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Gambling at Monte Carlo

A man went to Monte Carlo to try and make his fortune. Is his strategy a winning one?

Marbles and Bags

Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags. The marble is blue. What is the probability that it was removed from bag A?

Coin Tossing Games

You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by a head (you win). What is the probability that you win?

The Better Choice

Age 14 to 16 Challenge Level:

Here are two games you can play. If you played both games the same number of times, in which game would you expect to win more points?

Game 1:

In every round you flip four coins and win 3 points if you get two heads and two tails 

or

Game 2:

In every round you spin three 1 - 6 spinners and win 2 points for every six that appears

 

The interactivity below allows you to simulate both games (including versions in which it 'costs' a point to play each round).

Can you explain the result of playing each game a large number of times?