Thread: 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

Hello, Mike!

If I understand your question, there is no unique answer.

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?