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View Full Version : raising with TT,JJ, QQ..

flopdanutz
03-09-2003, 09:12 PM
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
03-10-2003, 04:36 AM
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 /forums/images/icons/smile.gif) , 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%

03-10-2003, 12:25 PM
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
03-10-2003, 01:34 PM
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
03-10-2003, 06:14 PM
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
03-11-2003, 05:00 AM
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.