Another Hold em Odds Question

If a player holds AK / A/Q or A/J in a nine or ten handed hold em game, what are the odds that they will pair at LEAST one of the cards in their hand on the flop?

I am looking at an odds chart that says 1 out of 6 times the flop will produce and Ace. I assume that also means 1 out of 6 times it will pair the undercard rather than the Ace?

This chart also says that 1 of 2.1 times ONE of any two hole cards will pair on the flop. This would mean that roughly 1 out of 3 hands I will pair at least one of the cards in my hand regardless of whether it is an Ace, King or whatever?

Are these odds close to accurate?

Doesn't seem so to me based on my experience, which has been overwhelmingly at online tables...

[TaintedRogue]

First we need to know how many flops there are:

50 unknown cards * 49 * 48 /3*2*1 = 19,600
The 3*2*1 removes the permutations.

Then we need to know how many flops will not pair out hand:

44*43*42/3*2*1 = 13,244

19,600 - 13,244 = 6,356 flops will make our hand.

13,244/6356= 2.08:1

the poster is correct in his numbers... although don't get confused on 2:1 vs. 1 in 3. it's the same thing.

to do it fairly easily but with some inaccuracy.

you have six outs to pair, times 3 draws.

so 18 chances and there are 50, 49, 48 cards, but to make it simple 50 cards. so 18/50 or 36% chance...

although it overstates because it gives some value to hitting two pairs, three of a kind, four of a kind, full house (very, very slim for the last 3 possibilities).

so if that calculation is somewhat overstated, but gives you 36% chance, cut it back to 33% chance, which is 2:1 or 1 in 3 (very close to the other guy's exact answer).

i agree, it seems like it hits more often, but i think we get excited when it hits and don't care that much when it doesn't, so we remember the good flops more.

So mathematically speaking, every time I am dealt an A/K, A/Q, or A/J I should expect to pair at LEAST one of those cards every third hand...on average, correct?

So in other words, when I get dealt A/K and A/Q 78 times on Partypoker and only pair up one of the two hole cards THREE out of 78 times, I can assume that this is a statistical improbability?

[AaronBrown]

That would only happen one time in two billion.