My friend has decided that next time he goes to the casino, he is going to take some $1,500 dollars and play roulette. His strategy is going to be to bet 5 dollars on one particular color and if it doesn’t come up, he will double his bet and bet on it again. He can cover his bets unless some 9 colors in a row come up that he ins’t betting on. What I want to know is… what are the odds of getting 9 consecutive colors in a row on the roulette wheel? And for that matter what are the odds of getting 7 or 8 consecutive colors in a row?
Nine colors in a row correct: .2% chance!
Eight colors in a row correct: .8% chance!
Seven colors in a row correct: .4% chance!
One color in a row correct: 50% chance! 
Oooops! Switch the Seven and Eight!
Seven in a row should be .8% and Eight should be .4%.
This is an old gambling theory. The problem is, it doesn’t work. What your friend is getting at is the odds of going through a long losing streak and how s/he could overcome that through the doubling strategy.
To start with, you need to use a “doubling plus one” strategy. If you bet five and lost, then bet ten and won, you’d only be even, which is not the point of gambling. So, if you bet five and lost you’d bet at least eleven so that if your strategy worked you’d come out ahead.
It still doesn’t work, though. While the odds of actually getting eight or nine losing numbers in a row are low, if you do the math you will see that it happens often enough to more than wipe out the many one-dollar gains you will make.
There’s also the matter of table limits. If you were at, say, a table with a $1000 limit and started with five dollars and kept losing, your bets would go like this:
Bet Loss Cum
5 5 10
11 11 21
22 22 43
44 44 87
88 88 175
176 176 351
352 352 703
704 704 1407
Now you’re stuck. Even if your friend has the courage to actually put the $1408 on the table that, even if s/he wins, will only net a $1 profit (!), the $1000 table limit has taken that option away, and in this case after “only” eight rolls. You can find a higher-limit table, of course, but that really only makes it worse.
How often would that really happen, though? As noted, not very often, BUT statistically it WILL happen more than once every 352 sessions or 704 sessions or however long you want to play. Remember that the odds of winning on any given roll are not 50%, but rather either 47.4% or 48.6% (for a double- or single-zero wheel, respectively). So, let’s say you’re at a double-zero wheel (it’s hard to find a single-zero wheel in Las Vegas). Let’s say your limit is six rolls. The odds of losing six rolls in a row are about 0.526^6, which is about 2.1%. So, if you this a thousand times, you’ll be successful 979 times and gain $979. You’ll lose 21 times and be out $351 each time for a total loss of $7371. Your net loss is $6392. By fiddling with the bets you can help yourself a little bit, but if the rolls of the wheel are truly, random, you simply can’t win.
Bear_Nenno’s a little off - she forgot to take into account “0” and “00”. So, the odds of getting one color in a row correct is 47.4%, not 50%.
MadHatter, your friend is planning to play the most basic and traditional roulette system there is. Lots of people swear by it, but computer simulations show that the system usually fails. There are two primary problems with the system, and one problem added by most casinos.
The two primary problems are as follows - 1) The zeros. The addition of two more spaces on the wheel reduce your odds below 50-50. The system you friend plans to play depends on exact 50-50 odds to work. 2) The house has (for our purposes) an infinite stake, and your friend has $1500. Therefore, the house can ride out bad streaks better than your friend.
The problem added by the house (deliberately, to help foil this system) are the minimum and maximum bets. The house will require a relatively large minimum bet and will place a relatively low limit on maximum bets. With these limitations, the amount of bets your friend will cover drops, and he can’t cover as long of a bad streak.
Roulette, even played perfectly (“perfect”, BTW, means the system your friend plans) has the worst odds of any traditional table game in the casino (don’t know about Pow Gai Poker, etc.) IIRC, the house has a 5.4% advantage on double zero wheels.
Sua
Your friend is doing what is commonly known as a “Martingale”. The problem is that you are taking an increasing risk for constant return, and if you keep playing it, you will eventually hit the run of bad luck that will wipe you out, or you will hit the house limit, at which point you cannot cover your losses with a larger bet.
A good book for you to read:
Lady Luck - the theory of probability, by Warren Weaver
Some may view this book as somewhat dated (my copy was published in 1963), but I think it is a good basic readable “probability for the layman” book, and will help a lot with the kind of questions you’ve been asking.
Just one more comment, although it has more to do with gambling in general:
The easier a casino game is to play, the higher the house advantage.
I’ll let somebody else do the math, but what this means is that games that require thinking (e.g., blackjack and craps) are more beatable (with a little luck) than non-thinking games like roulette or the slots.
We can cut to the chase here, BTW, and state that there is no winning strategy for casino gambling games which are based on a series of identical independent trials, and which do not have a winning bet on an individual trial.
“Independent trials” covers most of them. Blackjack is not, since you bet on something dependent on the outcome of the previous hand. Hence the interest in that one.
Cut to the ultimate chase and tell your friend to consider how many millions of dollars it takes to build and operate the casino he’s sitting in. Then he should ask himself where all those dollars came from. The only winning system in a casino is owning the casino.
