Stupid question about drawing to sets and implied odds.

[cnfuzzd]

Ok, i was just thinking about this, and couldnt come up with a decent answer either way, and now feel like a moron.

Assume you have 44 and the flop is AJ7r. Assuming that this is utopia, and making a set on the turn will hold up 100% of the time. Given the doubled-size bets on the later streets, do i only need eleven bets in the pot to make it +EV to call? I feel like such a dumbass.

peace

john nickle

[Alobar]

how many people are in the pot, and will you get a chance to raise or checkraise?

[JeffO]

your about 23-1 to make your set. Assuming your behind you need about 18-1 with implied odds to make the call.

[LinusKS]

Your chances of hitting your set on the turn are two out of 47, or 1:22.5. If you're calling for one small bet on the flop, you'll have to average 11.5 more small bets to break even, or 6 big bets to show a profit.

[Luv2DriveTT]

Can someone pleae show how to calculate the odds that a player will hit his or her set on the flop when they hold a pocket pair pre-flop? This has been one odds question that has eluded me for a while, good thread to ask it in.

TT /images/graemlins/club.gif

[AngryCola]

I learned how to calculate this through "Mike Petriv's Hold'em's odd(s) book". The math it requires is not something I had previously learned about.

Let's say you hold:

6 /images/graemlins/spade.gif6 /images/graemlins/heart.gif

50 cards remain in the deck which will give us our flop. The total number of 3 card combinations with 50 cards is

50*49*48/3*2*1 = 19600

So there are 19,600 flops you can expect to receive with any 2 hole cards.

Here is the model for flopping a set with 6-6:

6xy

x & y = Any two card combination which is not a pair from the remaining 48 cards.

The number of two card combinations which can be made from 48 cards is
48*47/2*1= 1128.

Some of those combinations contain pairs, and we have to get rid of them to find out the odds for flopping a set. The number of pairs possible from the 12 remaining ranks is 12*6= 72

1128-72= 1056

Those 1056 combinations can combine with either of the remaining two sixes.

2*1056 = 2112 6xy combinations

The probability of flopping a set on the flop is
2112/19600= .108= 10.8%.

The odds against flopping a set are
(19600-2112):2112= 8.3:1.

Notice those odds are for flopping only a set. The odds against flopping a set or better (quads/boat) are 7.51:1, or 11.8%.

[Makata]

[ QUOTE ]
Some of those combinations contain pairs, and we have to get rid of them to find out the odds for flopping a set.

[/ QUOTE ]
Maybe I'm missing something, but why are you elimating flopped boats? You could argue there's an increased chance of losing, but really, if I have 66 on an AA6 flop, I want the AK to cap me every street, so I'm not seeing your reason for eliminating pairs.

[AngryCola]

Because sets are not boats.

The point was to show how to figure out the probability of flopping a set. It was just an example. You can use the same math to figure out the odds against flopping a set or better. Regardless, your point was not the the original question I was responding to.

What I posted is the exact math for figuring the odds against flopping a set.

As I stated at the bottom of the other post, the odds against flopping a set/quads/boat are 7.51:1

[driller]

Another way to arrive at the odds of hitting AT LEAST a set (the second part of your answer) is to calculate the percentage of time you won't hit at least a set and then subtract that from one:

Since you have 2 cards out of 50 unseen cards:

48/50 x 47/49 x 46/48 = 0.8824 pc you won't hit at least a set.

1-0.8824 = 0.1176 or 7.5:1 against

This is the number I use since most of the time hitting a full house is better. An exception is when you have 66 and your opponent has JJ and the flop comes J66. That was very good for me and very bad for the other guy. /images/graemlins/smirk.gif

[driller]

Your odds of making your set on the turn are 22.5:1 against. Your odds of making it by the river are 10.9:1 against. If everybody was all in, then you would at least 10.9 bets in the pot to justify the call.

Normally though, if you don't make your set on the turn you have to call another bet, at least (with odds of 22:1 against). Of course if you hit your set and win, you will win more than is in the pot at the time you call the flop bet. Its not cut and dried, but most of the time if you have to hit your set to win, you rarely have the odds to call with a 2 outer.