Make: More Electronics: Journey Deep Into the World of Logic Chips, Amplifiers, Sensors, and Randomicity by Platt Charles

Author:Platt, Charles [Platt, Charles]
Language: eng
Format: azw, pdf
ISBN: 9781449344047
Publisher: Maker Media, Inc
Published: 2014-04-28T16:00:00+00:00

Background: Alternative Game Arrays

If Player 2 has a 12.5% advantage in a sixteen-coin game, would it be the same in a game with fewer or additional coins and slots?

No, the advantage will be different. To see why, I’ll take an extreme example. Suppose we have a game in which there are only two slots. In this game, the person who goes first gets his own coin back if he wins and loses it if the second player wins. So the first player never wins anything! On average he will win half the games and lose half the games, so in an average game, he should expect to lose half a coin, while Player 2 should expect to win half a coin.

In fact, no matter how many coins and slots there are (so long as it’s an even number), Player 1 always loses an average of half a coin per game, and Player 2 always wins an average of half a coin per game. Extra coins and slots simply mean that each game lasts longer, and Player 2 has to put up a higher stake, to win that half a coin.

Extra coins and slots help to hide the fact that Player 2 has an advantage. In a two-slot game, the advantage becomes obvious. In a sixteen-slot game, it’s not obvious at all.

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