Proposition bet

[Guernica4000]

Player “A” propositions Player “B” to a bet.

The rules are that Player “A” will go all-in for one unit ($100) in the dark. Player “B” looks at his two cards and decides if he wants to call or fold. If he calls the best Poker hand wins after the river.
If player “B” loses he must pay player “A” 2 to 1 or $200 and another hand is played.


Please keep in mind that player “A” all-in is always for $100 regardless of the hands he has won or lost.
We are making the assumption that player “B” is a good player with a good understanding of poker.
There are no blinds or antes.


My question is:
Who is getting the better of this bet and what would be the minimum number of hands that would have to be played in order to remove or at least reduce the “luck” factor.

[Pokerscott]

Given player B has an option to fold at no cost this cannot ever favor player A.

All player B needs to know are the starting hands that are 2-1 favorites against a random hand and call those.

There is no amount of hands that make this fair. In terms of the number of hands needed where B would approach his average advantage with any confidence, you would need to look at the distribution of hands that are better than 2-1 and see how much better they are on average.

Compute a standard deviation of the bet based on that data then away you go! /images/graemlins/smile.gif

Pokerscott

[Guernica4000]

Thanks for the reply Pokerscott. What if we change the bet a little to incorporate a blind?

What would be the exact blind structure to make this mathematically EV=0?

Also do you know what hands is 2-1 or better against a random hand?

[Paul2432]

I don't think too much. Maybe $2 or $3 per hand.

Here is my thought process. Maybe 10% of hands are a 2:1 favorite over a random hand. On average those hands are a 3:1 favorite. Over 200 hands you'll play 20, win 15 and lose 5, for a net gain of 500 or $2.50/hand.

I just guessed at these figures. Actual amount is probably different but not by much.

Paul

[Siegmund]

2-1 or better vs. a random hand? Not very much. AKs, and pocket 8s or better. Kind of a boring game, with folds happening 96.5% of the time. This game has EV of about +$1.02 (96.5% nothing happens; equity of 76.4% to the player for net profit of $29.27 if he calls)

And yes, there exists a size of small blind that makes this a fair game. That size will be around $1.06. Adding the blind might tip the odds enough to make 77 and AQs playable.

For answers accurate to more than the nearest 2 or 3 cents, we need to be clearer about what happens with ties, whether the blind is part of or in addition to the $200 if he loses, and so on.