Quick odds question TD.

[dibbs]

I get dealt 86532. With no knowledge of other cards, how often will 27xxx catch up to make a seven by the river?

What about 237? around 40%?

[MarkGritter]

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I get dealt 86532. With no knowledge of other cards, how often will 27xxx catch up to make a seven by the river?


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I ran 27AQJ through my draw results tool (with 86532 as dead cards); it says there is about 16% chance of making a 7. (There is only a 12% chance if villian will screw up and keep an 8.)

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What about 237? around 40%?

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About 23%. I tried working this one out by hand using permutations, but I came out with a different answer and realized I'd double-counted. And I'm too lazy to go back and fix my math.

[euri10]

15.87% for the first question, a friend of mine constructed a rough monte carlo simulation, so the 16% is gooooooood./
btw Mark what do you use to calculate that ?

[MarkGritter]

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15.87% for the first question, a friend of mine constructed a rough monte carlo simulation, so the 16% is gooooooood./
btw Mark what do you use to calculate that ?

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A software tool I wrote myself. It calculates the end result of a draw given some simple constraints (drawing to 7, 8, or a 9). There are some tricks I use to make calculating the exact probability work in a short amount of time (without using monte carlo techniques) but the code doesn't handle potential flushes well at the moment.

I'm working on a version which will calculate hot+cold EV for perfect play (i.e., no betting in later streets, always drawing with knowledge of other players' cards) but I haven't made much progress lately.

[euri10]

that sounds great, my friend wrote some bunch of code in VBA / Excel, it seems robust but not very good in terms of calculus performance, it took 10 minutes to makes 200,000 monte carlo simulations on this hand /images/graemlins/frown.gif
at least it gives me quite the same results you have /images/graemlins/smile.gif