Finding the most profitable option 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)

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).