NLHE royal odds calculations
April 20th, 2023 at 4:15:23 AM
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Need the odds of getting a royal flush, in No Limit Hold'm, using BOTH hole cards.
So...
Something like: Pick 7 out of 52, match 5 (first two PLUS any three of next 5)
So...
Something like: Pick 7 out of 52, match 5 (first two PLUS any three of next 5)
April 20th, 2023 at 7:40:51 AM
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Quote: bigleftieNeed the odds of getting a royal flush, in No Limit Hold'm, using BOTH hole cards.
So...
Something like: Pick 7 out of 52, match 5 (first two PLUS any three of next 5)
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I get 1 in 64,974.
The probability of getting two-to-a-royal using the two hole cards is (pick 1 out of 4)*(pick 2 out of 5) / (pick 2 out of 52).
And the probability of completing the royal in the next five cards is (pick 3 out of 3)*(pick 2 out of 47) / (pick 5 out of 50).
The product of these is:
[(4)(10) / (1,326)] * [(1)(1081) / (2,118,760)] = 1 / 64,974
April 20th, 2023 at 9:23:15 AM
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I agree with the math, but of course, that doesn't factor in that you may get bet out of the pot on the flop and fold and not have an active hand to get the royal.
April 20th, 2023 at 1:12:38 PM
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So, taking it a little further...
Lets say there were exactly 5,440 hands dealt.
The odds of three of those 5,440 hands being ANY royal flush, where the two hole cards were both part of the royal flush, would be:
( 64,974 * 64,974 * 64,974 ) / 5,440 => 274,295,581,802,424 / 5,440 => 50,421,981,948
So, 1 in 50,421,981,948
Is this correct?
Lets say there were exactly 5,440 hands dealt.
The odds of three of those 5,440 hands being ANY royal flush, where the two hole cards were both part of the royal flush, would be:
( 64,974 * 64,974 * 64,974 ) / 5,440 => 274,295,581,802,424 / 5,440 => 50,421,981,948
So, 1 in 50,421,981,948
Is this correct?
April 20th, 2023 at 1:24:46 PM
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No, I get 1 in 11,121. You want to use =BINOMDIST(3, 5440, (1 / 64974), 0) in your spreadsheet.Quote: bigleftieSo, taking it a little further...
Lets say there were exactly 5,440 hands dealt.
The odds of three of those 5,440 hands being ANY royal flush, where the two hole cards were both part of the royal flush, would be:
( 64,974 * 64,974 * 64,974 ) / 5,440 => 274,295,581,802,424 / 5,440 => 50,421,981,948
So, 1 in 50,421,981,948
Is this correct?
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N Probability Cycle
0 0.91968281 1
1 0.07700236 13
2 0.00322300 310
3 0.00008992 11121
4 0.00000188 531604
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