Odds Of 7 Reds In A Row Roulette

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  • For European roulette, the house edge is 2.7%, due to the difference between true odds and casino odds. For American roulette, the house edge is higher at 5.26%, due to the game featuring an additional zero pocket, while failing to account for that in the paytable.

The record for the number of reds in a row was set in the US in 1943 when the colour came up 32 times in a row. The probability of this happening on a European Roulette table is (18/37) to the power of 32 which comes to 1 in 10,321,314,387. It has also been reported that red came up 39 times in a row in the Casino Monte Carlo, Monaco.

By Ion Saliu, Founder of Roulette Mathematics

This question was posted in mathematical newsgroups (alt.math.recreational, alt.math.undergrad, alt.sci.math.probability): 'Winning and Quitting on Red/Black in Roulette'.

    'Obviously in roulette betting on in the long run you are going to lose your money but at some point chances are you'll be in profit. To take an extreme example if you had $1000 you could reasonably expect to be up $1 at some point. Is it possible to generalize this? I want to win W dollars at which point I will quit. How much cash C would I need to have probability P of succeeding? Let's say I'm betting on a 37 number roulette wheel (18 red 18 black and one green 0)?'

On the surface, the best probability for the roulette player to be ahead is in one trial (spin): 48.6% to win (versus 51.4% to lose), as far as even-money betting is concerned. I don't agree that it is the best strategy (betting all your bankroll on one spin).

Theoretically, no bankroll will put a player ahead guaranteed, IF flat-betting and playing very long consecutive sessions. There are moments, however, when the roulette player can be ahead by at least one betting unit. Even in even-money bets, the player has a good chance to be ahead by at least one unit after 5, or 10, or even 100 spins. But more than 20 spins are NOT recommended; the probability (odds) to lose go(es) above 50%! Think about it!

The main thing, mathematically, is the number of player's wins in N trials. To be ahead, means the player has won at least one more roulette spin (number of successes) than the number of losses in N trials. The question then becomes:

'What are the probabilities for the player to be ahead in various numbers of trials?'

Everybody can use my probability software SuperFormula, option L: At Least M successes in N trials.
Winning probability: p = 18/37; M must be at least (N/2) + 1.
Here is a number of cases from the player's perspective.

The figures are applicable to all even-money roulette bets: black or red; even or odd; low or high (1-18 or 19-36).

1 trial (spin)
- probability (odds) to win: 48.6%; odds = 1 in 2.05
- probability (odds) to lose: 51.4%; odds = 1 in 1.95
(the probability to lose is 19/37; adding zero to unfavorable cases).

2 trials (spins)
- probability (odds) to win 2 of 2: 23.7% (1 of 2 doesn't mean 'being ahead')
- probability (odds) to lose 1 of 2: 76.3%

3 spins
- probability (odds) to win at least 2 of 3: 48%
- probability (odds) to lose at least 2 of 3: 52%

10 spins
- probability (odds) to win at least 6 of 10: 34.4%; odds = 1 in 2.91
- probability (odds) to lose at least 6 of 10: 41.1%; odds = 1 in 2.43

20 spins
- probability (odds) to win at least 11 of 20: 36.5%
- probability (odds) to lose at least 11 of 20: 46.2%

100 spins
- probability (odds) to win at least 51 of 100: 35.5%; odds = 1 in 2.82
- probability (odds) to lose at least 51 of 100: 56.8%; odds = 1 in 1.76.
It's getting worse for the player...

The roulette strategy (or system) is a totally different ball game! But there are professional gamblers out there, including roulette players! They must have strategies, some roulette systems deduced from some figures like the ones above! The player can be ahead at any point in the game. If so, maybe it's time to move to another (or casino) table: It improves the odds of winning!

Always keep track of the losing and winning streaks. Be strong and put an end to a winning streak. You are ahead, you quit the roulette table. Go to another table and wait until you are ahead. The bankroll is of the essence: It must assure going through long losing streaks. Divide the streaks in 10 spins or 20 spins. Never fight aggressively short or mid-term losing streaks. This is the best approach for those who do not know Ion Saliu's casino gambling systems. A good approach to gambling is the next best thing to a good gambling system! Applicable to blackjack and baccarat, too!

Axiomatic one, everybody knows that the casinos have an edge or house advantage (HA) in all the games they offer, roulette including. The house advantage is created by the payouts in rapport to total possibilities for the respective bet. We can apply this simple formula based on units paid UP over total possibilities TP:

HA = 1 – (UP / TP)
(always expressed as a percentage.)

