Re: 2nd Flip of a bent coin
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I have a friend bend a coin as much as he wants out of my sight. We agree on an even money bet on the 1st flip. I randomize my choice 50-50.
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So you're betting with your friend who bent the coin? Is that the way you intended to set it up? If it is then it's a good thing the agreed to bet allows you to call the flip after the bet's been made. You are really betting on that fair coin you are flipping to call the bet. You are betting it will flip to a match.
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It flips heads, 3rd party judge reports to us blind.
I want to do another even money bet on the 2nd flip. I'm +/=EV taking heads this time.
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Not if you're betting with your friend and he knows how he bent the coin and he agrees to the bet. Chances are he has folded it away from tails to produce a tails bias. Since it just happened to land heads first flip he gets a nice +EV for himself when he agrees to your second bet.
So maybe you didn't intend such a complication. Let's assume you are gambling with someone who knows nothing more about the Bent Coin than you do. I can't see any way it could be argued that Betting Heads at Even Money is not +EV, assuming the Bent Coin has any bias at all. The Big Question is, what are the worst odds you would take to bet Heads? Your randomizing Call of the coin on the first bet really begs the question of how you view the No-Information condition for the First Flip in terms of Probalities involving the Bent Coin. You could know the Bent Coin has a Tails bias and your randomizing Call would work just as well. Your even money on the First Bet is the payoff on P(Fair Coin flips to a Match).
What are the worst odds you would take to bet Heads after the First Flip? That will tell us how you are incorporating your No-Information into your Known Information about the First Flip.
PairTheBoard
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