raising with TT,JJ, QQ..

[flopdanutz]

what is the probability that over cards will come on the flop

when u hold TT?
when u hold JJ?
when u hold QQ?

[BruceZ]

Probabability of at least one over card on flop = 1 - probability of no overcards.

TT: 1 - (34/50)(33/49)(32/48) = 69.5%

JJ: 1 - (38/50)(37/49)(36/48) = 57.0%

QQ: 1 - (42/50)(41/49)(40/48) = 41.4%

This includes times you flop an overcard and also make a set or quads. If you want the probability of flopping an overcard and no set or quads (since you don't worry when you flop the nuts [img]/forums/images/icons/smile.gif[/img]) , we can add the probabilities of 1,2, and 3 overcards with no set or quads:

TT: (16*3*32*31 + 16*15*32*3 + 16*15*14)/(50*49*48) = 62.9%

JJ: (12*3*36*35 + 12*11*36*3 + 12*11*10)/(50*49*48) = 51.8%

QQ: (8*3*40*39 + 8*7*40*3 + 8*7*6)/(50*49*48) = 37.8%

[brad]

i thought it was almost 50/50 of overcard when you have QQ?

any idea what im thinking of? 41 vs ~50 seems like i must be thinking of something else.

[BruceZ]

It is almost 50/50 of NO overcard AND no set with QQ, or equivalently it is almost 50/50 of an overcard OR a set. I only know that because I computed this first. I don't think that's very useful since overcards hurt your hand while a set helps it.

probability of no overcard and no set with QQ =
(40/50)(39/49)(38/48) = 50.4%

The 41.4% counts only the times you get overcards but also includes the times you also flop a set in addition to overcards. This is what was asked for, but it isn't completely useful either though it's closer. The 37.8% is the times we get overcards with no set which I think is most useful.

[heavybody]

Since you no math pretty good how do the equations(38/50)(37/49)(36/48)equal 57%. The reason I ask is that in the first equation 50 is the amount of unseen cards and 38 are undercards, or Jacks so on this equation alone you are about a 3/1 favorite to get an undercard(75%) .Is this correct? How do these 3 equations then come out to 57%? Math is not my strong suit so a detailed explanation would be helpful.

[BruceZ]

38/50 is the probabity of getting an undercard or jack on just the first card of the flop, and this is 75% as you say. (38/50)(37/49)(36/48) is the probability of getting an undercard or jack on every card of the flop (no overcards), and this is 43%. 1 - 43% is 57%, and this is the probability of getting at least 1 over card. Note this includes times you get an overcard but also make a set. That's why I did the second part of the calculation.

[brad]

thanks.

[ACPlayer]

You may have been thinking about the fact that QQ and AK are about 50/50 in terms of relative strength (hot and cold). If so you will need to adjust Bruce's formulas for the AK that is in the opponent's hands and then calc the probability of the an A or K appearing in 5 cards (not just the flop). Dont forget to count the times that both AK appear as well as the situation when the overcard flops and you hit your set. Adding in little things like straights should get you to approx 50/50.

Bruce has pointed the way.