Chapter Six: Inside Situational Bets

The same principles that inform the outside situation bets can also be applied to inside bets. Once again we want to know "When is the gambler's fallacy not a fallacy?" That is, under what circumstances can one analyze a set of spins and use that data to predict, within reasonable limits, what will soon happen with inside bets involving just a few numbers.

Let me stop right now and explain that I deal with the inside bets in sets of no less than 2--a pair. I do this for several reasons. First, it is too cumbersome to track and bet on single numbers. Second, if you are on a biased wheel but do not know it, a pair is safer than relying on a single number to appear. Third, single-number sleepers simply take too long to wait for (as mentioned earlier, a number can go to sleep for over 300 spins). So, from here on out, I am mostly going to be talking about pairs of numbers.

The numbers are most simply and logically paired as 0/00, 1/2, 3/4, 5/6, 7/8, etc. The numbers are near each other on the betting area, plus they are opposite one another on the wheel.

Most systems that bet on single numbers fail because they underestimate how long numbers can go to sleep and/or they overestimate the value of trying to track and catch a "hot trend" when a part of the wheel hits repeatedly.

Later I will offer a mathematical critique of some of these Roulette systems, but for now trust me when I say they fail for the same reason any continuous betting strategy fails. Once again I recommend Russell T. Barnhart's Beating the Wheel for a mathematical explanation for why betting on single numbers continuously will lose you money.

The question we want to answer is when is it safe to bet inside on a pair? Based on what we discovered with the "correction effect" earlier, we can hypothesize that a long improbable streak would not be followed by another improbable streak. The theoretical rationale is simply the idea of correction discussed earlier and is implicit in what mathematicians call the law of large numbers. In a given data set, if the average frequency of a randomly-distributed number appearing is 1 in 38 (or 1 in 19 for a pair), then at some point sequences where the number or pair appear less than average must be offset by sequences where the number or pair appear more than average. That is what we mean by the "correction effect." Without imputing motivations to an inanimate object, we can say that an unbiased wheel "must" eventually generate results that "correct" a bias that has accumulated randomly.

Even the most hardened statisticians would agree with me in theory, but they would contend that in practice it is impossible to predict when the correction will take place. I disagree. I believe there are ways to track what I call the "cumulative variance" of a given frequency (say of a pair of numbers) such that one can say that once the frequency of a pair reaches a certain number of standard deviations away from the norm (the mean), one can anticipate the reappearance of that pair. Now, let me pause right here and stress a very important point: Though I believe the inside betting strategies. I am about to describe are the best money makers of all my strategies, they are not foolproof. The longer you play them the better the chance that somewhere down the line you will have a losing sequence because you will run into an extremely unlikely sequence. So I urge you never to "bet the farm" (that is, put your entire bankroll at risk in one sequence) on an inside strategy. The variance demon is just too extreme. Having issued that warning, I think you will find these three strategies to be the most fun, exciting, and profitable of all the strategies Roulette 2000 describes.

My first test of this concept was to track the appearances of 0/00 in a set of 100,000 simulated spins. The 0/00 hit an average of once every 19.2 spins--very close to the expected mean of 19. The standard deviation was 18.6331. I then looked at every single hit in sets of three. We can describe these series as a set of three numbers, X, Y, and Z. X is the number of spins it took to get a 0/00, Y how many spins before the second 0/00 after the first, and Z how many spins to get the third 0/00 after the second one. Three back-to-back zeros would produce an X Y Z of 1, 1, 1.

Three perfectly average scores would be 19, 19, 19. Most sets of X, Y, Z would vary around the mean, such as 23, 9, 26.

I then focused only on those series of X, Y, and Z that began with an X that was equal to or greater than 40. I picked 40 in part because it is a convenient number and in part because it is a tad more than 1 full standard deviation above the mean.

I then looked at how long the 0/00 took to return after the sequence where X took 40, 50, 60 or more spins. In other words, when X is at least one or two standard deviations over the average, what is the expected value of Y and Z?

I found in this test that the number of Ys that were equal to or greater than 50 were non-randomly distributed. There were more short sequences (Ys less than 50) than longer sequences (Ys equal to or greater than 50) following XX’s of 40 or more. Of course one would expect an imbalance, but I found the imbalance was larger than standard probability theory would predict. But the results did not suggest a practical betting strategy. There was still too much risk of a long series to be very useful as a betting option.

