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 Ł100. 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 Ł1, 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 Ł63 out of his Ł100. You will have won about Ł37.

EXAMPLE GAME


Customer starts with Ł100 so he bets Ł50 CARD 1 = BLACK Customer wins! Total money = Ł100 + Ł50 = Ł150	Customer has Ł150 so he bets Ł75 CARD 2 = RED Customer loses! Total money = Ł150 - Ł75 =Ł75	Customer has Ł75 so he bets Ł37 CARD 3 = BLACK Customer wins! Total money = Ł75 + Ł37 = Ł112	Customer has Ł112 so he bets Ł56 CARD 4 = RED Customer loses! Total money = Ł112 - Ł56 = Ł56	Customer has Ł56 so he bets Ł28 CARD 5 = BLACK Customer wins! Total money = Ł56 + Ł28 = Ł84	Customer has Ł84 so he bets Ł42 CARD 6 = BLACK Customer wins! Total money = Ł84 + Ł42 = Ł126	Customer has Ł126 so he bets Ł63 CARD 7 = RED Customer loses! Total money = Ł126 - Ł63 = Ł63

The customer will always lose, regardless of what order the seven cards appear!

HOW DOES IT WORK?

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 Ł100 back, he was already down to Ł75. If the two cards had appeared the other way round he would have first lost (Ł100 - Ł50 = Ł50) and then won (Ł50 + Ł25 = Ł75) and still have finished with Ł75.

A BLACK card has the effect of multiplying the current total of money held by 3/2.

A RED card has the effect of multiplying the current total of money by 1/2.

The game offers four BLACKS and three REDS, so the final fraction of money left will be (3/2)⁴ x (1/2)³ = 81/128 = about 63%. So if the player starts with Ł100, he will only finish with about Ł63 regardless of what order the cards are picked.

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

This trick and many others appear in Brainbenders

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