HU probability question

[Moonsugar]

I want to know what the odds are that my hand will be a preflop 60/40 (or better) favorite than my HU opponent's hand on any one hand. Can someone show me how to figure that out?

TIA

[AaronBrown]

There's no easy way to figure it out. You have to consider all the starting hands against each other, look at all the boards that could be dealt, and count how many are better than 60/40.

You can get a pretty good approximation. The average hand, of course, is 50/50. The standard deviation of the heads-up all-in probability is about 10%. So the chance of getting 60/40 or better is about 1 in 6, because it's about one standard deviation above the mean. The actual probability is 19.2%, which is a bit higher.

[well]

I'll answer the following question, and I hope it's equivalent to yours:

Heads up, two players are both dealt a random starting hand from the same deck. What is the probability that player I has an equity of .6 or more.

The answer is .35469, or about 35.5%

To calculate this, I used a HU equity table. Then it's simply a matter of selecting the two-hand combinations for which your criterion is true and adding the according probabilities.

Regards.

[Moonsugar]

Thanks for the replies. I was worried that a problem like this had to be solved via simulation.

Now, which one of you is right?

LOL

[AaronBrown]

We might have interpreted the question differently. I was looking for hands that had 60% chance of winning against a random other hand. I think the hands that meet that definition are pairs five or higher; suited Ace with 6 or higher, King with 9 or higher or Queen Jack; offsuit Ace with 8 or higher, King with Jack or higher. That's 208 out of the 1,326 starting hands, or 15.7%.

[Moonsugar]

He answered the question I wanted answered. TY for answering another interesting question.

I suck at english /images/graemlins/frown.gif

[well]

[ QUOTE ]
I was looking for hands that had 60% chance of winning against a random other hand. I think the hands that meet that definition are pairs five or higher; suited Ace with 6 or higher, King with 9 or higher or Queen Jack; offsuit Ace with 8 or higher, King with Jack or higher. That's 208 out of the 1,326 starting hands, or 15.7%.

[/ QUOTE ]

The equity of A6s is about .599058,
the equity of K9s is about .599885 and
the equity of A8o is about .598726, so that leaves 208-(4+4+12)=188 hands, or 14.178%.

Do you agree?

Regards.

[AaronBrown]

Yes. I guess I rounded before applying the cut-off.