# Expected value and decimal odds

• Apr 25th 2011, 03:49 AM
mas89
Expected value and decimal odds
Hi guys

In a game of chance where the player knows the expected value (say -0.37), how do you work out what the decimal odds should be in order to break even in long run?

(Decimal odds 2.0 = 1/1)

Any help much appreciated :)

Mike
• Apr 25th 2011, 05:17 AM
Soroban
Hello, Mike!

Quote:

In a game of chance where the player knows the expected value (say -0.37),
how do you work out what the odds should be in order to break even in long run?

Without knowing the rules of the game,
. . the expected value is insufficient information.

Game 1

You flip a coin.
. . If you get Heads, you win \$0.63
. . If you get Tails, you lose \$1.00
The expected value is -\$0.37.

I'm not sure how to "work out the odds"
. . since the nature of a coin flip cannot be changed.
We can, however, change the payoffs (and bet "even money").

Game 2

You roll a die.
. . If you get a "1", you win \$0.78.
. . Otherwise, you lose \$0.60.
The expected value is -\$0.37.

Game 3

You randomly select a card from a full deck.
. . If it is an Ace, you win \$1.19.
. . Otherwise, you lose \$0.50.
The expected value is -\$0.37.

Get it?