# Wheel of fortune

Info
Balance € 300,-
Method

### Statistics

Expected gain: Maximum gain Maximum loss — — Possible: — — Observed: — — Possible: — — Observed: — — — —

### Utility functions

Power utiliy:   Logarithmic utility: 0.000000 0.000000

Multiple turns

## Motivation

Possible profits and losses are not known at the stock market, which makes investment decisions quite difficult. The wheel of fortune is a simple way to generate investment strategies.

## Instructions

At the beginning you have at your disposal, which you can bet on any of these three colors: red, blue and yellow. The probability for each color to be choosen is different as well as their respective profit-multipliers:

 red 1/2 wager x 3 blue 1/3 wager x 2 yellow 1/6 wager x 6

The stakes are lost every time; with a little luck, however, you might win more than you have wagered!

You control your bets (either a percentage of your balance or a fixed amount thereof) with the "+" and "–" bottons or simply via dragging the respective bar. You should not perhaps bet everything at once lest you loose all of it. Try to gain as high a fortune as possible in as little turns as possible!

## Strategies

Here are some suggestions for possible strategies offered:
• Does it make sense to bet EVERYTHING on yellow? Mind the fact that you can gain 600% of the seeded money.
• Think of the probability of each color. Would it make sense to bid everything on red, because it's most likely to win?
• How much risk can you take? Higher stakes may get you higher profit.
• Assumed that you MUST bet all your money: How do you bid if you want to make sure to lose no money?
• Smart investors split their money on several colors. What percentage of money will you back on which color?
• Does it make sense to place on blue? Red has a higher probability and does also offer more profit.
• Think on a long-term basis. A slow growth of wealth may be better than a fast one, as long as it is safer.
• Do you think there is a perfect strategy?

## Literature

• David G. Luenberger: Investment Science, Oxford University Press (1998), ISBN 0-19-510809-4, Chapter 15 (Optimal Portfolio Growth).