How to get 1.35% HE on La Partage?

I know the House Edge for a single zero roulette table is 1.35% on the even money bets. But I don't know the math formula to get that number. My understanding of house edge is... Expected Value(EV) - Loss Possibility(LP) = House Edge. But when I put the rate of return as -.5 in the LP part, it doesn't add up. What am I missing? Where does the -.5 fit in the equation? I know if you just divide the house edge in half you get 1.35. But to say that without the mathematical proof is purely suggestive and coincidental. The wizard has suggested that with La Partage, the LP changes from .5135 to .5000(with no explanation as to why). I can't see how that should change at all because you are still losing, just not as much. And, your chances of losing something are still .5135. If I could see a long form formula I could sleep better at night. Thnx.

Check out the Wiz' Roulette page.

Go about 1/2 way down to the section on European Rules.

That doesnt help since it only shows the end result. I need to see the formula on how he got those numbers. Also, those are for imprison. there is no push in la partage, only losing half. How do you figure out the push faactor?

Quote: ikusa

I know the House Edge for a single zero roulette table is 1.35% on the even money bets. But I don't know the math formula to get that number. ... If I could see a long form formula I could sleep better at night. Thnx.

EV is sum of (p(outcome) * v(outcome)) over all outcomes, where p is probability and v is value. For Euro roulette with partage, there are three outcomes: win, lose, and lose half. The probabilities for each are 18/37, 18/37, and 1/37. The values are +1, -1, and -0.5. The sum of the products is +1*18/37 + -1*18/38 + -0.5*1/37 = -0.5/37 = -0.0135135...
Sleep well. :)

Thank you, thank you, thank you. I never would have figured how the -.5 came into play. my night terrors are now gone. zzzzzzzzzzzzz