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Old 02-16-2017, 06:10 PM   #1
PLBlow
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Join Date: Sep 2011
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triple draw high full house probability

lets say i have J-J-J-10-5

what is the probability of making a full house OR better if I...

1) Hold J-J-J and draw 2 cards over three draws

2) Hold J-J-J-10 and draw 1 card over three draws

?
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Old 02-17-2017, 05:52 AM   #2
md46135
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Join Date: Mar 2015
Location: where they don't respect my raises
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Re: triple draw high full house probability

if you draw just 1 card probability of getting a full house or better at some stage is:
1 - (43/47 * 42/46 *41/45) = 0.24.

if you draw 2 cards things get more complicated because of card removal effect, every next draw is dependent on the previous one and there are more combinations of things that can happen. it's tedious to go through all of that, I hope someone using some kind of software can give you the answer on that. my speculation would be that it's better to draw 2 cards, I think when I played jacks or better on some site which tells you the right move it was to change 2 in a situation like this.
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Old 02-17-2017, 08:06 AM   #3
md46135
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Re: triple draw high full house probability

you could make an approximation for 2). if you had just one attempt to draw, then it's (46C1*1C1 + 2C1*3C2 + 10C1*4C2) / 47C2 = 0.1036, this is the chance of getting a full house or better in the first draw. 1 - 0.1036 is the chance for not getting anything good in the first draw, so 1 - (1-0.1036)^3 = 0.2797 would be an approximation which should be good enough for 2).

just for comparison, if you approximated 1) in this way, you would get 1 - (43/47)^3 = 0.234, which is pretty close to 0.239 which is the exact answer.
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