So I took the analysis another step. What happens when one has a large X followed by an equally large Y? What happens to Z when X is greater than 60 and Y is greater than 50? Here with a chi square analysis I found some remarkable results. Sequences of 30 or more spins should happen approximately 20% of the time. According to standard probability theory, that probability of 20% is true at all times. The value of X or Y should be totally irrelevant if the events (each spin) are truly independent. While I do not challenge the idea that each spin is independent, I must insist that sets of spins do not necessarily behave as they were independent. In my data analysis there were no Zs that were equal to or greater than 30.

Now I realize this is fairly technical, but hang in there while I explain why this is valuable information. If we can track pairs of numbers to identify 2 series where X 60 and Y 50, then we may be able to predict at a high level of confidence that the third series, Z, will be less than 30. This may sound so rare as to be useless, but I will explain in a little while why that is not true. The good news is that my chi square results were significant at the .06 level of significance. That means that there is a 94% probability that the results were not merely accidental.

My first data set was rather limited, however. Out of over 5000 hits of 0/00 in a set of 100,000 spins, only 219 were over 60. Of those 219 cases of X that I looked at, only 14 were followed by Ys of more than 50. Of those X-Y sequences none were followed by a Z of more than 30. While I was encouraged by the results, I decided I needed more data to see if these trends were consistent enough to be predictable.

So I hired a computer consultant to write a program that allows me to test this very specific strategy. The computer first randomly generates a number of simulated spins. It then tracks each pair and measures how long it takes for each pair to repeat. I can then tell it to look at all streaks above 60, 70, or whatever value I assign to X, then check to see how many of the next series (Y) are above or below 60, 50, or whatever. It is a very helpful program for testing different versions of the strategy, and I am happy to have the opportunity to share the results with you here.

To simulate a number of trips to the LIVE dealer casino that were of typical length, I ran 100 sessions of 300 spins each (a total of 30,000 spins). In these sessions I looked at each and every instance of a pair going 60 or more spins without a hit (X 60) to see how many were followed by a series where the same pair required 51 or more spins to hit again (X 60, Y 51). And of those I checked how many were followed by a third series of 31 or more (X 60, Y 51, Z 31). In those 100 sessions, 97 sessions (of 300 spins each) there were no instances of a losing series where X 60, Y 51, Z 31. In the 3 sessions that had a loss, they only had one loss each. Since each session had a number of wins (from 6 to 13), there were over 900 wins versus 3 losses using this strategy in 30,000 spins. That is a win rate of 99.7%.

Now, in my opinion the 99.7%-win rate probably underestimates what you could do. If you were to bet on the neighbors of the pair for only the first 4 or 5 spins in the Z betting sequence, I suspect you could go a year without losing with this strategy. I know I have.

OK, so we have the theory, how do we use it in practice? I will describe three strategies that you can use. The first strategy, chasing zeros, is appropriate only if you have a number of American (0/00) roulette tables to play on and like to roam. The second strategy, "chasing bunches of pairs," can be played effectively either at one table or combined with table hopping.

The third strategy, "chasing the sleeper pair," works only if you plan to sit and play at the same table for an extended length of time.

#1: Chasing Zeros

I got hooked on LIVE roulette games once I won $5000 playing this strategy in less than three days in Atlantic City. It is not as precise as what I have been describing with all the X Y Zs, but it is fun and profitable.

This is a roaming roulette strategy. That is, you roam from table to table or casino to casino. The place I won most of my winnings with this strategy was in one casino where I could watch about 10 roulette tables at once. Why chase zeros as opposed to other numbers? Zeros are the easiest numbers to spot at a distance on results boards. With the red and black numbers, you have to be close enough to make out the details, but not the green 0 and 00. You can spot them 100 feet away. It is easy to track 0/00 on a dozen tables at a time because they stand out so clearly.

There is nothing mathematically sacred about zeros. This strategy could work on any pair. I pick zeros to chase for table hopping only because they are easy to track visually. Do not trust folks who try to tell you that zeros hit any more or less than any other pair. Unless they have discovered a biased wheel, they are just plain wrong. Sometimes we get sensitized and notice things we simply did not notice before, but that does not mean they really are more of them (like when you buy a red Honda and then start seeing a ton of red Hondas on the road).

What you want to do is to go to a table where there have been no zeros for a while - at least 20 spins. You cannot track the exact numbers of spins if you are watching lots of tables, but you can estimate. A good dealer in Vegas or Atlantic City should be averaging at least 40 to 60 spins per hour, depending on how many players they are dealing with. So you can typically assume that for each hour a table goes without a zero that 50 spins have passed. Once a zero or double zero hits, you are playing for a repeat.

