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 Probability Discussions of probability theory

 09-29-2016, 12:31 PM #1 donkey_king veteran     Join Date: Feb 2008 Location: Dallas, Texas Posts: 3,036 odds of two of the same suit or three of same suit on flop? Was playing in a game last night and a guy was betting this prop a lot. How big of an underdog is he? thanks in advance
 09-29-2016, 01:30 PM #2 whosnext Pooh-Bah     Join Date: Mar 2009 Location: California Posts: 5,476 Re: odds of two of the same suit or three of same suit on flop? I am not entirely sure what the prop bet was, but here is a framework for standard flop prop bets. How many total flops are possible (ignoring anyone's hole cards)? Clearly there are 52 cards in the deck and 3 come on the flop. So, in words, it is choose any 3 from 52. In math, we write this as C(52,3). Either by looking up the formula for the "C" (Choose) function or by using a calculator, this is easily found to be 22,100. How many of a suit can appear on the flop? There are clearly only three ways a flop can come if you are only interested in the suits that appear: - 1 suit on the flop, meaning that all three cards are of the same suit; - 2 suits on the flop, meaning that there are two cards of one suit and one card of another suit; - 3 suits on the flop, meaning that there is one card each from three different suits. It is straightforward to tally how many flops are possible in each case. Three suits on flop There are four suits in all, and we need to choose three of them here. Of course, there are 13 cards in each suit, and we need to choose exactly one card from each of the three chosen suits. So we have: C(4,3)*C(13,1)*C(13,1)*C(13,1) = 8,788 Two suits on flop There are four suits in all, and we need to choose two of them here. And then among these two chosen suits, we need to choose one of them to have the two cards (and the other suit to have one card). Finally, we need to choose exactly two cards from the "two-suit" and to choose exactly one card from the "one-suit". So we have: C(4,2)*C(2,1)*C(13,2)*C(13,1) = 12,168 One suit on flop There are four suits in all, and we need to choose one of them here. And then we need to choose exactly three cards from that chosen suit. So we have: C(4,1)*C(13,3) = 1,144 From these tallies, the true odds of several prop bets can be easily determined. If the prop bet you are talking about is not covered above, please give more details. Last edited by whosnext; 09-29-2016 at 01:44 PM.
 09-29-2016, 02:53 PM #3 suited fours Pooh-Bah     Join Date: Nov 2012 Location: East Coast USA Posts: 4,147 Re: odds of two of the same suit or three of same suit on flop? Are you a math teacher/professor? Your explanations are patient and well explained. I'd lean probability tree for this one. Tomayto Tomahto
01-22-2019, 05:14 AM   #4
sparrrx
enthusiast

Join Date: May 2018
Posts: 73
Re: odds of two of the same suit or three of same suit on flop?

Quote:
 From these tallies, the true odds of several prop bets can be easily determined.
Well I can't determine it that easily :S

can someone give a % for the flop having 2 cards of the same suit (be it 2 clubs or 2 hearts or 2 diamond or 2 spades)?
I don't know what to do with a "tally"

01-22-2019, 11:56 AM   #5
heehaww
Pooh-Bah

Join Date: Aug 2011
Location: Tacooos!!!!
Posts: 4,613
Re: odds of two of the same suit or three of same suit on flop?

Quote:
 I don't know what to do with a "tally"
Yes you do. If 12168 flops have 2 of the same suit, out of 22100 possible flops, then what % of flops have 2 of the same suit?

01-22-2019, 12:07 PM   #6
sparrrx
enthusiast

Join Date: May 2018
Posts: 73
Re: odds of two of the same suit or three of same suit on flop?

Quote:
 Originally Posted by heehaww Yes you do. If 12168 flops have 2 of the same suit, out of 22100 possible flops, then what % of flops have 2 of the same suit?
ahh, turned out I did know what a tally is, so 55%

 01-22-2019, 12:34 PM #7 statmanhal Pooh-Bah   Join Date: Jan 2009 Posts: 4,412 Re: odds of two of the same suit or three of same suit on flop? Whosnext showed the following flop possibilities: Number of flop combos: 22,100 Number of 2 of a suit combos: 12,168 Number of 3 of a suit combos:1144 Therefore the number of 2 or 3 of a suit combos is 12,168 + 1,144 = 13,312 So, out of 22,100 possible flops, 13,312 will be a “success”, assuming a success is having 2 or 3 of a suit. Thus, the probability of winning the bet is 13,312/22,100 = 60.23%, equivalent to odds for winning of 0.6023/.3977 = 1.51 to 1. OP didn’t give details on payoff but if it was an even-money bet, it’s printing money to bet on flopping 2 or 3 of a suit.

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