Chapter Five: Outside Situational Bets
When is the Gambler's Fallacy not a Fallacy?
Outside Situational Betting the Gambler's Fallacy refers to the belief that one can predict a given spin based on a set of preceding spins. It is a fallacy because each spin is an independent event that cannot "cause" a future event to occur. The wheel does not know what color a number is and it has no memory of what number just appeared. But is the gambler's fallacy always a fallacy? Doesn't every system or strategy attempt to make some sort of prediction of upcoming spins based on past spins?
Let us get more specific. What does it mean to "predict" a number or result?
The classic example of the gambler's fallacy happens in the LIVE casinos all the time. Many times in Las Vegas or Atlantic City I have been at a table where the reds or the blacks have hit 5 or 6 times in a row. Let us say the streak is a streak of 6 reds in a row. All of a sudden a bunch of naïve roulette players rush to the table to start betting on black. "It can't keep going red!" they exclaim. I have seen many of these unfortunate folks lose literally every dollar they brought to the casino as they stare in disbelief as the number of consecutive reds climbs higher and higher. I have seen even an experienced roulette player drop $8,000 on a single streak that lasted longer than his bankroll could stretch.
But is the intuition of the naïve gambler entirely wrong? Not really. There are predictable limits to streaks of red or black, for example. The problem in this case was that the players did not know enough about the odds of the streak continuing to a particular length. Allow me a mathematical proof that the so-called gambler's fallacy is not always a fallacy.
The strict version of the gambler's fallacy is based on simple probability theory. The odds of a given spin being red or black is always about 47%.
That is true each and every spin. Accordingly, it does not matter what has happened in previous spins. If I bet on black 8 times, doubling my bet each time, I will always average the same result because the events are always the same.
Or are they? My argument is that the gambler's fallacy is not a fallacy during what I call statistically-anomalous sequences. A technical definition of what I mean would be something like "events that happen only beyond a specified number of standard deviations from the norm." A simpler way of putting it is that there are limits to extremes.
For example: I generated 100,000 spins and then calculate exactly how many streaks occurred of the even money bets: red/black, even/odd, and 1-18/19-36.
Cumulatively this represents 300,000 spins of experience on an even money bet. In no case did a streak go any longer than 16 in a row. In Russell T. Barnhart's book, Beating the Wheel, he reports on the results of over 46,000 spins from an actual roulette wheel in Monte Carlo. In that case the longest streak of red or black was 15.
Accordingly, imagine that you only bet on an even money bet when a streak reached 10 in a row. In these data sets, one of 100,000 and another of 46,000, you would have no losses. The win/loss rate would have been 100%.
In these situations, the gambler's fallacy is not a fallacy. The results of situational betting (waiting for 10 in a row) are different from betting in continuous sets of 8 bets at any other times.
Now have we really disproved the gambler's fallacy? Not completely. We can describe what happens in these situations with standard probability theory. While one can never predict the result of one spin, we can predict, with some precision, the probability of a given event over a series of spins. One calculates this by multiplying the probability of one event times the probability of another. If you flip a fair coin the odds that it will come up heads is .5 or 50%. The odds that it will come up heads twice in a row is .50 x .50 = .25 (or 25%). Now, let us say you have flipped the coin twice and it came up heads both times. What are the odds it will come up heads again for the third time in a row? Careful! The odds are still .5 on any given flip because these are independent events. So, even though in general the odds of three heads in a row is only 12.5% (.5 x .5 x.5 =.125), on any single flip they are still 50/50.
Now the question becomes What are the limits to extremity? If you can have a coin come up heads 10 times in a row, despite the fact the odds are very small (.0009765), when is it "safe" to bet that the streak will end?
Because you are in the process of becoming an increasingly sophisticated player, you can decide for yourself what your comfort level is. My personal suggestion is that for even money bets you need to be able to outlast a streak of 17. I see streaks of 9 and 10 often enough (especially in a large casino with lots of tables) that if I can increase my bets to outlast a streak of 17, I feel pretty darn confident.
The specific probability I want to obtain is 99.999%. That is, I want to be beaten only by an event that has a probability of less than 1 in 100,000. If you consult the Bernoulli trials in the appendix you will see that the odds of an even money bet (which covers 18 of 38 numbers) winning on your first spin is about 47%, the odds of winning at least once within two spins is about 72%, and so on. The odds of losing a given number of consecutive bets is simply 1 minus the probability listed. You reach odds of less than 1 in 100,000 if you can outlast a streak of 17, so that is the "limits of extremity" I am willing to bet on for the even money bets.
