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Right now, I have 1€. And I know exactly how to invest that euro to make profit, but I have 3 options:

  1. Invest the euro, and win exactly 1€ (I'd have 2€ then)
  2. Invest the euro, and earn some money between 0,5€ or 1,5€ (I'd have an amount between 1,5€ or 2,5€)
  3. Invest the euro, and win either nothing or 2€ (I'd have an amount between 0€ or 4€)

After investing that euro one time, I would be investing one euro again and again.

So, what's the best option of these 3 to earn some money?

Are they proportionally equal, and happens the same with all the different values?

If that's true the winnings would be just the average of both min and max values.

(Not real try to earn money)

Garmen1778
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  • If you only have 1€, gambling might not be the best strategy. – vadim123 Apr 24 '13 at 23:09
  • As I said, I'll be investing that euro again again, infitely many times. – Garmen1778 Apr 24 '13 at 23:10
  • Do you know what expected value, and variance is? – Calvin Lin Apr 24 '13 at 23:10
  • What is the probability distribution on options 2 and 3? I'd imagine if you had a 99.9999999% chance of the higher option that may skew things a bit though you don't state what the odds are of each result in the case of the last 2 options. – JB King Apr 24 '13 at 23:11
  • @JBKing Are the odds necessary? Things can't mach up being random odds? – Garmen1778 Apr 24 '13 at 23:15
  • The odds would help give more confidence as to which option to take. If the odds are 999999999:1 for the lowest outcome then I'd say the first becomes the best while if the odds are reversed then it becomes likely that the 3rd option becomes the best. Random odds would presume something either an even distribution or low confidence in the result I'd think. – JB King Apr 24 '13 at 23:27
  • Presumably in option 3 it is each result with probability $\frac 12$ and if you win, you win 3 to get a total of 4. – Ross Millikan Apr 24 '13 at 23:55

1 Answers1

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If losing the euro doesn't stop you from participating in the future, after a long series of bets you will (on average) be the same place in all three options. The expected value of each is +1 euro. After a large number of plays you will converge on a normal distribution with mean the number of plays and some variance. Option 1 gives you no variance, option 2 some and option 3 even more. Many people prefer the sure thing, except they irrationally favor low chance high payout events (see the lottery).

Ross Millikan
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