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Parrondo’s Paradox

Parrondo’s Paradox. Noel-Ann Bradshaw University of Greenwich. Game A. Biased Coin: Heads I win £1 Tails you win £1 P(Heads) = 0.5 – ε where ε = 0.005 A losing game for heads. Game B. Two Biased Coins: Heads I win £1 Tails you win £1

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Parrondo’s Paradox

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  1. Parrondo’s Paradox Noel-Ann Bradshaw University of Greenwich

  2. Game A Biased Coin: Heads I win £1 Tails you win £1 P(Heads) = 0.5 – ε where ε = 0.005 A losing game for heads

  3. Game B Two Biased Coins: Heads I win £1 Tails you win £1 If your winnings are a multiple of 3 play with coin 1 otherwise use coin 2.

  4. Game B Coin 1: P(Heads) = 0.1 – ε Coin 2: P(Heads) = 0.75 – ε A losing game for heads

  5. I lose!

  6. Next Offer Suppose we play a random mixture of games: So randomly play Game A or Game B Same odds / same conditions. Do you still want to play?

  7. I Win!

  8. Parrondo’s Paradox

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