Hypothetical Heads Up Gambling Situation

[thechainsaw]

I did understand but didnt really express myself well.

Lets change the 10 to a 1 and ask what hand you would play. Well any 50% hand is better than a coin flip, so the correct answer is any hand of 50% or better i.e Q5 and above. QED.

Lets now say you have 2 chances, what hands do you play? Well on the 2nd trial, you would take the strategy above. On the first trial you can shorten your calling range, but to what I dont know - perhaps you would want a hand in the top third, my gut tells me. Maybe not.

You can continue the extrapolation until you get 10 goes, and I'm again guessing that on the first go you will need a hand in the top 1/10th, etc.

Does that make more sense, i'll try and work on a proof.