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You have 25 numbers on a wheel.

  • 12 are number 1 : Doubles your bet. (x2)
  • 6 are number 3 : Triples your bet. (x3)
  • 4 are number 5 : Quintuples your bet. (x5)
  • 2 are number 10 : Decuples your bet. (x10)
  • 1 is number 20 : (x20) what is the name for x20?

You can bet on multiple numbers at a time and the amount you want.

For example : You could bet 5 on 1, 5 on 3, 10 on 5, 0 on 10 and 6 on 20.

How can you maximise the amount of money you make ? Or minimise the amount you lose?

Thanks !

EDIT : One number only will win.

EDIT2 : I am aware of the martingale betting strategy, where I could put an amount of money on a number and double everytime I lose until I win, but I'm looking for a better strategy.

EDIT 3 : Ok so the answer I received made me realise some things, which I tried.

Lets say I bet like this :

- 200 on 1 : (Win) 400, (Lose) -200, (Total Cost) 400, (Balance on win) : 0.
- 80 on 3 : (Win) 240, (Lose) -80, (Total Cost) 400, (Balance on win) : 240.
- 60 on 5 : (Win) 300, (Lose) -60, (Total Cost) 400, (Balance on win) : 300.
- 40 on 10 : (Win) 400, (Lose) 40, (Total Cost) 400, (Balance on win) : 400.
- 20 on 20 : (Win) 400, (Lose) 20, (Total Cost) 400, (Balance on win) : 400.

If this is correct, I would never lose. But is this correct? If it is, is there a way to maximise this?

Sudoky
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  • Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments. – José Carlos Santos Aug 13 '18 at 14:17
  • I assume "doubles your bet" means that if you start with $1, put it on number 1, and win, then you now have $2? Or do you now have $3? –  Aug 13 '18 at 14:22
  • Yes, if you bet 1 on 1, then you have 2. – Sudoky Aug 13 '18 at 14:24
  • So if you bet $1$ on $3$ and win, do you get $2+1=3$ back or $3+1=4$ back? – Henry Aug 13 '18 at 14:58
  • Sorry, this seems to be unclear. If you bet 1 on 3, you collect 3 only. So you end up winning 2. – Sudoky Aug 13 '18 at 14:59
  • @Sudoky: It's not your fault; it's an unfortunate reality that there are two different conventions for discussing payouts, and I think people don't even realize that. It all boils down to whether people conceive of a bet as "you always pay your bet, but you might win more than you paid" or "the house only takes your bet when you lose". I was sure you meant what you did, but I had to ask because of the similarity to roulette, which traditionally has its payout described the other way. (i.e. a color bet "pays 1 to 1" meaning you double your money when you win) –  Aug 13 '18 at 21:51
  • (P.S. I think the convention you used to described payouts is the "right" way to do so, at least for mathematical discussion) –  Aug 13 '18 at 21:53

1 Answers1

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Compute the expected value of betting $1$ on each number. If you bet on $1$ you have $\frac {12}{25}$ chance of getting $2$, for an expected return of $2\cdot \frac {12}{25}=\frac {24}{25} \lt 1$. Similarly for each of the other numbers, the expected return is $\frac {18}{25}$ or $\frac {20}{25}$. It is a losing bet, so the way to minimize your losses is not to play.

In your system, you bet $400$. That should be the cost you deduct from the winnings for any number. You break even if $1,10$ or $20$ come up and lose if $3$ or $5$ comes up. Your nets should be $0,-160,-100,0,0$. You can never win this way and may lose.

Ross Millikan
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