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jimbob68
Posted by jimbob68
Mar 01, 2018

poker odds

can someone explain to me the ways to get 4 of a kind from a pair (draw 3) in draw poker. the published number of ways is 40 which is (47 cards - 4 -3) =40

but for 3 of a kind to get 4 of a kind (draw 2) the published number of ways is 46 = (47 cards - 1 card to match the 3 of a kind) = 46. The 5th card can be any of the remaining 46 cards because it cannot be on of the 4 of a kind so 46 ways is published number.

why if it is 46 for 3 of a kind to 4 of a kind, is it not 45 for a pair to 4 of a kind 45 = (47 cards - 2 cards to match pair) = 45

bless you and thank your for your help, Jim

Comments

Mission146
Mission146 Mar 02, 2018

Jim,



Okay, I'm going to go about this a different way than you're looking at it, so I hope you're able to follow this.



Quads from a Pair



The number of combinations drawing three cards from 47 remaining is simply:



47 * 46 * 45 = 97290



What we are going to do is figure out the possibility of the two remaining needed cards for the 4OaK to come in, and for that, we just need to know how those cards can appear. Let's pretend we are holding a Pair of 7's and let x represent the non-seven:



77x, 7x7, x77



Okay, so there are only three configurations that allow the seven two appear. There are two different sevens, of course, but you'll see that works itself out:



(2/47 * 1/46 * 1) + (2/47 * 45/46 * 1/45) + (45/47 * 2/46 * 1/45) = 0.00277520814



That can be expressed 1/0.00277520814 = 1 in 360.333333413



Quads From Trips



Okay, so we have 777xx and toss xx leaving 47 cards of which one is a seven. It can come x7 or 7x:



(1/47) + (46/47 * 1/46) = 0.04255319148



1/0.04255319148 = 1 in 23.5000000052



Anyway, I hope that's what you were wanting to know. If not, please clarify what it is you want to know and I'll do my best to answer you.