The double-up strategy is called a “Martingale” system, as yabob indicated. The double-up + one is often referred to as a “Grand Martingale” in which you are even worse off, because you reach your (or the House’s) upper limit faster.
This is a bad system, for the reasons mentioned above. I’ll re-iterate one of the more obvious flaws. Follow this sequence of Martingale bets:
Bet $5: lose
Bet $10: lose
Bet $20: lose
Bet $40: lose
Bet $80: lose
Bet $160: lose
Ok, you’ve now put out $315 and it has all gone away. If you think losing 6 bets in a row is hard to do, guess again.
So now, you are faced with putting out $320, and for what? An overall win of $5!. The wheel has no memory. It doesn’t care that you’ve lost 6 in a row. The odds of you winning that 7th very expensive bet is still less than 50-50.
Sitting at a computer is a lot easier than digging for that $320 just to come out $5 ahead. And if you lose that $320, you are now down a whopping $635. Are you going to tell me you are prepared to put out $640 to win $5? Probably a moot point because many casinos have a $500 bet limit.
I hardly ever gamble, but when I do I play roulette. I have a system – as in a routine I follow religiously, not a way to “beat the house.” My system is designed for maximum peace of mind, and minimum regrets.
Anyway, I like roulette for the esthetics, not the odds. But, if I did want to “play to win” I’d play Baccarat. Like roulette, it “plays itself” – there’s none of the effort and fuss of strategy or card counting – you just bet, and go along for the ride. And the odds are very good – at least compared to many other games, roulette included. The rules are obscure but very, very simple – much simpler than that big favorite, craps.
Baccarat is the ulimate elegant European casino game, I’ve read, but Americans seem to have no taste for it, despite the good odds. There are very few tables in most casinos, and the ones that do exist are sparcely filled, and usually with no Americans. So MadHatter, you’re obviouly in a gambling mood. I say you should try to start a trend and try to become the Baccarat King of Vegas. (Just don’t forget to tip the tout. Stuyguy’s the name.)
While baccarat does have very good odds (-1.17% for the house), it’s still double that of blackjack played with basic strategy.
But there’s another reason why the house can offer good odds on Baccarat - the game plays fast. And when the house has the advantage, speed kills.
If you play an hour of baccarat, betting $10 per play, you’ll get maybe 200 plays in that hour. That means a total amount of money wagered of $2000, and the house will keep about $23.40 That’s your cost for one hour’s entertainment.
If you play blackjack for one hour, wagering $10 per hand, you’ll get about 70 plays. If you play basic strategy, the house odds will be around .5%. Your cost of gambling for that hour will be about $3.50.
Also, the more plays per hour you get, the less chance you have of being ‘lucky’. The house edge has a much greater chance of asserting itself over 200 plays than over 70.
If you play roulette with $10 wagers, you’ll get maybe 100 spins in an hour, with a house edge of 5.26%. Your cost of gambling: $52.60.
So, the difference between playing one hour of blackjack with basic strategy and one hour of roulette is MASSIVE. We’re talking about a cost of $52.60 vs $3.50, with the same size wagers.
OK, MadHatter, one more thing.
I beg you, please, please, please, stop trying to figure out ways to beat the house. There is no way to beat the house, if there were a way to beat the house there would be no house. Maybe these questions are academic, but I can just see you down at the casino, your eyes glazed from the lights, throwing down chips until you’re cleaned out. It’s making me a nervous wreck, and it’s not even my money at stake!
If you like gambling and want a game where the house odds are often in your favor, consider the stock market. But remember that even there the best way to make money is to invest in good companies and stay with them for years.
Please, just take it for granted that you can’t win, you can’t break even. But you can refuse to play.
In general, you are correct, and people going to gamble for enjoyment should always do the following:
- Assume you are going to lose your entire stake, and only bring with you money you can afford to lose;
- In order to enforce that, DO NOT bring with you ATM cards, credit cards, or anything else that can get you more money once you are at the casino; and
- Once you are down, assume you are going to stay down. Do not keep playing in order to “get your head above water.” In particular, do not withdraw more money in order to win back what you have lost (I can tell you really dumb stories from personal experience about that).
That being said, you can beat the house at one game – blackjack. However, in order to do it, you must seriously study and practice card counting and basic play until you can accurately keep count regardless of distractions, and know exactly what you are supposed to do in any situation. It took me six months before I felt confident enough to go to casino and count. Learning card counting is not worth it if you are going to a casino once or twice.
Sua
SuaSponte’s advice is excellent.
Just to clarify, here is a list of games that can be “won” in a casino:
1.)Blackjack, if you’re counting. As SuaSponte said, counting is not worth the effort for the occasional gambler. (Unless, like me, you’re just intersted.)
2.)Some progressive video poker machines will eventually go positive. However, they are difficult to find, and not at all worth the effort for the small advantage, especially considering how many hands you have to play before you can expect a Royal Flush. The same might be said for progressive slot machines, but I don’t really know anything about them.