For example, in single-zero roulette, the one-number (straight-up) bet has payout of 35 to 1. The to qualifier is very important: the casino pays you 35 units and they give you back the unit you bet; thus, you get 36 units. There are 37 possibilities in single-zero roulette: 36 numbers from 1 to 36 plus the 0 number. Therefore, HA = 1 – (UP / TP) = 1 – (36 / 37) = 1 – 0.973 = 0.027 = 2.7%.

Let's calculate HA for the 1 to 1 bets: black/red, even/odd, low/high. HA = 1 – (UP / TP) = 1 – (2 / 2.055) = 1 – 0.973 = 0.027 = 2.7%. There are little differences among bets depending on how many decimal points we work with in our calculations.

The point is, the casinos have an advantage, or the players have a disadvantage. Nonetheless, the players' disadvantage is far better than what they face in state-run lotteries. Yet, most casino gamblers lose big, including at roulette tables. They do not have sufficient bankrolls to withstand long losing streaks.

However, around 45% of the roulette numbers lead the gamblers to profits in a few thousand spins. That is, with a sufficient bankroll, a player has a pretty good chance to make a profit, even if playing a random roulette number, or a favorite number. I analyzed about 8000 roulette spins from Hamburg Spielbank (casino). Quite a few numbers ended up making a profit: roulette systems, magic numbers.

By contrast, the more lottery drawings a player plays, the higher the degree of certainty of a loss. Let's make a comparative analysis to the roulette long series above (spins: total roulette numbers, 37, multiplied by 200). If playing the pick-3 lottery for some 100,000 drawings, it is guaranteed that all pick-3 straight sets will be losers. Some numbers will hit up to 3% to 5% above the norm — but that is not nearly enough to assure a profit. A frequency of 3% to 5% above the norm leads to profits in roulette, however.

Ion Saliu's Paradox and Roulette

Ion Saliu's Paradox of N Trials is presented in detail at saliu.com, especially the probability theory page and the mathematics of gambling formula. If p = 1 / N, we can discover an interesting relation between the degree of certainty DC and the number of trials N. The degree of certainty has a limit, when N tends to infinity. That limit is 1 — 1/e, or approximately 0.632....

If you play 1 roulette number for the next 38 spins, common belief was that you expected to win once. Not! Non! Only if you play 38 numbers in 1 spin, your chance to hit the winning number is 100%. Here is an interesting table, which includes also The Free Roulette System #1 presented at the main roulette site.

The maximum gain comes when playing 38 numbers in one spin: 36.3%. Obviously, it makes no sense to play that way because of the house advantage. On the other hand, a so-called wise gambler is more than happy to play one number at a time. What he does is simply losing slowly! Not only that, but losing slowly is accompanied by losing more. That cautious type of gambling is like a placebo. A roulette system such as Free System #1 scares most gamblers. 'Play 34 or 33 numbers in one shot? I'll have a heart attack!' In reality, the Free Roulette System #1 offers a 28.8% advantage over playing singular numbers in long sessions. That's mathematics, and there is no heart to worry about, axiomatic one.

You can also use SuperFormula to calculate all kinds of probabilities and advantage percentages. The option L — At least M successes in N trials is a very useful gambling instrument. If you play 19 numbers in one spin, the probability to win is 50%. If you play 19 numbers in 2 consecutive spins, the probability to win at least once is 75%.

Editor's note
• In an apparent change of heart, the Hamburg casino (Spielbank) offers online roulette results for free. The new link is (for the time being!):

Odds Of 7 Reds In A Row Roulette Rules

www.spielbank-hamburg.de/spielsaal/permanenzen.php4

• • Real-life roulette spins are also available from the Wiesbaden, Germany, Casino (Spielbank)

www.spielbank-wiesbaden.de/DE/621/Permanenzen2.php: Wiesbaden Spielbank Permanenzen

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Record Breakers….
What is the record for the number of reds that have been recorded in a row on a roulette table? Actually, we are interested in any of the even money bets, so red/black, even/odd, high/low and so on.

This question is particularly interesting for players of the Martingale Roulette system and goes right to the heart of the Gambler’s Fallacy- that mistaken belief that if you see 5 reds in a row, the next result is more likely to be a black. This is a myth, of course- each and every roulette spin is what’s known in statistics as a mutually exclusive event. There is always an equal chance of red and black coming up on an individual spin- the result is in no way affected by previous results.

