Does Roulette have the best edge on a 35:1 bet?
We can simulate a many:1 payout on a 1:1 game by doubling the bet size if we win, until we reach our goal. (Yes, this is a betting system, don't kill me just yet - the goal is not to beat the house, but simply to modify the payout schedule.)
So for example, suppose we're playing EZ Baccarat, betting on the banker, which is a 1:1 bet with a 1.02% house edge. We bet one unit, and we double the bet size while we're winning, until we have 32. We can treat this operation as a single bet with a 1:31 payout, roughly approximating Roulette. By my calculations, the house edge on the composite bet is 5% - almost as bad as American Roulette, and much worse than European.
So if your idea of fun is 35:1 (or thereabouts) payouts, as opposed to 1:1, is European Roulette your best bet? Is there a way to get a similar payout schedule with a lower house edge?
Quote: lamentThe edge on Roulette is pretty bad if compared to, for example, Baccarat. But Baccarat is a roughly 1:1 game. The inside bets on Roulette are 35:1, and it's understandable that casinos would charge extra for increased variance.
We can simulate a many:1 payout on a 1:1 game by doubling the bet size if we win, until we reach our goal. (Yes, this is a betting system, don't kill me just yet - the goal is not to beat the house, but simply to modify the payout schedule.)
So for example, suppose we're playing EZ Baccarat, betting on the banker, which is a 1:1 bet with a 1.02% house edge. We bet one unit, and we double the bet size while we're winning, until we have 32. We can treat this operation as a single bet with a 1:31 payout, roughly approximating Roulette. By my calculations, the house edge on the composite bet is 5% - almost as bad as American Roulette, and much worse than European.
So if your idea of fun is 35:1 (or thereabouts) payouts, as opposed to 1:1, is European Roulette your best bet? Is there a way to get a similar payout schedule with a lower house edge?
I'm not familiar with EZ Baccarat. If it's a 1:1 bet with a 1.02% house edge, that should mean the probability of winning any give bet is .4949, right, and .5051 probability of losing. If that's the case, it would be easy enough to figure the probability of getting ahead by 32 units, except that you have not provided other necessary information, like how much money can be invested and how long do you keep trying to achieve 32.
For example, there is a formula for determining the probability of achieving a win goal, given a loss limit, in a fair game. It looks like this:
p(WG) = L / (L + W)
IOW, the probability of reaching some win goal is equal to the loss limit divided by the sum of the win goal and loss limit. A case:
I want to win $50, and I'm willing to lose $100.
p($50) = 100 / (100 + 50) = .6667
There are two problems with this:
1. craps is not a "fair" game
2. the formula assumes you either reach the win goal or bust, but this could take a very, very long time
So, I don't think there's enough information to figure the probability of getting ahead 32 units, which is necessary to figure the HA.
You said "by my calculations"; how did you figure it?
Cheers,
Alan Shank
In order to win 31, you need to win 5 times consecutively, and double the bet size each time (i.e. bet your winnings plus the original amount). If you lose at any point in the sequence, you only lose your original wager.
The probability of winning once is 0.4949.
The probability of winning five times in a row is 0.4949^5 = 0.02969.
The expected value of the composite bet is (0.02969 * 31) + ((1-0.02969)*-1) = -0.04991
That is, you lose 5% of the original bet. This is the house edge.
Quote: lamentThe plan is not to achieve the goal or bust. The plan is to create a sequence of bets which, if considered as one bet, either loses 1 unit or wins 31 units. This approximates Roulette, where we either lose 1 unit or win 35 units.
In order to win 31, you need to win 5 times consecutively, and double the bet size each time (i.e. bet your winnings plus the original amount). If you lose at any point in the sequence, you only lose your original wager.
The probability of winning once is 0.4949.
The probability of winning five times in a row is 0.4949^5 = 0.02969.
The expected value of the composite bet is (0.02969 * 31) + ((1-0.02969)*-1) = -0.04991
That is, you lose 5% of the original bet. This is the house edge.
Yes, but that's only for one sequence, which can last from one to five bets. Are you going to just do this once in your life? If you provide a starting bankroll, you can figure what your chances are of coming out ahead after some number of bets, or your chances of winning the 31 before you lose all your bankroll.
Cheers,
Alan Shank
Quote: lamentI don't think you understand my question. I'm only interested in the house edge, which is calculated on a per bet basis. In this case, the five-bet sequence (or less than five, if you lose) is considered as a single bet. My question is not about betting systems.
