Lil's Dead Giveaway Trick!

This is one of the many tricks that Riverboat Lil plays in the Last Chance Saloon to win money. It looks like a game that the customer cannot lose, but they always do!

• You need seven playing cards: four BLACK and three RED. You shuffle them up and put them face down on the table.
• The customer starts with £100. Everytime he plays he must bet half his money.
• The customer turns over the first card.
  If the card is BLACK he wins his bet.
  If the card is RED he loses his bet.
• Keep going. All seven cards must be played and the customer must bet half his money each time. ( Numbers can be rounded up or down to the nearest £1, it doesn't affect the trick much.)
• Obviously the customer will win four times and only lose three times. Therefore it looks like he should end up winning!
• After the 7th card is played, the customer will be left with about £63 out of his £100. You will have won about £37.

EXAMPLE GAME

Customer starts with £100 so he bets £50 CARD 1 = BLACK Customer wins! Total money = £100 + £50 = £150	Customer has £150 so he bets £75 CARD 2 = RED Customer loses! Total money = £150 - £75 =£75	Customer has £75 so he bets £37 CARD 3 = BLACK Customer wins! Total money = £75 + £37 = £112	Customer has £112 so he bets £56 CARD 4 = RED Customer loses! Total money = £112 - £56 = £56	Customer has £56 so he bets £28 CARD 5 = BLACK Customer wins! Total money = £56 + £28 = £84	Customer has £84 so he bets £42 CARD 6 = BLACK Customer wins! Total money = £84 + £42 = £126	Customer has £126 so he bets £63 CARD 7 = RED Customer loses! Total money = £126 - £63 = £63

The customer will always lose, regardless of what order the seven cards appear. The reason becomes clearer if you look at what happened in the example after the first two cards. The customer won one and lost one, but instead of ending with his £100 back, he was already down to £75. If the two cards had appeared the other way round he would have first lost (£100 - £50 = £50) and then won (£50 + £25 = £75) and still have finished with £75.

If you like this then try The Red and Black Mystery!

This trick and many others appear in Brainbenders

Links:

Teacher Resources

The Murderous Maths Home Page

Copyright (c) Kjartan Poskitt 2002