Heads Up Matches situation

[Rekwob]

OK, say that you have two players that play heads up and one player has a 70% chance of winning any given match.

Now, how do you find out, knowing that hes 70% to win each match, what his percentage chance of winning is in a best of 3 matches, or a best of 25?

Is it easy enough that theres a simple formula or is it more complicated?

Thanks

[fnord_too]

Easy enough for 3, get's to be a pain for many.

Chance of winning a best of 3 =
Chance of winning all 3 * ways to win all 3+ chance of winning 2 * ways to win 2
= (.7)(.7)(.7)*1 + (.7)(.7)(.3)*3 = .784

There may be some nice formula that I am just not familiar with for big numbers, like best out of 25, but basically you are looking at a binomial expansion (if my memory of terms is correct) and summing over the winning ways (or losing ways and subtracting this from 1).

This is very similar to a random walk. In a random walk you start at zero and can take a step in either the positive or negative direction (based on some probability, usually 50/50 but no reason it cannot be 70/30). Where you end up after n steps will follow a normal distribution.

At any rate, the more games in the match the more likely the 70% guy will win.

[Greeksquared]

Just for a stupid side note. If this is no-limit, I don't think anyone could possibly be a 70 percent favorite as the "worst" player just has to push in preflop every hand.

[Jazza]

depends on the structure of the blinds

[fnord_too]

[ QUOTE ]
Just for a stupid side note. If this is no-limit, I don't think anyone could possibly be a 70 percent favorite as the "worst" player just has to push in preflop every hand.

[/ QUOTE ]

That is assuming the worse player knows this. Some people play worse than this strategy (typically by playing too weak tight HU).

[ThinkQuick]

[ QUOTE ]
[ QUOTE ]
Just for a stupid side note. If this is no-limit, I don't think anyone could possibly be a 70 percent favorite as the "worst" player just has to push in preflop every hand.

[/ QUOTE ]

That is assuming the worse player knows this. Some people play worse than this strategy (typically by playing too weak tight HU).

[/ QUOTE ]

Agreed.

There was a therad somewhere about rock/paper/scissors champions, and a poster said something like " I could throw a random symbol every time and the best player would have no edge on me"

This is true except that a) You'd have to recognize when you were up against someone better than you, otherwise you'd be giving up your edge

b) people think they are good and smart and play to win, not get a 50% chance. They play out their suboptimal strategies while believing in them.

[PairTheBoard]

I think this would be the perfect time for the inferior player to adopt the Sklansky All In strategy on offense. Is there a corollary strategy to this for Calling all in bets?

PairTheBoard

[PairTheBoard]

For large numbers you would probably want to use the Normal Aproximation to the Binomial.

PairTheBoard