How To Calculate Average Outcome

By Gjosefsberg @gjosefsberg

I love gamblers, they make me look smart

Earlier this week I talked about running the numbers and I mentioned that you should run multiple scenarios and then average them together to see the average outcome.  A reader sent in a question asking how to do that.  So here’s a real quick lesson on calculating expected outcomes.

1. Come up with all the possible outcomes.
2. Assign odds to each
3. Multiply likely outcome by odds
4. Add together to get predicated outcome

Let’s run through an example.

You’re a gambling man.  A friend offers you a bet.  You will pay him a dollar.  In return, he will roll a dice.

• If the die shows a 1, 2 or 3, you lose your money
• If the die shows a 4 or 5, you win 1 dollar
• If the die shows a 6, you win 2 dollars

Is this a worthwhile bet?  Mmm… it sounds good.  50% chance of losing but 50% chance of winning and one of those possible prizes is worth more than the money I put in….  Hey, numbskull!  RUN THE NUMBERS!

Come Up With All Possible Outcomes

Possible outcomes are:

• \$0
• \$1
• \$2

Assign odds to each

• 3 in 6 (.5) odds that you will make \$0.  This is if the die shows a 1, 2 or 3
• 2 in 6 (.33) odds that you will make \$1.  This is if the die shows a 4 or 5
• 1 in 6 (.17) odds that you will make \$2.  This is if the die shows a 6.

Multiply Likely Outcomes By Odds

• .5 * \$0 = \$0
• .33 * \$1 = \$.33
• .17 * \$2 = \$.34

Add Together To Get Average Outcome

\$0 + \$.33 + \$.34 = \$.67

In other words, for every dollar you put in, you’re likely to get \$.67 back.  Doesn’t sound like a very good bet now, does it?

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Now if I can do this for a \$1 bet, why oh why didn’t I do this for a \$160,000 education?!?!?  But that’s a whole other story.