3.)Poker. Remember that you’re not playing against the casino here, but against other players, so a better than average player should be making money. However, you must consider the rake, or the casino’s take, so you have to be somewhat better than average to win with any consistency at all.
4.)Sports book. If you really, really, really know what you’re doing, you might be able to out-guess the Vegas odds-makers. I wouldn’t count on it, though.
That’s it. There is no way to shift craps, roulette, keno, Carribean Stud, Let It Ride, Pai Gow Poker, baccarat, standard slots/video poker, or any of the other casino games into your favor without outright cheating.
My recommendation to anyone who likes to gamble (in addition to SuaSponte’s advice) is to be extra-friendly, tip well, and play at places that offer good comps. A free meal or room can really help cushion the house advantage. Just don’t expect to make any money.
Dr. J
When at the casino, I only play roulette and have always come out ahead. But, there are no guarantees. I’m going to try to teach this as quickly as possible.
Question: There have been 4 reds in a row. Is the next turn more likely to yield red or black?
If you said red or black you don’t understand the game and are looking for a world of hurt. The next spin is never affected by the previous spins, so it is not more likely to land anywhere. The chances are exactly the same that it will land on a different number every time as they are for it to land on the same number all night without fail. Make sure he knows this when he goes out there. When you realize this, you’ll realize that there is no sure fire way to beat the house. And, remember that if you play long enough you will lose. Know when to walk away.
Anyway, sorry about that. The startegy I use is simple, but I can’t remember the numbers. I always play the six-streets. If you place a chip between two columns at the top(does that make sense), you’ll be betting on 6 numbers and it pays 5 to 1. He can take 5 dollars and place the same bet 5 times. Always bet in the same place. Your odds are the same. If he wins at any time in those 5, who will either come out ahead or even. If he doesn’t win in that time, he can douple the bet and I believe go up to 3 or 4 times. I don’t feel like doing the math right now, but hopefully you get the idea. The money will go a lot farther and the odds are more in your favor than his method. All in all, though, the odds are still in the house’s favor, and it’s very well possible that you can never win.
Oh, one other thing. In some of the smaller casinos, they use older roulette wheels because those things are damn expensive to replace. If you watch the table for a while before hand, not always but sometimes, you will find that the ball seems to land in a certain area more times than others. And not randomly so. Some of the wheels will favor a few numbers sometimes because of heavy use. If they’re paying attention though, like they’re supposed to, as soon as they notice this, they’ll replace the wheel.
Anyway, tell him good luck and to expect to lose everything.
Congratulations - you just found the worst bet on the roulette table.
In Roulette, every single bet you place has exactly the same house odds: -5.26%. EXCEPT for the 5-way bet mentioned above, which is around -7.5% if I recall correctly. So the only roulette strategy worth mentioning is “Don’t play the 5-way bet”.
Actually, there is more to say about strategy - the best ‘bets’ on the roulette table are the individual numbers, because they have the highest payoff. You’re paying -5.26% for a chance at a 35-1 payoff, which is a hell of a lot better than paying -5.26% for an even-money payoff. So stay away from red and black, and put your money on the numbers. The only way you’re ever going to beat this hellacious house rake is to go for the longshots and hope that variance works for you. If you sit there plunking your money down on even money bets all night, you WILL be busted out.
Or even better, stay away from the roulette table, which is one of the worst gambles in the house.
In Europe, Roulette is much more popular than in the U.S. And there’s a simple reason - it’s a much fairer game. First, there’s only one zero, which lowers the house edge to 2.63%. Then they have the en prison rule, which effectively cuts it in half again for even money bets, to about 1.32%.
I don’t understand the reasoning behind the 5-way bet being -7.5%, while all others are -5.26%. I’m not saying you’re wrong, I just don’t understand. Could you explain it to me, please? I’ve been using the same strategy for the last year(I just turned 21 last November) and I’m ahead almost $3000 overall. I assumed that was pretty good and that odds would state that the ball is more likely to land on one of 6 numbers than on one. I know in reality, neither is more likely, but in practice it seems to work. What am I missing?
Sam, I think you’re thinking of a different bet. You’re thinking of the basket, which is 1,2,3 and the two 0’s. Which is not a good bet.
Aglarond seems to be talking about a six way bet, which is the same odds as putting bets down on the six individual numbers the bet encompasses.
Either way, roulette is THE worst table in the room. Tell your friend that if he’s willing to bring $1,500 to a casino, spend $5 and get a strategy book and learn what he’s doing.
Conner: I think you’re right. That makes sense to me. But, yeah, roulette is the worst bet. The reason I play it is because it’s the only one I understand. I always make money at the roulette table and I’ve lost my ass everytime I’ve tried any kind of card game. I don’t understand the strategy, nor have I really tried. A strategy guide would probably be a good investment. Word of warning: I’ve seen strategy guides that GUARANTEE winnings. Bullshit. There’s no such thing in any casino game. That’s exactly the point.