2006-12-18 05:25:34 · 4 answers · asked by Shamia B 1 in Science & Mathematics ➔ Mathematics
The expected return should equal what you pay in.
So for a $1 bet, the expected value should be $1, for a fair game.
For example, if you bet me $1 and I promise to pay you $2 if it lands heads and nothing if it lands tails, then the expected return is:
1/2 x $2 + 1/2 x $0 = $1
So that would be a fair game.
On the other hand, if I say that I'll pay you $5 if a die lands on a certain number, then the expected return is:
1/6 x $5 + 5/6 x $0 = $0.83.
So you expect a return of 83 cents on your $1 bet... this is not a fair game.
Note: all the games in Vegas are unfair and favor the house. The expected return on $1 is always less than $1. Some games are better or worse in terms of the expected return. Black Jack (21) is supposedly the best game for getting close to even returns, at least for you as an individual. In the long run even that favors the house for the table as a group.
2006-12-18 05:28:24 · answer #1 · answered by Puzzling 7 · 2⤊ 0⤋
Zero.
This can be taken as a definition of 'fair' for what's known as a ' zero sum' game.
A zero sum game means that whatever is won is also lost by someone else. All gambling is zero sum. This doesn't mean that they are fair, of course.
Another way to think of 'fair' in the game context is that if a payoff is 'true mathematical odds' then it's fair.
The worst single roll play on the Craps table is 'any 7'. It pays 4 to 1 but the probability of getting a 7 in a single roll is 1/6. So, if you only made that play :
E = 4(1/6) - 5/6 = -1/6 = 16.67% ! Terrible!
2006-12-18 05:54:57 · answer #2 · answered by modulo_function 7 · 1⤊ 0⤋
The expected value is breaking even, or "zero". Thus, if the game involves two outcomes, and one is a 1/3 chance of my opponent winning $24, then the other, with a 2/3 chance of happening, should result in my winning $12 for the same price, because 1/3 of $24 and 2/3 of $12 equal the same thing: $8.
I admit I could've explained this better....
2006-12-18 05:35:37 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Fair is when all (more than one ) players pay the same sum and all will receive their sum back. The expected value is thus 0.
2006-12-18 06:22:09 · answer #4 · answered by gjmb1960 7 · 1⤊ 0⤋
Equal for all players. Most games are zero-sum in which case it's zero.
That is, with the cost of playing included in the outcome variable.
2006-12-18 05:28:25 · answer #5 · answered by Anonymous · 2⤊ 0⤋