Sadly, there is no way to ever get to 100% probability. But by identifying the extreme limits of even money bets at 17, we have seen that you would have had a perfect winning record for two large data sets: My simulated 300,000 spins and the 46,000 spins in Monte Carlo. And, for what it is worth, in my years of experience I can say I have never seen a streak go past 14.
Depending on how much you play and how fast your dealers are, 100,000 spins is a very, very long time. A strategy that can win in data sets of 100,000 spins is something to be confident about. You might literally go through the rest of your roulette career using this strategy without a loss.
The Practice of Outside Situational Betting
Almost all outside betting systems require the player to bet continuously. I have described a strategy that is situation-specific; that is, the player bets only when a statistically-anomalous sequence (9-in-a-row or more) occurs. This can be used on the even/odd, red/black, or 1-18/19-36 bets. The obvious limitation of this strategy is that you have to wait to find a streak of 9 or 10 (or even more if you are particularly conservative). I doubt you will get rich with this strategy alone, but at least by conserving your bets to these unusual streaks you can play with confidence.
In practical terms there are two ways you can pursue this strategy: Table Hopping and combining this strategy with others at a single table. "Table Hopping" refers to moving from one roulette table to the next in search of unusual streaks to take advantage of. The most visible example of such a streak is the streak of red or black, since most results boards are color-coded and one can see from a distance a block of red or black numbers.
If you intend to use this strategy, however, you should also look for streaks of even or odd numbers, or of high (19-36) and low (1-18) numbers. Many players forget to look for these sequences and miss four more betting opportunities. Note: When you walk up to a table you should ask one of the players if the results board is working properly. Players generally watch these boards carefully and can warn you if it is falsely repeating or omitting numbers.
Atlantic City is the best place to table hop because there are a number of casinos with a group of tables all within sight of one another. My personal favorite casino in AC is Harrah’s because of the number of tables (typically $5 tables) within sight of each other.
If I am feeling restless or want to exercise then I will wander through casinos looking for potential betting situations. More often than not, I will stay put at one table in order to play Step-by-Step or to pursue the Inside Situational bets I describe in the next chapter. In those cases, you simply pay attention to the results and keep your eyes open for an outside situational betting opportunity.
OK, so by now you want me to get more specific about how to use these ideas in actual play. I will give you five specific outside situation betting strategies:
- Even money against-the-streak.
- Even money "correction effect."
- 2-for-1 sleeper.
- 2-for-1 "correction effect."
- 2-for-1 against-the-streak.
1) Even money against-the-streak.
Betting against the streak is pretty obvious. You find a streak of 9 or 10-in-a-row of an even money bet (red/black, even/odd, 1-18/19-36) and you bet against it. You must progress your bet after each losing spin, but how much you progress it is up to you (your bankroll size and risk-comfort level). If you want to be conservative, you can progress your bet Step-by-Step, as described last chapter. If you want to be more aggressive, you can double your bet after each loss until you win. Your profit will be the amount of your original bet. Or you can increase your bet by more than doubling it each time. I will describe a medium-level risk strategy here, but feel free vary it according to your own preferences of risk and profitability:
Sample progression #1: Wait for 9 in a row, then bet
- 1st spin 1 unit
- 2nd spin 2 units
- 3rd spin 4 units
- 4th spin 9 units, 1 on 0/00
- 5th spin 21 units, 3 on 0/00
- 6th spin 48 units, 6 on 0/00
- 7th spin 108, 12 on 0/00
- 8th spin 255, 30 on 0/00
Why the bets on 0/00? Because a streak can be brought to an end by either the opposite bet (the one you are betting on) or by the appearance of a zero.
That is why I "insure" my bet with a side bet on 0/00 once the bet gets to a certain level.
Note: If you are on a European (single zero) table or are playing in Atlantic City, the rules are a bit different. If 0/00 hits, you lose only 1/2 of your outside bet, in which case you would want to use something like this:
Progression #2: Wait for 9 in a row, then bet
- 1st spin 1 unit
- 2nd spin 2 units
- 3rd spin 4 units
- 4th spin 8 units
- 5th spin 18 units, 2 on 0/00
- 6th spin 41 units, 3 on 0/00
- 7th spin 90, 6 on 0/00
- 8th spin 222, 16 on 0/00
Remember, 1 unit can be any consistent amount of money you want. On video roulette you can bet only $1, but in most casinos a minimum outside bet would be $3 or $5, so that would have to be your basic unit. The sample progression would also work if your basic unit is $10 at most casinos, but make sure you check the table maximums before you start your betting sequence.
2) Even money "correction effect."
