Mathematical possible to flop sets and turn quads....

[jrforman]

I am playing two tables of 5/10 NL online...I get dealt 55 and 1010 respectively...I flop two sets on a 5 4 4 board and Q 10 4 board...The turn brings a 4th 5 and 4th 10 at the same time!!! What do you think the odds are for that???

[AaronBrown]

With a pair in your hand, there are two cards out there to make your set. There are 48 other cards, so you can flop a set but not quads 2*48*47/2 = 2,256 ways out of the 19,600 possible flops. That's 11.5%.

Once you do that, there's 1 card out of 47 that gives you quads. The probability of both flopping the set and getting quads on the turn is 0.245% or a bit worse than 1 in 400.

To do it twice in a row is 1 in 166,000. But you have to be careful. Something unusual happens in every Poker hand, if you play 1,000 hands there's likely to be some 1 in 166,000 shot in there.

[KJL]

Aaron, why do u divide 2*48*47 by 2. I know that it is the right answer, I just can't figure out why you divide it.

[BruceZ]

[ QUOTE ]
Aaron, why do u divide 2*48*47 by 2. I know that it is the right answer, I just can't figure out why you divide it.

[/ QUOTE ]


Because 48*47 counts each pair of cards twice. For example, As2c and 2cAs are the same two cards. When we count the total flops as 19,600, this counts each combination of 3 cards only once, so we must do the same in the numerator.

[KJL]

ooooh ok

[ichudfold]

This is quite interesting but I would like to know, how can you calculate that in your head at the poker table? Is there an easy way? Are the pros able to do that or do they simply study them?

[LetYouDown]

You'd never need to know something like that in a real-time situation. Most players memorize odds for common scenarios. In the event that they haven't run into the situation previously, shortcuts to getting roughly the correct odds based on the number of outs can be useful.

[jrforman]

Thanks for the replies guys, I honestly thought it was going to be higher...