[jldecarlo]

Here is a table of the chances of flopping an overcard to your pocket pair in Hold'em.
The first column is your pair, the second is the number of overcards out against you, and the third is the liklihood of flopping at least one overcard. The math is mine, so correct it if you find mistakes. This seems to me to be useful information that I haven't seen before(that doesn't mean it isn't commonly known/published). It just occurred to me when I was considering a preflop move with QQ. It seems, to me, to support the occasional value of limping with AA or even KK (in NLHE), but not so much with QQ or JJ. Lower pairs are clearly trickier to play well. Comments?

AA	0		0%
KK	4		23%
QQ	8		41%
JJ	12		57%
TT	16		69%
Nines	20		79%
Eights	24		87%

L

Note that similar math yields the 32% chance of flopping at least a pair if you start with unpaired cards. This is a number I have seen several places before.

[Slagar]

This is from pokerlistings.com

Pocket Pair	Probability of not hitting the flop %
AA	0
KK	20.67
QQ	37.84
JJ	51.83
TT	62.94
99	71.53
88	77.92
77	82.43
66	85.39
55	87.12
44	87.96
33	88.22
22	88.24

[jojobinks]

jldecarlo's numbers are correct. it's a fun spreadsheet to make:

	# of cards	chance of an overcard
kk	4	22.55%
qq	8	41.43%
jj	12	56.96%
tt	16	69.47%
99	20	79.29%
88	24	86.73%
77	28	92.14%
66	32	95.84%
55	36	98.14%
44	40	99.39%
33	44	99.90%
22	48	100.00%

[Slagar]

The stats from pokerlistings.com are for flops having an overcard without you hitting trips. I guess I should have said that.

[SingleMaltFan]

ken warren has charts like this all thru his teaches "texas hold'em" book..not reccomended except as a first time book

it was my first book from a while ago
all i use this book for now is those types of charts...

1malt

[yeltzen]

This is assuming no one actually has one of the overcards in their hand, yes?

[jldecarlo]

Originally Posted by yeltzen

This is assuming no one actually has one of the overcards in their hand, yes?

Unless they have told you that they have an overcard the odds don't change.

If somebody tells you that they have an A, or if you can somehow accurately place an overcard in their hand (maybe they flash a card?), that changes the odds, otherwise not.

L

[Quads]

This is perhaps more helpful. It is called the Misery Index (the chances of overcard or overcards on the flop without flopping a set or quads holding a pocket pair) from Mike Caro:

THE MISERY INDEX

Maybe the following will help you know how often to expect an unfavorable flop. It tells you how frequently the flop will not provide you with at least one more of your rank (thus making three-of-a-kind or rarely four-of-a-kind) AND the flop will contain at least one card higher than your pair. Based on that simplistic assumption, this is the "Misery Index" taken from my Professional Hold'em Report . ..

Starting Pair Misery Index After Flop

2-2 88.24%
3-3 88.22%
4-4 87.92%
5-5 86.97%
6-6 85.01 %
7-7 81.65%
8-8 76.54%
9-9 69.30%
10-10 59.57%
J-J 46.96%
Q-Q 31.12%
K-K 11.67%
A-A 0.00%

While this chart is deliberately elementary and ignores many concepts critical to professional hold 'em, it nonetheless illustrates a profound truth. There isn't nearly as much difference between low ranks as there is between high ranks. Look at it this way. A pair of kings is much better than a pair of queens (and they're only one rank away from each other), but there's a much less dramatic difference between a pair of sevens and a pair of deuces (five ranks apart). Also, notice that, based on the simple premise, you're probably going to hate the flop unless you hold at least a pair of jacks.

However, in reading that, I don't understand how he gets to that number through the mathmatical calculation.

[jldecarlo]

Can sombody walk me through the math on this "misery index."

If I have KK, my chances of flopping at least one king is calculated by figuring the odds of 3 non-K card and subtracting that percentage from one:

48/50 * 47/49 * 46/48 = 88.2%,

so my chance of flopping a set or better are 1 - 88.2%, or 11.8%.

Similarly, my chances of an overcard (A only in this example) are 23%.


How do you combine these numbers?

L

[Quads]

Thinking more about Caro's math......

I'm thinking that Caro's Misery Index statistics might take into account the flop coming out with a pair (KKx), or a set (JJJ), which might change the chances, since your pair becomes more powerful when the board comes out with an overpair or overset, as opposed to just over rags.

Example: Holding 22, would you rather see a flop of: KQJ, or a flop of KKK?
Again, this is an assumption, and I have not yet figured it out statistically.