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18 October 2011 - 10:36am

Odd's Tried and Tried. Hold-em

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Off and on over the last year I have been looking for a way to figure out unique poker odds. Tons and tons of info everywhere, but.


Str8 F

When two of the cards have to be in your hand, and any three off the board. Question revolves around home games where guys rake for

bonuses and come up with what I think are incredibly high profit margins by requiring that 1 or 2 cards have to be in your hand.

So question is what are the odds of a Royal when 2 of 7 cards must be in your hand? Same question when 1 has to be in your hand.

Also for str8 flush and quads.

Thanks so much

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18 October 2011 - 1:09pm

what you want i can`t get

you want % ? how many % is there chance to have Royal flash or what ? ? ?

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19 October 2011 - 3:06am

Hi maikl10, what you are describing is pretty much how most bad beat poker jackpots work online - ie you have quad Aces but are beaten. In those cases both players usually have to have 2 cards in their hand that were dealt to them.

To work these things out you can use the combin function in Excel which works out the combinations of numbers based on the number you need to draw. But its tricky stuff and it makes my brain hurt sometimes!

First, the total number of 7 card combinations that can be dealt in a hand of Texas Hold'em using a 52 card deck is combin(52,7) which equals 133,784,560. The reason we use 7 is that there are 5 cards on the board plus 2 in your hand. We'll use that later.

You can see the odds of getting various hands on this page in wikipedia.

You can see there that the probability of getting a royal flush in Texas Hold'em is 4,324 / 133,784,560 which works out to be 1 in 30,940. You can check it using this formula:

4 * combin(47,2) / combin(52,7) = 1 in 30,940

The 4 represents that there are only 4 ways to form a royal flush in a game of hold'em (one for each suit). The combin(47,2) part means that when 5 of the cards form a royal flush the remaining 2 cards can be any of the 47 other cards in the deck. The combin(52,7) part is the total number of 7 card hands that can be dealt which I showed you above.

Now the odds that any individual card in your hand or on the board holds any one of the 5 royal flush cards is 5 in 7.

Therefore the odds of getting a royal flush where you are dealt two of the cards is:
1 in 30,940 * (5/7) * (5/7) = 1 in 60,642

For other flushes you can do the same thing. For simplicity's sake I'll just treat everything as a 5 card flush and ignore 6 or 7 card flushes which actually make the odds a tiny bit better than what they appear below.

Straight flush:
1 in 3,217 * (5/7) * (5/7) = 1 in 6,306

1 in 33 * (5/7) * (5/7) = 1 in 64

Quads (only 4 cards needed):
1 in 595 * (4/7) * (4/7) = 1 in 1,822

So in the flush situation, requiring you to be dealt 2 of the 5 cards to win the bonus or bad beat jackpot roughly halves your chances. In the quads situation it is around 3 times less likely.

Disclaimer: my maths is rusty. Happy to accept any corrections if I made a mistake.

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19 October 2011 - 11:51am

I've just looked through your "calculations" and have not found any mistake yet Smile Maybe because I am quite poor at maths too lol

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19 November 2011 - 11:10am

oh,i cant understand these mathematics.

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22 November 2011 - 8:08am

Me neither Johan, but sometimes it all appears to be so easy, mostly people are just threatened by the figures lol

By the way, welcome to the forum Smile

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