Calculate straights / flush

sc2zerker

Joined: 21.12.2012

Posts: 219

13.11.2013, 23:18 0

How do we caculate the chances of hitting a flush / straight with suited connects...

For example 45s

4 :heart:5 :heart:

(x)(x)(x)4 :heart:5 :heart:(x)(x)(x) so any of the x's can give us a straight

(A)(2)(3)4 :heart:5 :heart:(6)(7)(8)
(8%)(8%)(8%)4 :heart:5 :heart:(8%)(8%)(8%)

What's the % of hitting a straight on the flop, then How is the math done? For the river and turn...

Also how would the math be done for a gapping connector, for 57s

(x)(x)5(x)7(x)(x)
(8%)(8%)5(8%)7(8%)(8%)

You can clearly see with a gap, you loose 1 X but what is that in %?

Same question for flushes.

45s
4 :heart:5 :heart:
9hearts left, 8 hearts left, 7hearts, left...
(18%)(16%)(14%)

wtf??! am I doing something wrong? - Blog

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3 replies

TJtheTJ

Joined: 12.10.2011

Posts: 6,581

15.11.2013, 10:08 0

Hey sc2zerker,

Sorry for the late reply!

Calculating the odds of hitting a straight or flush is relatively simple. It just requires some probability calculations and counting.

Say you have 87s. There are now a few ways for you to flop a straight.

1) 4,5,6
2) 5,6,9
3) 6,9,T
4) 9,T,J

The order in which these cards come on the flop is irrelevant. Therefore, for each different board there's 4^3=64 ways to make the straight. Since there are 4 different ways to flop a straight, there are 64*4 = 256 flop combinations on which you flop a straight. There are 19,600 different flop combinations available (calculation in spoiler for reference).

Spoiler

50! / (3! * (50 - 3)!) = 19,600

50 different cards, out of which we need 3.

Therefore, the chance of flopping a straight is 256 / 19,600 = ~1.3%

You can apply the same theory to flopping anything else. You have to figure out how many flop combinations will give you a specific hand, and then divide that by 19,600 to find out the probability of flopping that hand.

Hopefully that makes sense

Kind regards,
Tino