# Math Help - Expected value and decimal odds

1. ## 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

2. Hello, Mike!

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?