3 x 5 x 32
3-2	4 x 10 x 3 x 10
3-1-1	4 x 10 x 3 x 25
2	4 x 10 x (32 x 31 x 30) / 6
2-1	4 x 10 x 3 x 5 x (32 x 31) / 2
2-1-1	4 x 10 x 3 x 25 x 32
2-1-1-1	4 x 10 x 125
2-2	6 x 100 x 32
2-2-1	6 x 100 x 2 x 5
1	4 x 5 x (32 x 31 x 30 x 29) / 24
1-1	6 x 25 x (32 x 31 x 30) / 6
1-1-1	4 x 125 x (32 x 31) / 2
1-1-1-1	625 x 32

Here is a breakdown of the 2,598,960 dealt hands by number of high cards (10 through ace) per suit - for example, there are 4 hands with 5 high cards of the same suit, and 4 x 10 x 3 x 5 x 32 = 19200 with 3 high cards of one suit, 1 of another, and the fifth card is 2-9:
You keep the highest number (so, for example, in 3-1, you keep the 3 cards of the same suit; in 2-2-1, you keep either of the sets of 2 cards of the same suit).
If you have five suited high cards, obviously that's a Royal Flush - in fact, 100 of them - and the probability is 1.
If you have 4, you have a 1/47 chance of getting the fifth card, which means you have a 46/47 chance of not getting it, so you have a (46/47)¹⁰⁰ chance of not getting any royals in 100 of these hands, and a 1 - (46/47)¹⁰⁰ chance of getting at least one.
Similarly, with 3 suited high cards, you have a 1 - (1 - 2 / (46 x 47) )¹⁰⁰ chance of at least one royal;
with 2, a 1 - (1 - 6 / (47 x 46 x 45) )¹⁰⁰ chance;

Poker Royal Flush Probability Table

with 1, a 1 - (1 - 24 / (47 x 46 x 45 x 44) )¹⁰⁰ chance;
with none, a 1 - (1 - 120 / (47 x 46 x 45 x 44 x 43) )¹⁰⁰ chance.
Multiply the numbers of each hand by the appropriate probability, add them together, and divide by 2598960.

Royal Flush Poker Probability