You can place your bet either as a split bet directly in between the 0 and 00 on the betting area, or you can put your bet on the "courtesy line," which is the line that separates the second and third dozen between 22/23/24 and 25/26/27. There are three ways to pursue this strategy.

Version A) The most cautious way is to just bet 4 times and leave if you have not had a hit. Your odds of a hit are 20%, but the payoff is great. Normally the minimum bet is $5, so just bet a $5 chip 4 times. If you lose 4 times in a row then take your bet up to $10. If you lose that twice then go to $15. If you lose twice more you could take it up to $25, but I would not recommend going any higher. This is a hit and miss way to go but you can slowly but surely pile up wins this way (I did and I know of others who do the same strategy). An advantage to this approach is that you do not get stuck at a table for long and can move on. Do not feel you have to progress your bet strictly with this strategy. You can afford 2 or 3 losses for every win and still come out ahead. Set a goal that is reasonable and walk out of the casino when you get to your goal. This is a fun strategy that you can play with relatively short money ($200 to $300). Set a goal of winning $100 and then quit once you get there.

Version B) A closely related strategy is to bet 4 times but also cover the neighbors of the zero. I do not recommend this strategy unless your session bankroll is between $500 and $1000 because it can get expensive. Or: After a hit with the above strategy where you are betting only on 0/00, use your profits on the next table to cover the neighbors. The immediate neighbors are 1/2 and 27/28. If you want to branch out another set of pairs, bet on 13/14 and 9/10. Statisticians will tell you that betting on neighbors is silly since the odds of any pair of numbers is the same. That is true, but that also means there is no reason not to bet on these neighbors, plus if the table has even a slight physical bias that might lead it away from 0/00, you might catch it with a neighbor.

Version C) The most serious way to chase zeros is to sit down and plan to chase it for 20 to 40 spins. Check the Bernoulli trials in the appendix to see exactly what your odds are for how many spins. For 20 spins your chances of success hitting a single pair like 0/00 are 66%. Not bad, but certainly not high enough to risk a ton of money on. This variation of "chasing zeros" requires the largest bankroll and it risks the largest losses if you don't hit. I do not recommend it as a consistent style of play. If you are going to settle down at one table, then the strategies I am going to describe below are better bets. But if you see a table that has not had zeros for a really long time and you decide to chase it for a while, at least you should know how much to bet.

Chasing Zeros Version A:

Bet 1 unit 4 spins, repeat at other tables unless you lose at 4 consecutive tables;

bet 2 units 4 spins, repeat unless you lose at 2 consecutive tables;

bet 3 units 4 spins, repeat unless you lose at 2 consecutive tables;

bet 5 units 4 spins, repeat until you figure you have lost or won enough for the day.

Chasing Zeros Version B:

Bet 1 unit each on 0/00, 1/2, 27/28 for 4 spins, repeat unless you lose at 2 tables;

bet 2 units each on 0/00, 1/2, 27/28 for 4 spins, repeat unless you lose at 2 tables;

continue to double your bet until you reach your win or loss limit.

Chasing Zeros Version C:

spins 1 - 16, bet 1 unit on 0/00

spins 17-24, bet 2 units on 0/00

spins 25-29, bet 3 units on 0/00

spins 30-33, bet 4 units on 0/00

spins 35-37, bet 5 units on 0/00

spins 38-39, bet 6 units on 0/00

spins 40-42, bet 7 units on 0/00 (session bankroll required for 42 spins: 117 units)

#2: Chasing Bunches of Pairs

Recall the earlier discussion of tracking pairs over an extended number of spins that we described in three sequences of X, Y, and Z where we were willing to bet that we could avoid a losing sequence where X 60, Y 51, Z 31. You may respond by thinking these sorts of sequences are so rare as to be useless. However, that is not the case. Multiplication is associative, which means 1 x 60 is equivalent to 1 x (2 x 30), which is equivalent to 1 x (3 x 20), etc. Put another way, the odds that one pair will go 60 spins without a hit are the same odds that three pair will go 20 spins without a hit (about .04). Once this principle is understood you will find all sorts of good betting opportunities.

Go back to the tracking system I described earlier, where we had the following results after tracking only 20 spins:

Chart #1

0/00 ||

1/2 0

3/4 |

5/6 ||

7/8 |

9/10 0

11/12 0

13/14 ||

15/16 |

17/18 |

19/20 ||

21/22 |

23/24 0

25/26 |

27/28 |

29/30 ||

31/32 |||

33/34 0

35/36 0

Note the pairs that have not hit in at least 20 spins: 1/2, 9/10, 11/12, 23/24, 33/34, and 35/36. Once any one of these pair’s hits, you can "bunch" that pair with the rest of the unit pairs and treat the bunch as one big pair (as a Big X).