Marty System
Martingale players are also interested in this question, because this system involves you doubling your bet after a loss. It’s generally played on the even money bets, and the idea is that at some point you will win and claw back all of your previous losses.

Players often look out for long strings of the same result, such as R,R,R,R,R. They’ll then bet on black in the hope that the results will flip back to black to restore the long term equilibrium, something that the D’Alembert system also tries to do.

If you are going to play the Martingale…….

Start your bets low and choose a table with a high limit. That way you will at least give yourself the biggest room for manoeuvre if you suffer a string of losses.

Luxury Casino accepts Martingale bets

Odds Of 7 Reds In A Row Roulette Game

But if you experience 10 reds in a row, that will blow most Martingale players out of the water, as they’ll either throw in the towel or hit the table limits, after which they won’t be able to double their bets and cover their losses. It’s difficult to figure out the best roulette strategy under these circumstances.

Repeat after me……
These long strings of the same even money results are rare, but they do happen, so you need to factor this risk in if you are playing the Martingale. There are two main risks to this system- one is that you experience a very long string of the same result. The other is that the ball drops in to the zero pocket- that pesky little area that gives the casino its house edge.

You can devise strategies to counter this of course. You could bet with the flow of results rather than against it after you see, say, 5 in a row (but you might have picked the exact time that this wheel of all roulette wheels decides to behave more “normally”). You could also choose a game that offers La Partage which will at least soften the blow of the ball landing in the zero pocket. La Partage is a rule followed by some casinos where they refund half your even money bet when the zero drops in. Many French roulette games offer this.

The Record For the Number Of Reds in a Row

So, this will scare you Martingale players! What is the record for the number of reds in a row? Check out this picture from the Rio All Suite Hotel and Casino in Las Vegas. This had all the punters thinking that the wheel was rigged- 7 reds came up in a row (you will see 7 in a row at some point for sure) but these were all the number 19!

Wow
The record for the number of reds in a row was set in the US in 1943 when the colour came up 32 times in a row. The probability of this happening on a European Roulette table is (18/37) to the power of 32 which comes to 1 in 10,321,314,387.

it has also been reported that red came up 39 times in a row in the Casino Monte Carlo, Monaco.

You can see how it doesn’t come up much, but it can happen! Luckily, I should think if anyone was playing the Martingale on that table, they hit the table limits WELL before the 32nd spin.

Roulette

That’s a Slim Chance, But it Happened
This was probably seen on an American roulette table which makes it even more incredible, because in this case the probability of it happening was (18/38) to the power of 32 which comes to 1 in 24,230,084,485, almost 2.5 times less likely because the American wheel has 2 zeros.

Here’s the thing though- on the 32nd spin, the probability of the next spin coming up red or black was the same- 47.3%. Talking about individual spins and 32 spins is a whole different ball game, and in roulette you can only bet on one spin of the wheel.

If you do a search on Yahoo, you’ll see that many people claim to have seen over 10 in a row on the roulette table. One guy claims to have seen over 15 at least 5 times (I guess we don’t know how much roulette he plays to gauge the percentage of his visits that this represents). Even so, it does happen. 5 in a row, 6 in a row, 7 in a row, 8 in a row and so on is going to happen more frequently. 14 in a row seems to be the big one that people are talking about in their personal experiences.

What About Black?

The weird thing I find about these stories, is that everyone always talks about red. I mean, what about the record number of blacks in a row? Or the record number of evens in a row? Or odds? Or high numbers? Or low numbers?

Odds Of 7 Reds In A Row Roulette Numbers

There is a famous session where a roulette ball on a specific wheel landed on black 26 times in a row in a Monte Carlo Casino in the summer of 1913- August 18 to be precise. This even spawned the name “Monte Carlo Fallacy”. Players at the table lost millions of francs betting against the black.

Odds Of 7 Reds In A Row Roulette Games

But generally, all the noise is on red, right?

Why People See Red and Not Black
I think here we are into human psychology. Red is an emotive colour, and it’s the one that people talk about the most. Black also gets noticed to a lesser extent, but the others? There has probably been a case of 20 high numbers or odd numbers occurring in a row in a casino, but no-one probably noticed.

So, this brings up an interesting point for us, one that we touch on in our Even Money Switcher system.

If you are tracking the even money results, you don’t just need to bet on red/black. You can look for patterns on the other bets as well. 23 reds in a row has been documented, but I have never heard of 23 high odd red numbers in a row.

Maybe it happened and no-one noticed!

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