Flop odds calculations

Hello Everyone,


I needed some help regarding figuring odds for a flop you want. For example flopping a set is 8:1.....what is the precise calculation to figure this?


Thanks,


Allan

This may not be completely correct...someone correct me if it's not, but...


if you have a pocket pair, then there are 2 cards out of the remaining 50 unknown cards that will give you a set. Odds are 48 to 2 against, reduced to 24 to 1. There are 3 opportunities (3 cards on the flop) to hit the set. 24/3 = 8.

I'm simply going to quote directly from Hold'em Odds Book by Mike Petriv.


You're holding pocket 8's.


[i]The probability of floping a set is represented by the model 8xy, where x and y represents any two card combination which is not a pair from the remaining 48 cards. The total possible number of two card combinations which can be made from 48 cards is 48*47/2*1 = 1,128. A certain number of those combinations are pairs which must be subracted from the 1,128 two card combinations. The number of pairs possible from the 12 remaining ranks is 12*6 = 72. The number of two card combinations not containing a pair is 1,128-72 = 1,056. Each of those 1,056 combinations may combine with either of the remaining two 8's, giving 2*1056 = 2,112 8xy combinations. The probability of hitting a set on the flop is 2,112/19,600 (19,600 is the total # of possible flops calculated earlier) = .108 = 10.8%. The odds against hitting a set are (19600-2112):2112 = 8.3:1.


The odds of flopping a set, full-house, or quads is 7.5:1.

Your method fails to take into account duplication of events. But For events that are quite unlikely (such as snagging one of 2 8s) your method is only slightely wrong. Your method calculates on average how many you'll get altogether in the long run.


For likely events such as the chances of flopping an A, K, Q, J, or T you will find your method falls apart completely (you'll calculate a greater than 100% of it happening!!)


- Louie

"The odds of flopping a set, full-house, or quads is 7.5:1."


Does that mean when you hold a pocket pair, you'll flop either a set, full-house, or quads once every (roughly) eight flops?


Thanks in advance for your reply. Your posts are always informative and helpful.

"Does that mean when you hold a pocket pair, you'll flop either a set, full-house, or quads once every (roughly) eight flops? "


yes, but the majority of those will be just sets.

There's a book called something like The Holdem Odds book that explains a lot of this stuff. It's not the greatest book in the world but it will probably answer most of your questions. I'm pretty sure Conjelco sells it on their website.


TRLS

Gamblers book club carries the book.