POKER question

FLASH1296

FLASH1296

Well-Known Member
NLHE

What is the probability of one of the two players holding a Full House when the board is paired ?

What is the probability when there are 3 players ? Four?
 
This seems like one of those problems you solve in math class which has little application to the real world. Even if you do know the exact probability for any player, each specific situation would have a different probability depending on your read of the player. For example if a player limps in and/or flat calls a small preflop raise, they're more likely to have a small pocket pair hoping to flop a set. If they're raising and reraising on the flop, chances are they have a set. And if the board pairs by the river and they're still aggressive, they likely have a boat. While it's good to know the absolute probability someone has a boat, you need to put your opponents on a range based on their betting and previous play, and from that, figure out the probability they have a boat.

Anyways, the probability of the board pairing is 49.29%. The probability of one person getting a pocket pair is 5.9%. The probability of the pocket pair improving to a set by the river is 22%. So it's a 1.29% chance they have a boat when the board is paired. Multiply 1.29 by the number of players.

Sure, it's a low probability, but you have to use the information you have by observing how they're playing the hand to figure if they have a boat or not.
 
When the board is paired, there are two ways to have a boat. 1) pocket pair that matches one of the unpaired board cards, and 2) one card matches the board pair and one matches an unpaired board card. So total combinations that result in a full house:

3 * [(3 * 2)/2] + 2 * 9 = 27

If you are also interested in someone getting 4 of a kind, add one more combination.

Total combinations possible in 1 specific hand:

47 * 46 / 2 = 1081

So odds of any one specific person having a full house or quads:
28/1081 = 2.59%

This next part is where I may be off slightly, but it should be close...
Odds of at least one of two people having a full house or quads:

1 - (1053/1081)^2 = 5.11%

And for 3 people:

1 - (1053/1081)^3 = 7.57%


Like I said, the last two are estimates, but they should be reasonably accurate.
 
alwayssplitaces said:
This seems like one of those problems you solve in math class which has little application to the real world.
Click to expand...

Exactly. For a real world example, If I have a flush, I'll often stop raising when the board pairs up. There's a theoretically mathematical remote chance the other player has the boat (~2-3% as mentioned by others), and you would think you should raise,, but in real life, I would say don't raise, especially with multiple players.

This is due to the effect that the players are in the hand for a reason. Similarly, if you have KK's in your hand, and and Ace shows up on board, your usually toast.
 
Gamblor said:
Exactly. For a real world example, If I have a flush, I'll often stop raising when the board pairs up. There's a theoretically mathematical remote chance the other player has the boat (~2-3% as mentioned by others), and you would think you should raise,, but in real life, I would say don't raise, especially with multiple players.

This is due to the effect that the players are in the hand for a reason. Similarly, if you have KK's in your hand, and and Ace shows up on board, your usually toast.
Click to expand...

Not always. I had kings, made a big preflop raise and got called by A8. Ace came on the flop. A8 checked to me, I made a big c-bet, got called. Turn was a blank, fired another c-bet and got called. The river was another blank, again I was checked to, I put him all in and he folded. Showed me A8 and told me that he put me on a bigger ace. And he got on tilt when I showed him kings. I would have folded if he reraised rather than just called, since there was a straight draw out there.
 
alwayssplitaces said:
Not always. I had kings, made a big preflop raise and got called by A8. Ace came on the flop. A8 checked to me, I made a big c-bet, got called. Turn was a blank, fired another c-bet and got called. The river was another blank, again I was checked to, I put him all in and he folded. Showed me A8 and told me that he put me on a bigger ace. And he got on tilt when I showed him kings. I would have folded if he reraised rather than just called, since there was a straight draw out there.
Click to expand...

No good can come out of calling a big pre-flop raise with A8 (non-suited especially). :grin: He got what he deserved :)
 
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