Roulette "system" math question.

Okay.
No Humor.
No Attempts at Humor.
I'm being 100 percent serious now.

This is the quotation:

"...One of these rebates was negotiated by a wealthy sheik who wanted half of his loss returned (a 50% discount on losses!), provided he would bet $10,000 per spin at roulette. Griffin shows that with a rebate of this magnitude, even at a terrible game like double-0 roulette (5.26% house edge), the sheik would clean their clocks to the tune of about $87,000 per trip, if he always played for exactly 234 spins, and also always bet the numbers (35:1 payout), rather than the even money bets (red/black, odd/even, etc.)."


IF 10,000 dollars per spin for exactly 234 spins will "clean their clocks" with a 50 percent discount on losses; why won't it also clean their clocks at 10.00 a spin for exactly 234 spins if we go to a wheel that is a European wheel and therefore at 50 percent less House Edge compared to the usual American wheel.

Because the house edge is the difference between wins and losses. This guy's losses are being halved, but his wins kept the same, so he makes money; the difference between single- and double-zero roulette (betting a single number) is only about a 0.07% decrease in losses and a 2.7% increase in wins.

(Yes, I know I'm comparing apples to oranges, since some "wins" by the latter definition are counted as losses, and some losses as wins, but it's a quick explanation.)

Quote: FleaStiff

IF 10,000 dollars per spin for exactly 234 spins will "clean their clocks" with a 50 percent discount on losses; why won't it also clean their clocks at 10.00 a spin for exactly 234 spins if we go to a wheel that is a European wheel and therefore at 50 percent less House Edge compared to the usual American wheel.

The player keeps all of his money in the event of wins, and he gets half of his money back in the event of a loss. The European Wheel, compared to the American Wheel, simply reduces the House Edge (i.e. the House's theoretical win) by roughly 50%. For example, if the casino in question ran this Double-00 Roulette promotion, but only offered to give back 50% of the player's theoretical loss (whether the player actually wins or loses), they would be at a long-term advantage of exactly 50% of the House Edge.


In this case, the player gets actual money back on his actual losses and keeps all of his wins. In this case, even with normal Variance (from session to session) the advantage to the player is huge.

There are a few recent posts from our very own Teliot at his blog, www.apheat.net addressing the very issue of Roulette loss Rebates. For all practical purposes, such rebates are useless at 20% (or lower) of the loss for Double-Zero Roulette, but I'm sure 50% would be a whole new ballgame.

So a fifty percent reduction in House Edge does not equal a fifty percent reduction in Player Losses?

Quote: FleaStiff

So a fifty percent reduction in House Edge does not equal a fifty percent reduction in Player Losses?

Exactly. House edge is dominated by the long run expectation value, while player losses are dominated by the short run variance (which can be huge compared to the expectation value, especially for the number bets).

Quote: FleaStiff

So a fifty percent reduction in House Edge does not equal a fifty percent reduction in Player Losses?

Right.

Here's the simplest way for me to put it, without getting as in depth as Teliot, as he does with his incredible simulations. I'm just going to go with one player, who does one spin, and rolls out.

This is what happens when you play Double-Zero with no rebate and bet $10,000 on a single number:

350000 * 1/38 = 9210.526315789473

-10000 * 37/38 = -9736.842105263158

Expected Value: -526.3157894736851 or -5.263157894736851% HE

This is what happens when you play Single-Zero with no rebate and bet $10,000 on a single number:

350000 * 1/37 = 9459.45945945946

-10000 * 36/37 = -9729.72972972973

Expected Value: -270.27027027027 or 2.7027027027027 HE

This is what happens when you play one spin of Double-00 with a 50% Rebate if you lose:

350000 * 1/38 = 9210.526315789473

See, but if your plan is to play one spin and stop, you can only lose $5,000.

-5000 * 37/38 = 4868.421052631579

Expected Value: 9210.526315789473 - 4868.421052631579 = 4342.105263157894 or 43.42105263157894% PE

But, if you only return a portion of the theoretical loss, then the House Edge will simply be reduced by the percentage of the theoretical loss you are returning. Let's briefly look at that in our Double-00 scenario and say you give back 50% of the theoretical loss:

526.3157894736851 * .5 = 263.15789473684253

Okay, so we know we are returning 263.15789473684253 in theoretical loss Rebate, win or lose:

(350000 + 263.15789473684253) * 1/38 = 9217.451523545705

(-10000 + 263.15789473684253) * 37/38 = -9480.609418282547

Expected Value: -9480.609418282547 + 9217.451523545705 = -263.1578947368416 or effective 2.631578947368416% HE

So, actual loss Rebates can kick a casinos ass, but always giving a percentage of the theoretical loss merely lowers the effective House Edge, unless the House gives more than 100% of the Theo, of course.

Quote: 24Bingo

Because the house edge is the difference between wins and losses. This guy's losses are being halved, but his wins kept the same, so he makes money; the difference between single- and double-zero roulette (betting a single number) is only about a 0.07% decrease in losses and a 2.7% increase in wins.
(Yes, I know I'm comparing apples to oranges, since some "wins" by the latter definition are counted as losses, and some losses as wins, but it's a quick explanation.)

Apples, Oranges, Greek .... its all math to me!

I don't see why everyone makes such a big deal about seeking out a Single Zero Wheel if its a lousy 0.07 percent decrease. That is not even worth the shoe leather much less the cab fare to get to a different casino! And women often like to stay in the same casino so it becomes not just a gambling matter but a domestic relations argument.


HOW did you derive this:
......... the difference between single zero and double zero roulette (betting on a single number) is only about a 0.07 percent decreases in loses and a 2.72 percent increase in wins.