The next strategy involves a fairly simple idea concerning probability. When a streak happens that is very rare, it is unlikely that it will be followed immediately by another streak that is very rare. Mathematically this is simple to explain. The probability of a streak of 9-in-a-row is .0031 or about 3/10ths of 1%. The odds of two consecutive streaks of 9-in-a-row is .0000096 or about one in 100,000. Accordingly, the even money "correction effect" strategy is to bet against a repeat of another long streak. So, if you have 9 or more reds in a row, you should have bet against the streak until a black or a zero hit. If it was a zero, walk away and count your profit. You are done. But if it was a black, then start betting red. You are betting that the streak of blacks that just began will not go 9 straight spins.
This strategy may seem counter-intuitive to you. After all, after a streak of 9 (or more) reds would not the blacks be "due" to repeat? The answer is not necessarily. Over a number of spins, yes, the blacks and reds will balance out. But in the short run of 20 or 30 spins one color can dominate the wheel hitting about 9 out of 10 times.
What you are betting on is not the color so much as the probability of another long streak. The "correction effect" is not by color but the unusual length of the previous streak. The wheel does not know what color the numbers are. Concentrate on probabilities. Since the odds of two consecutive streaks of 9 or more are less than 1 in 100,000 the appearance of this streak gives you two betting chances--one to bet against the first streak going to 18, and then another to bet that the second streak will not go to 9.
In addition to the mathematics of probability, I tested this strategy with 100,000 spins dividing the numbers into even and odd. I examined each and every occurrence of a streak of 8 or more. None were followed by a second streak of 8 or more. That was a 100% win/loss rate, which is also what I have experienced in the casinos so far with this strategy. The closest I found was a streak of 11 followed by a streak of 6, and a streak of 10 followed by a steak of 7. In both cases, using the betting progressions described above, the second streak would have been defeated.
Again, you will not have a ton of these betting opportunities, but at least each time you find a streak of 9 or more you have not one but two betting chances. When you realize that on any one table there are 6 even money bets that could have such a run, then multiply that times the number of tables in a large casino, you have a good opportunity to make some money with these two strategies.
I suggest using the same betting progression as you use in even money "against the streak" strategy (see the previous page) as for this even money "correction effect" strategy. You still need to "insure" yourself with side bets on 0/00.
3) 2-for-1 sleeper.
LIVE Roulette players call numbers that have not hit for a while "sleepers." The idea is that these numbers have fallen asleep and won't reappear until they "wake up." Betting on sleepers is generally a bad idea, as numbers can stay asleep much longer than most players realize. A single number can stay asleep for over 300 spins.
However, once again we find that on unbiased tables there are limits to extremity. When we deal with parts of the table that cover 12 numbers we can bet on sleeping sections under the right circumstances. The 2-for-1 bets are the dozen bets (1-12, 13-24, 25-36) and the column bets, which many players read left to right as A, B, & C with 1 at the head of the A column, 2 at the head of the B column, and 3 at the head of the C column.
Some commercial systems out there are based entirely on betting on these 2-for-1 bets. Be careful, because most of these systems misjudge the probabilities. It is true that the typical column or dozen will hit about once every three spins (31.6% of the time). And if you bet on one column or dozen 10 times in a row, the odds of a winning spin are above 97% (see the Bernoulli trials in the appendix for details). The problem is that when a dozen or column goes to sleep, it can stay asleep longer than most commercial systems acknowledge. We want to get to that comforting 99.999% confidence level where you are only beat by a sequence that is 1 in 100,000. That is, 99,999 times out of 100,000 a series of spins without a particular column or dozen hitting will be 30 spins or less. If you were betting continuously, you would have to last for 30 spins. Given most table limits and bankroll limitations, that is impossible.
The solution is, of course, situation betting. I can keep track of whether a number is even or odd, high or low, and which dozen it is in without any special notes other than simply writing down each number as it comes up. The one extra symbol I record is an A, B, or C to designate which column that number is in. As you record spins you should add a letter after each number to indicate which column it is in. You will soon learn that you can notice sleepers this way, as well as unusually long streaks.
Once again you need to progress your bets according to your bankroll and risk-comfort level. I personally would wait for a sleeper streak of at least 15 to 18 spins before betting, and then I would bet as follows:
Progression #3: Wait for 15 to 18 spins without a hit in a dozen/column, then bet
- spin 1 - 1-unit spin 6 6 units spin 11 47 units
- spin 2 - 1-unit spin 7 9 units spin 12 71 units
- spin 3 - 2 units spin 8 14 units spin 13 108 units
- spin 4 - 3 units spin 9 21 units spin 14 162 units
- spin 5 - 4 units spin 10 31 units spin 15 244 units
How successful is the 2-for-one sleeper strategy? I can answer three ways.
