Why are craps house percentages expressed deceptively - even by the Wizard???

A $5 place bet on the 4 or 10 pays $9 instead of the true odds payout of $10. The casino is keeping 10%, by common sense arithmetic!! By what sort of logic does the 6.66% ($9 payout + $5 bet = $14 instead of the true odds total of $15) make any sense except to deceive the player by underestimating the house percentage? This really irritates me. You didn't win $l4, you won only $9, and the casino kept a dollar. Sheesh!

Quote: riverbed

A $5 place bet on the 4 or 10 pays $9 instead of the true odds payout of $10. The casino is keeping 10%, by common sense arithmetic!! By what sort of logic does the 6.66% ($9 payout + $5 bet = $14 instead of the true odds total of $15) make any sense except to deceive the player by underestimating the house percentage? This really irritates me. You didn't win $l4, you won only $9, and the casino kept a dollar. Sheesh!

(1/3)*9 + (2/3)*(-5) = -1/3
(-1/3)/5 = -1/15 = -6.67%

6.67% looks right to me.

Expectation (house edge) has two components -- value and probability. You're only focusing on the first.

The casino keeps the $1 as their edge, and while that's 10% of what you should have won in a fair game, it's also 20% of what you bet. But that only happens when you win, which is 1/3 of the time -- the other 2/3 of the time you lose all of your bet.

20% of 1/3 is 6.67%.

JC -

I wouldn't question anyone's math, particularly if it agrees with the number the Wizard has posted, but could you re-do that formula and explain each of those calculations?



Edit:
MathExtremist provided a good explanation. Thanks.

Thank you. This concept (house edge) is clear to me now.

Quote: DJTeddyBear

JC -

I wouldn't question anyone's math, particularly if it agrees with the number the Wizard has posted, but could you re-do that formula and explain each of those calculations?



Edit:
MathExtremist provided a good explanation. Thanks.

Yeah I just quickly threw the numbers up there. It's not much help if you don't understand what they represent. ME explained it well.

Quote: MathExtremist

Expectation (house edge) has two components -- value and probability. You're only focusing on the first.

The casino keeps the $1 as their edge, and while that's 10% of what you should have won in a fair game, it's also 20% of what you bet. But that only happens when you win, which is 1/3 of the time -- the other 2/3 of the time you lose all of your bet.

20% of 1/3 is 6.67%.

Very nice.
Of course, this assumes that one knows the winning probabilities. If not...

Here is another method...
(In school, my math professor gave this formula, and later I found it this was first shown by John Scarne :) another handsome man like ME.
It only works if you know the house payoff and the true odds payoff.

So for the pass line in Craps I doubt that most know the true odds payout for the pass line bet. (If I recall it would be (1-p) / p) But this can get messy.

(true payoff - house payoff) / (Bet + true payoff)

where (true payoff - house payoff) = D (difference)

So... D / (Bet + true payoff)


$5 place 4
house pays $9
True odds pays = $10
10-9 = 1 = D

So,
1/(5+10) = 1/15 = ~6.67%

Another example $6 place 6. (I made this bet yesterday and won! Yahoo!)
$6 place 6
house pays $7
True odds pays = $7.2
7.2 - 7 = 0.2 = D
D / (Bet + true payoff)
So,
0.2/(6+7.2) = 0.2/13.2 = 1/66 = ~1.5152