I’m confused what the word “fairly” means in this sentence.
Do you mean that they make a zero-expected-value bet, e.g., 1:1 odds for a fair coin? (Then “fairly” is too strong; non-degenerate odds (i.e., not zero on either side) is the actual required condition.)
Do you mean that they bet without fraud, such that one will get a positive payout in one outcome and the other will in the other? (Then I think “fairly” is redundant, because I would say they haven’t actually bet on the outcome of the coin if the payouts don’t correspond to coin outcomes.)
If Alice and Bob bet fairly on the outcome of a coin, there is no arbitrage.
I’m confused what the word “fairly” means in this sentence.
Do you mean that they make a zero-expected-value bet, e.g., 1:1 odds for a fair coin? (Then “fairly” is too strong; non-degenerate odds (i.e., not zero on either side) is the actual required condition.)
Do you mean that they bet without fraud, such that one will get a positive payout in one outcome and the other will in the other? (Then I think “fairly” is redundant, because I would say they haven’t actually bet on the outcome of the coin if the payouts don’t correspond to coin outcomes.)