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.
- Come up with all the possible outcomes.
- Assign odds to each
- Multiply likely outcome by odds
- 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.