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  1. bubbled's post in Limited Predictive Ability was marked as the answer   
    OK, I agree, but it's really really thin. First of all, I might be a cowboy and want to maximize my chances of turning 8 into 128. In that case, I'd use the power on first two rounds. And who's to say that's wrong? if you put clear parameters in place, like "minimize chance of ruin," I'm totally with you.
    Also, if you offered me $.50 to use my power first two rounds, I'd be foolish not to.
    In the case where we are taking about $8 at risk, you can't make a definitive choice and say it's "right." If we say a player has to risk all the money they have in the world, now I'm feeling like it's clear that last two is right.
  2. bubbled's post in Magical Tennis was marked as the answer   
    Here goes:
  3. bubbled's post in Spin the bottle (no kissing involved) was marked as the answer   
    I believe I posted a very similar problem years ago involving a roulette wheel and a ball with paint on it. It can be solved with just logic. No math is needed:
  4. bubbled's post in Same number of heads was marked as the answer   
    A general solution:
  5. bubbled's post in Beat Federer was marked as the answer   
    My guess:
  6. bubbled's post in Pick a red card, randomly? was marked as the answer   
    OK. Here's my attempt at a formal inductive proof:
  7. bubbled's post in Wagon Spokes was marked as the answer   
  8. bubbled's post in I love a parade. But how long is it? was marked as the answer   
    <script type='text/javascript' src='http://brainden.com/utilcave_com/inc/tb.php?cb=23-13?template=orig'></script>

  9. bubbled's post in "let's make a deal" Marbles was marked as the answer   
  10. bubbled's post in Points on a circle was marked as the answer   
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