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Infinite Money, One Dollar at a Time (Weekly Brain Potion Discussion)

 
 
Picture of John Lensmire
Infinite Money, One Dollar at a Time (Weekly Brain Potion Discussion)
by John Lensmire - Friday, 1 December 2017, 11:20 AM
 

A common game of chance is called Roulette. A ball is rolled around a circular disk (called the wheel) containing some numbers. Players can bet on where the ball comes to a rest, such as one a red spot or on a specific number. A simplified Roulette wheel is shown below.

SampleRouletteWheel

For this discussion we'll focus on betting that the ball will stop on red. The following bet is made:

  • You can bet $N$ dollars that the ball will land on red.
  • If you are correct you win $2N$ dollars (you double your money), but if you are incorrect you win $\$0$ (you lose the money you bet).

After explaining the game to your friend Peter, he devises the following strategy, which he claims will allow you to always win $\$1$!

  • First bet $\$1$ on red. If you win you have won $\$1$ (remember you spent $\$1$ on the bet).
  • If you lose bet $\$2$ on red.
  • If you lose again bet $\$4$ on red.
  • If you lose again bet $\$8$ on red.
  • Etc. Continuing to bet until the ball lands on red.

Explain how Peter's strategy works in theory. On the other hand, explain how Peter's strategy does not work in practice (in the real world). If it did, we would all be at casinos playing Roulette right now!

Please share any thoughts or questions you have below. We'll monitor the responses and give our thoughts as well!

 
Picture of Christopher wu
Re: Infinite Money, One Dollar at a Time (Weekly Brain Potion Discussion)
by Christopher wu - Friday, 1 December 2017, 6:48 PM
 

This works in theory as every time you win you gain 1 dollar. You cannot lose forever, you have to win eventually

However, in real life it is impractical as if you lost a bunch in a row which will happen eventually you won’t have enough money to keep betting. You could end up losing all of your money.

A Zeraora
Re: Infinite Money, One Dollar at a Time (Weekly Brain Potion Discussion)
by David Tang - Sunday, 7 January 2018, 8:10 PM
 

I agree, Christopher

Picture of Dan Li
Re: Infinite Money, One Dollar at a Time (Weekly Brain Potion Discussion)
by Dan Li - Saturday, 13 January 2018, 7:03 PM
 
And yet, believe it or not, this was a "strategy" in real life.
Picture of Alan Cheng
Re: Infinite Money, One Dollar at a Time (Weekly Brain Potion Discussion)
by Alan Cheng - Monday, 29 October 2018, 6:23 PM
 

True, in real life you would eventually become broke.illuminati