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## Playing the Penny

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #9592 Fun: (2.61) Difficulty: (2.5) Category: Probability Submitted By: Marriot

You are in a bar having a drink with an old friend when he proposes a wager.

"Want to play a game?" he asks.
"Ok, here's how it works. You choose three possible outcomes of a coin toss, either HHH, TTT, HHT or whatever. I will do likewise. I will then start flipping the coin continuously until either one of our combinations comes up. The person whose combination comes up first is the winner. And to prove I'm not the cheating little weasel you're always making me out to be, I'll even let you go first so you have more combinations to choose from. So how about it? Is \$10.00 a fair bet?"

You know that your friend is a skilled trickster and usually has a trick or two up his sleeve but maybe he's being honest this time. Maybe this is a fair bet. While you try and think of which combination is most likely to come up first, you suddenly hit upon a strategy which will be immensely beneficial to you. What is it?

### Hint

Think what would be most likely to happen if you chose HHH, would this be a good decision?
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