Royal Institute Christmas Lectures 2006
The Secret of the Winning Streak
Rock, Scissors, Paper
This lecture begins with a number of the young attendees playing the school playground game of Rock, Scissors, Paper a game of chance. Professor du Sautoy finds a winner and declares him the Christmas Champion. Later in the lecture he will meet the World Champion and armed with a little mathematical strategy he will hope to take the World Championship.
Lottery
In this lecture he will reveal some of the mathematical secrets in the games we play. Starting with the National Lottery (Lotto). A young lady from the audience assisted the Professor by making the draw, and the results are shown below:
The Draw Results
There were approximately 400 people in the audience and the results were roughly as follows:
- Match none: 200
- Match 1: 110
- Match 2: 88
- Match 3: 2
- Match 4+: 0
This surprised the professor as, statistically, he anticipated that six or seven would have matched three of the drawn numbers as the odds for this are 1 in 57. Of course the odds of matching all six are 1 in approximately 14,000,000.
Marcus offers no mathematical strategy for picking the winning numbers, but does suggest a possible strategy for maximising your winnings should you be fortunate enough to win. Humans are not good at picking random numbers and tend to pick a pattern of numbers on the play slip. Others are likely to do the same so any jackpot would be shared. He suggests grouping numbers together to minimise this risk.
Rock, Scissors, Paper (Revisited)
Will, the Christmas champion is invited back on stage. Professor du Sautoy outlines his strategy for beating Bob "The Rock" Cooper, the reigning World Champion. Bob is very good at seeing patterns in his opponent and as mentioned earlier, humans are not good at making entirely random choices. The strategy is to have a pack of pre-printed cards with Will's possible movements printed on them. The cards are shuffled making them as random as possible. The professor will show each card in turn to give Will every chance. The experiment fails dismally with Bob "The Rock" winning in straight hands. Professor du Sautoy offers no explanation of the failure other than to say Bob's strategy was better.
Will "The Scissors" challenges Bob "The Rock"
Monopoly
As with all games of chance, statistical probability will play a part. Firstly consider which square on the Monopoly board is the most visited square. It the "Jail" square as there are so many routes to get there: Landing on the "Go to Jail" square, picking a "Community Chest" or "Chance" card, and throwing three doubles. The most common number to be thrown with two dice is seven, closely followed by six and eight. This makes the "Marlborough Street" and "Vine Street" properties the ones to have.
