Overcards to JJ

[HollywoodDB]

I read in one of my books, the odds of flopping an overcard and no set with JJ is 47%, QQ 31% and KK 22%. What is the math equation used to figure this out?

[Big Country]

with 50 unseen cards, each card has a 2% chance of coming up.

With KK, that means 4 aces 3 times(3 cards on a flop), so 4*3*2=24%, discount for the chance that you get both an ace and a king, and your 22% seems right. (I don't feel like figuring all the math for the possibilities of getting an ace and a jack, and I'm not 100% sure I would do it right)

Similar math for the queens and jacks, just with more cards to give the overcard, and greater discounts that you get a jack with those greater number of cards.

[HollywoodDB]

OK, I see. Thanks. So actually, it would start with 50 unseen cards, 49 unseen cards and then on the 3rd card of the flop 48 unseen cards.

[mce86]

What are the odds?

There are 50 cards left....

12 of them are overcards.

12 out of 50 is about 1 out of 4.2.

So, the flop is out of 3.....so the odds are slightly with you to not see an overcard on the flop....and against you to the river.

[xxxxx]

The odds the first card is not an overcard is 38/50. The odds the second card is not an overcard (given the first is not) is 37/49. The odds the third card is not an overcard (given the first two are not) is 36/48. The odds there are no overcards in the entire flop is (38*37*36)/(50*49*48)=43%. 57% of the time there will be at least one overcard.