In that case, I agree with your figure. However, the house edge is only one of the factors that should be considered. This "bet" has a high degree of variance. For each "bet" the standard deviation is 5.43 units. To compare, the bet on the 12 in craps, which pays 30:1, has a 13.9% edge and a standard deviation of 5.09 times the bet.
Cheers,
Alan Shank
Generally, I think if you want to play for high returns, then you should simply play roulette. If you want to play for low returns, then play craps. It's stupid to play roulette if you are playing reds or blacks or odds or evens. The house edge is ridiculous. But it's equally stupid to play boxcars and "yo" or other proposition bets in craps. Even hard-ways should be played in moderation just to add some excitement. If you crave more of the thrill of getting higher jackpots, then switch to the roulette table.
Craps is not about low returns. True that the lowest edge on the center bets is 9.09% for the Hard 6 and 8, but it is a game where at least where you get paid close to true odds on pass and come bets when they hit. It's actually a fairly volatile game as well.
If you want to play for REALLY low returns, try Pai Gow, or Baccarat.
Quote: boymimboRoulette is a fine game when there is only a single zero and the 1/2 return "en Prison" or "Le Partage" rules are in effect - the house edge drops to 1.35%. But American Roulette at 5.26% sucks.
Still, you cannot get a 35:1 payoff in craps at all, and the 30:1 bets have a 13.9% HA, compared to roulette's 5.26. So, I agree that if you want to bet on longshots, roulette is better than craps.
Quote: boymimboCraps is not about low returns. True that the lowest edge on the center bets is 9.09% for the Hard 6 and 8, but it is a game where at least where you get paid close to true odds on pass and come bets when they hit. It's actually a fairly volatile game as well.
In craps, you get high volatility two ways:
1. with high odds multiples
2. with progressive betting
Of course, no matter how much you bet on the odds, the payoff is never more than 2:1, but you can get monster variance, relative to the expected loss. For different odds multiples, here are the standard deviations, relative to the FLAT bet:
odds multiple SD / flat bet
0 .999
1 1.893
2 2.857
3,4,5 4.915
5 5.824
10 10.821
20 20.801
100 100.794
Of course, you can't get that volatility without risking a hell of a lot of money. I guess the attraction of roulette is that you can get that 35:1 with a minimum bet and still pay "just" 5.26%.
Cheers,
Alan Shank
Quote: boymimboCraps is not about low returns.
Well I meant that each play will only return 1:1 7:6 9:5 3:2 2:1 19:10 or in the field bet 3:1. You can get a high return over the course of the afternoon.
But sometimes it is fun to get lucky and be paid 10, 30, 200 or 400 times your original bet. You just don't want to piss away these opportunities at a super high house advantage. Roulette just seems like a good way to try for the single numbers. Compared to slot machines or keno or a lot of side bets, or craps proposition bets 5.26% seems a reasonable price to pay. I see a lot of people play roulette and put over half their money on even money pays, or 2:1 or 3:1 and some long shots. It just seems dumb. Play roulette for the long shots, and play craps for the low house advantage bets.
Quote: pacomartinPlay roulette for the long shots, and play craps for the low house advantage bets.
If I've just been having no luck at craps or PaiGow (whichever I've been playing), I usually try to leave the table with at least one red chip. Then I head over to roulette and drop it on the number 7 or 3, or both if I can. (I was born on July 3rd.) If it hits, then great, I've recouped some of my losses of the night. If it loses, then I go back to my room and weep until the pillows get soggy.
Well, if you are too drunk to know whether you are playing craps or PaiGow, I think I know why you are losing!!Quote: konceptumIf I've just been having no luck at craps or PaiGow (whichever I've been playing)
Why don't you try playing Basic Strategy at craps: Only LineBets and associated Odds bets. And at Roulette try making ONLY outside bets for awhile.
Then let us know how things go.
Why do you say it is stupid. It is a 5.26 percent house edge at Roulette. Its about the same with an ordinary Field Bet at craps. Sure, that 35:1 payoff is nice, but how often are you going to choose the exact number that the little white ball does?Quote: pacomartinIt's stupid to play roulette if you are playing reds or blacks or odds or evens. The house edge is ridiculous.
On average, 1 time in 38.Quote: FleaStiffWhy do you say it is stupid. It is a 5.26 percent house edge at Roulette. Its about the same with an ordinary Field Bet at craps. Sure, that 35:1 payoff is nice, but how often are you going to choose the exact number that the little white ball does?
