[AaronBrown]

Thanks for the kind words.

You're right that the first example is not like poker, there is no hidden information. The last sentence is correct in my accounting. You make $0.50 when he takes the bet, then you have an even $1.50 win or loss on the coin toss. If you win the toss, you get $0.50 from his mistake, and $1.50 from the luck of the flip, $2.00 total payout. If you lose the toss, you get $0.50 from his mistake but lose $1.50 from the luck of the flip, -$1.00 total.

In the second example, I assume the bet is a push if he draws the same card (although I worded it wrong). The reason you are ahead $0.1267 when he makes this offer is you have the option to accept it (which you do with a 9 or higher) or decline it (which you do on a 7 or lower, with an 8 it's a fair bet).

This case is very much like poker. He makes a bet, you can call or fold. It's simpler because it depends only on one card, there is no ante or blind, and you cannot raise. The point is that you make money from his bad bet, regardless of what you hold or what he draws. Those are random events that will add ot or subtract from your initial expectation.