- First, unlike most commercial systems, it passes the probability theory test. If you consult the Bernoulli trials in the appendix you will see that the odds of a set of 12 numbers failing to hit by the 30th spin is less than 1 in 100,000. So we have that 99.999% level of confidence.
- Second, I have never lost using this strategy, though you should not trust personal anecdotes by themselves because the data set is too limited.
- Third, I ran a trial of 100,000 spins and examined the results for a set of 12 randomly-selected numbers created as a hypothetical set (this would function like a dozen or column). The longest sleeper series was 25 spins.
Now, I would still urge you to rely on the magic number of 30 rather than 25 to be on the safe side, but obviously those results were reassuring. So with this set of 100,000 spins the success rate would have been 100%, which is precisely what probability theory would predict.
4) 2-for-1 "correction effect."
If you already figured out that there might be a "correction effect" for this betting strategy as well, give yourself bonus points. You are starting to think like a sophisticated roulette player. Once again, it is not so much a matter of a set of 12 numbers being "due" as much as the odds are against another unusually long series of spins where the same dozen or column fails to reappear. Accordingly, if you see a dozen or column go more than 15 spins without a hit and bet on it using the 2-for-1 sleeper strategy, you can turn around and bet on that dozen or column to repeat with the next 15 spins.
Once again, like the even money "correction effect" bet, the odds of another streak of greater than 15 happening back to back are remote--about 1 in 100,000. Use the same betting sequence as described in sample progression #3.
Did I test this? Of course. Once again I analyzed a set of 100,000 spins.
I examined each and every sequence where a dozen failed to hit for 10 or more spins. In no case was a series of 15 losing spins followed by another series of 15 or more losing spins--which is precisely the result that probability theory would predict.
The two closest were a series of 18 losing spins, followed by a hit, followed by 11 more spins before a hit, then another series where a series of 19 losses were followed by a hit, then followed by 10 losing spins before a hit.
Once again the success rate of this strategy for this set of 100,000 spins was 100%. Your results could vary, of course, but again you can see why you should be pretty confident with this strategy.
5) 2-for-1 against-the-streak.
As many roulette books and systems will tell you, the best bet mathematically on a single spin would be to bet on two of the dozens or columns. That way you cover 24 numbers (out of 38 on an American wheel, out of 37 on a European wheel). The disadvantage is that you are laying odds. That is, you are betting two units at a time in hopes of winning 1 unit. But on the other hand on each spin your odds of a win are over 63% (almost 65% on a European wheel). If you cover the 0/00 in addition to the 2 columns or dozens, your odds go up to over 68% on a single spin.
When I first started to play roulette I was convinced I could make my fortune by betting progressively on two columns or dozens. I quickly figured out, however, that to keep even I had to triple each bet in order to make up for each loss. Well, it would be worth it if you could be sure of winning. If I could bet even twice (2 units, then 6 units) I could reach a 90%-win rate. I soon learned that streaks of 3, 4, 5, and 6 in a row within a dozen or column were not as rare as I had hoped. Then I did some computer simulations and found streaks up to 10 in a row within the same dozen or column. Yikes! I abandoned the strategy.
Once I gave up continuous betting and settled on situation betting, I brought the strategy back. It is capital-intensive and I am not a huge fan of it. But if you use it carefully it can bring in additional profit with the same sort of mathematical confidence as the other outside situation bets.
Basically, you wait until a streak within a given dozen or column reaches 6 in a row, then be prepared to bet 5 times on the two other dozens or columns.
Sample progression #4:
- spin 1 - bet 1 unit in each of two columns/dozens
- spin 2 - bet 3 units in each of two columns/dozens
- spin 3 - bet 11 units in each of two columns/dozens plus 2 units on 0/00
- spin 4 - bet 42 units in each of two columns/dozens plus 7 units on 0/00
- spin 5 - bet 150 units in each of two columns/dozens plus 25 units on 0/00
I would only use this betting progression if I was reasonably confident that the wheel involved is not biased. If I had any doubts, I would bet more modestly, perhaps betting only a side bet on 0/00 or waiting for the streak to reach 7.
In a data set of 200,000 spins the longest such streak was 10 in a row, which means this strategy as described here would have won 100% of the time.
Additionally, standard probability theory predicts that if you cover 26 numbers (2 dozen or columns plus 0/00) the odds of a streak going to 11 are less than 1 in 100,000.
Strategies #2 through 6, then, are Even money against-the-streak, Even money "correction effect," 2-for-1 sleeper, 2-for-1 "correction effect," and 2-for-1 against-the-streak. You now have 6 different strategies in your menu of options.