## Friday, 20 November 2009

### Using Decision trees to see how probability and impact relate to each other

We can use the simple example of a dice game.  In this game, you bet \$1 on the throw of a dice.  Throwing a six wins a prize; throwing any other number means you lose your \$1.

In version A of this game:

A bet costs \$1, but you can win \$10

Faced with this game, you have two alternatives - to play or not to play.

Once playing, there is nothing you can do to affect the outcome - so your decision on whether to play has to be made on the basis of the probabilities and impacts involved.

Because the situation is simple, the probabilities of the various possible outcomes can be objectively known.  There is no subjectivity over the probabilities.  The impacts, too, are fixed and clearly set out by the rules of the game (the prizes and the cost of playing).

If a choice is made to play, the probability of winning is 1 in 6 (0.166 or 16.66%) and the probability of losing 5 in 6 (0.834 or 83.4%).

If a choice is made not to play, risk is avoided (there is a single outcome that is certain) but there is also no potential benefit.

Decision tree for dice game version A:

Decision:  Play dice game with chance of winning \$10?  Yes or No

NO
Decision ---->  Risky Event  ---> Possible outcomes ---->   Probability ----->  Impact

No   ----->  Nil ------>  Avoid risk, keep money in pocket ----> 1.0 (certain) ----->  Neurtral: spend ntohing, win nothing

YES
Decision ----> Risky Event ---> Possible outcomes ----> Probability -----> Impact

Yes ----->  Stake \$1 on throw of dice ----> Number 6  ----> 0.166 (1 in 6) ----> Gain Spend \$1 Win \$10
or
Yes -----> Stake \$1 on throw of dice -----> Number 1, 2, 3, 4, or 5  -----> 0.834 (5 in 6) ---->  Loss Spend \$1 Win nothing