triple draw high full house probability
Join Date: Sep 2011
Posts: 445
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
?
Join Date: Mar 2015
Posts: 420
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.
Join Date: Mar 2015
Posts: 420
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.
