Does Roulette have the best edge on a 35:1 bet?

The 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?

Wouldn't video poker fulfill your criteria of a bet with a big jackpot and low house edge?

Strictly speaking, yes. But since there's no video poker in any nearby casinos, I'm more interested in the table games.

I would also like an answer to this, just to throw that in there. Personally, I have a feeling that the edge is higher than 1.02 but less than 5%.

Quote: lament

The 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

The 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.

Quote: lament

The 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

I 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.

Quote: lament

I 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

I believe for a pure luck bet (discounting blackjack and video poker) and you want to get a mini-jackpot of 35:1 then roulette is the game with the lowest house edge.

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.