I have 100 coins, 99 that are heads/tails and one that is double sided heads. If I pick one of the coins at random, flip it seven times, and get 7 heads in a row, is the coin more likely to be double sided heads or a regular heads/tails coin.
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'how much do you want to bet on a dice game where you can reroll if you don't like your first try?' (roughly paraphrased) = What is the expected outcome of a dice game where you can re-roll if your first roll is 1-3?
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Which is bigger, 2^(1/3) or 10^(1/10)?
We are playing a game where the first person to say "40" wins, and each player must add 1-10 to the previous number. For example, I say 5; you can say any number 6-15 to which I have to react. For you to say "40" first, what is your strategy? Hint: You need to choose whether or not to go first, then your strategy going forward.
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