## Main Question or Discussion Point

I recently got beat in playing poker in the worst way that I have ever seen before. I was playing on a poker site online (pokerstars) and got beat with four of a kind to a higher four of a kind. The game was texas hold'em. For those of you who don't know texas hold'em, that means you get dealt 2 hole cards and combine the 2 hole cards with 5 community cards to make your best 5 card hand. As you all probably know there are 52 cards in the deck with 4 different suits and 13 different rankings for each suit. Could someone please tell me the odds of losing with 4 of a kind, four 3's to be exact, in the game of texas hold'em.

## Answers and Replies

What beats 4-3's in Texas Hold Em'?

4-anything higher
flush
royal flush
full house

Does a high enough two pair beat four threes?

4 of anything higher beats 4 3's.

not that might not need to know but the hands go as follows

royal flush-10JQKA of one suit
striaght flush-5 cards in sequential order of same suit
4 of a kind-2222,3333,.....AAAA- AAAA being highest
full house-55522 three of a kind with a pair
three of a kind-QQQ
2 pair-33JJ
1 pair-AA
high card

card rankings-A K Q J 10 9 8 7 6 5 4 3 2
suits-clubs diamonds hearts spades

nicksauce
Homework Helper
Let's assume you hold 33 and on the board is 33XYZ... your opponent holds AB. So we need to find the probability that 4 out of {A,B,X,Y,Z} are equal. This would be
(47/47) * (3/46) * (2/45) * (1/44) * 5C4 ~= 1/3036. There will need to be a slight correction since four 2's lose to four 3's.

Now, let's assume you hold 33 and the board is 33XXY and X > 3. We need to find the probability your opponent holds XX. This would be (2/47) * (1/46) ~= 1/1081.

Now let's assume you hold 33 and the board is 33XXX and X > 3. We need to find the probability your opponent holds XY. This would be ~= 1 / 23.

So it all depends on what you define as your given variables.

Maybe some mistakes here, my probability is a little rusty.

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nicksauce
Homework Helper
Using Monte Carlo simulations with the program "pokerstove" http://www.pokerstove.com/download/ [Broken]

I found the following probabilities

Probability of winning given that you hold 33 and the board is 33XYZ -> 99.955%
Probability of winning given that you hold 33 and the board is 33XXY -> 99.710%
Probability of winning given that you hold 33 and the board is 33XXX -> 95.556%
Probability of winning given that you hold 3X and the board is 333YY -> 99.899%

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quasar987
Homework Helper
Gold Member
What was the board when you played?

nicksauce
Homework Helper
Note also that the calculated probabilities are valid for being against one opponent and you should (roughly) multiply the probability by itself N times where N is the number of opponents in the hand.

the board was AA333. I, of course, was holding Q3. So the odds of him flopping a quads are incredible, let alone me catching runner runner 33 for my quads. I have literally played millions of hands and have never seen that before in texas hold'em. Of course in other games like 5 card draw with wilds and so forth I have seen quads up against quads. I play poker maybe 5 days a week sometimes putting 5-12 hrs in a single session and I get quads maybe about once or twice a month. So you could imagine my disbelief when the guy flipped over quads to my quads. The worst part about it was that I was a big blind,ie. forced bet,
so i had no choice but to play my hand. The guy didn't raise before the board cards were put out; I was doomed no matter what lol. (quads= four of a kind)

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quasar987