winning on a single number playing US roulette

The chances of wins are:

For 100 players, over 100 spins, each with probability 1 in 38, on average there will be 263.2 wins.

Over 100 spins, on average there will be 2.6 wins for each of the players.

Probability

  • 0.026316
  • As a percentage

  • 2.6316%
  • As a rounded-off proportion

  • 1 in 38
  • As approximate fair betting odds

  • 37 : 1
  • Representative example

    For wins

  • 100 players x 100 spins = 10000 chances for wins
  • Observed wins: 267 = 2.670% (expected average: 263.2 = 2.632%)
  • For players (columns)
  • Summary for players: {'min': 0, 'max': 8, 'mean': 2.67, 'median': 2}
  • Counts: How many wins for each of the players? [Click to show]
  • [3, 0, 5, 5, 1, 2, 3, 2, 2, 3, 0, 4, 2, 4, 1, 3, 7, 2, 2, 2, 1, 2, 1, 1, 3, 3, 4, 2, 4, 3, 1, 2, 2, 1, 6, 2, 3, 1, 1, 8, 0, 4, 2, 6, 2, 2, 4, 3, 2, 4, 2, 2, 3, 4, 2, 3, 1, 2, 3, 4, 5, 4, 2, 1, 4, 2, 3, 1, 1, 2, 4, 2, 2, 6, 1, 4, 1, 3, 3, 4, 5, 1, 5, 1, 0, 5, 1, 1, 6, 2, 2, 6, 1, 5, 1, 2, 4, 2, 1, 2]
  • Distribution: How many players for each different number of wins? [Click to show]
  • 4 with 0 wins; 22 with 1 wins; 30 with 2 wins; 15 with 3 wins; 15 with 4 wins; 7 with 5 wins; 5 with 6 wins; 1 with 7 wins; 1 with 8 wins;
    For spins (rows)
  • Summary for spins: {'min': 0, 'max': 8, 'mean': 2.67, 'median': 2}
  • Counts: How many wins for each of the spins? [Click to show]
  • [4, 2, 3, 2, 1, 1, 2, 4, 7, 3, 2, 2, 3, 2, 2, 4, 1, 2, 5, 2, 4, 3, 2, 5, 3, 0, 0, 7, 1, 0, 5, 1, 5, 6, 1, 2, 3, 6, 6, 0, 2, 1, 3, 0, 2, 8, 2, 3, 4, 3, 1, 2, 3, 2, 2, 1, 1, 5, 3, 3, 2, 1, 2, 3, 3, 3, 2, 4, 5, 2, 1, 3, 4, 6, 3, 8, 0, 2, 2, 0, 1, 1, 3, 0, 5, 3, 5, 1, 2, 3, 2, 1, 1, 1, 3, 2, 3, 4, 1, 4]
  • Distribution: How many spins for each different number of wins? [Click to show]
  • 8 with 0 wins; 19 with 1 wins; 26 with 2 wins; 22 with 3 wins; 9 with 4 wins; 8 with 5 wins; 4 with 6 wins; 2 with 7 wins; 2 with 8 wins;

    What are the Chances of That? - The Book

    Five reasons that we find it hard to think about uncertainty. To be published by Oxford University Press in 2021.

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