Odds of getting a pair on the flop?

[blah730235]

I'm trying to figure what I did wrong when I tried to come up with odds of getting a pair on the flop with two unpaired hole cards(ie K8, 35, 96, A2).

http://www.texasholdem-poker.com/calcul ... decimals=2

"Chance of getting 1 Pair on the flop: 1 in 3.71"
"Chance of getting 1 Pair on the flop: 26.94% "


So let me explain my thinking...

The odds of hitting a pair on the flop are the same whether you have 68 or AK (yes technically if there are alot of people betting heavy preflop, there is a better chance someone has an ace in the hole but I don't want to take that into account)

So there are 6 cards in the deck that could pair up one of your hole cards. There are 50 possible cards that could be in the deck. Each card that is layed down on the flop that does not give you a pair reduced 50 possible cards by 1...

6/50, 6/49, 6/48

.12%, 12.24%, 12.5% = 36.74%

So there's a 36.74% of getting a pair on the flop but the website says 26.94% What's up?

[suitedaces84]

So let me explain my thinking...

So there are 6 cards in the deck that could pair up one of your hole cards. There are 50 possible cards that could be in the deck. Each card that is layed down on the flop that does not give you a pair reduced 50 possible cards by 1...

6/50, 6/49, 6/48

.12%, 12.24%, 12.5% = 36.74%

If you flip a coin twice what's the probability of it landing on heads at least once?

By your logic it would be 1/2 + 1/2 = 1. Which means you're guarnteed heads at least once. Which means that it is impossible to flip two tails in a row. This approach is not correct.

I'll give you a hint: think about the probability of not flopping a pair.

[xDiamond_CutteRx]

What suited is alluding to is that the true probability is [1 - P(not flopping a pair)]. The odds of flopping EXACTLY one pair is about 26%, but the odds of flopping one pair or better is a little over 32%.

[Ensano]

So let me explain my thinking...

So there are 6 cards in the deck that could pair up one of your hole cards. There are 50 possible cards that could be in the deck. Each card that is layed down on the flop that does not give you a pair reduced 50 possible cards by 1...

6/50, 6/49, 6/48

.12%, 12.24%, 12.5% = 36.74%

If you flip a coin twice what's the probability of it landing on heads at least once?

By your logic it would be 1/2 + 1/2 = 1. Which means you're guarnteed heads at least once. Which means that it is impossible to flip two tails in a row. This approach is not correct.

I'll give you a hint: think about the probability of not flopping a pair.

you MULTIPLY the numbers for the odds of BOTH to happen..

.5 x .5 = 0.25

so odds of flipping heads twice in a row is 1/4 or 25%

or in this case... you take the odds of it NOT happening...

44/50 * 43/49 * 42/48 =
.88*.87755102*.875 =
.675714286 or 67.5714% to NOT happen

or 32.4286% to happen

[xDiamond_CutteRx]

Ensano, suited was asking the probability of getting heads at least once, not the odds of getting it twice in a row.

So you have the right operation, but it should be [1 - (0.5)(0.5)] or 75% chance of getting heads at least once.

Your numbers for flopping at least one pair are correct though.