Our Big X consists of the pairs 1/2, 9/10, 11/12, 23/24, 33/34, and 35/36. These 6 pairs going at least 20 spins without a hit is the same as one pair going at least 120 spins without a hit.

The odds are extremely low that such a long sequence with these 6 pairs asleep will be repeated. Accordingly, what we want to do is to treat all 6 pairs as if they were 1 pair--a Big X. If any of the 12 numbers of these 6 pairs hit, we will bet on all 6 pairs. Do not start betting on the pairs until you get a hit. The Big X should be considered "asleep" until one of the pairs hits. How many spins you bet on after the Big X (or "bunch of pairs") wakes up depends on your bankroll. I would not try this strategy unless you can go at least 10 spins (which requires a bankroll of 558 units).

If you can afford to go even farther, you can feel even more confident.

Now, there are two great things about this strategy. First, you can play it a lot. If you have 5 or more pairs that have failed to hit in the previous 20 spins, you can pursue this strategy and chase this bunch of pairs. If you have 4 or less, do not chase them. If you have 5 or more, smile. You have a great bet coming up. I would estimate that you will be able to play 8 or 9 times out of each 10 sets of 20 spins. And your confidence on this bet should be very high. That is the second bit of good news. You will very rarely if ever lose this bet. I have used it for over 7,000 spins so far with only one loss. But even if you should have a loss, which eventually we will, the odds of two straight losses are astronomically small. You can quickly make up for lost ground. If you want to avoid even one severe loss, I will explain how.

Chasing 6 pairs for 12 spins in my computer simulation I went 200,000 spins and only had one loss, so that is my preferred way to play this strategy. If you cannot afford that, chasing 6 pairs for 10 spins after they wake up is still a great bet. Chasing 6 pairs for 10 spins I averaged less than one loss for every 10,000 spins, but none of the losses were followed by another consecutive loss. In all I ran 600,000 spins and had no streaks of 2 losses in a row.

Chasing 5 pairs is not quite as great a strategy in the computer simulations, though I personally have never lost with this bet. Chasing 5 pairs for 12 spins for 100,000 spins yielded 1 loss every 10,000 spins. Chasing 5 pairs for 14 spins in a test involving 100,000 spins yielded only three losses, which means an average of 1 loss every 33,000 spins. Again, in no case out of the 200,000 spins was one loss followed by another consecutive loss.

What about if you track 20 spins and have more than 6 pairs without a hit? It happens a good deal: You could have 7, 8, 9 pairs open, maybe more. When that happens, start chuckling to yourself. Chasing 7 pairs 10 spins for 500,000 simulated spins I had a total of 2 losses, which were not back to back. Chasing 8 pairs for 8 spins for 500,000 simulated spins I had no losses. Chasing 9 pairs for 7 spins for 500,000 spins I had 1 loss.  Those are good odds, folks.

A couple of reminders: Track the pairs for 20 spins. If you have 5 or more without a hit in that set of 20, be prepared to treat the pairs as a big bunch, a Big X. Do not start betting on the bunch until they wake up with a hit. Then bet as follows:

Chasing 4 or less Pairs

Don't to it.

Chasing 5 Pairs Chasing 6 Pairs

spin 1 bet 1 unit per pair spin 1 bet 1 unit per pair

spin 2 bet 1 unit per pair spin 2 bet 1 unit per pair

spin 3 bet 1 unit per pair spin 3 bet 2 units per pair

spin 4 bet 2 units per pair spin 4 bet 3 units per pair

spin 5 bet 2 units per pair spin 5 bet 4 units per pair

spin 6 bet 3 units per pair spin 6 bet 6 units per pair

spin 7 bet 4 units per pair spin 7 bet 9 units per pair

spin 8 bet 6 units per pair spin 8 bet 14 units per pair

spin 9 bet 8 units per pair spin 9 bet 21 units per pair

spin 10 bet 11 units per pair spin 10 bet 32 units per pair

spin 11 bet 16 units per pair [Total of 558 units required]

spin 12 bet 22 units per pair

[Total of 385 units required]

Chasing 7 Pairs Chasing 8 Pairs

spin 1 bet 1 unit per pair spin 1 bet 1 unit per pair

spin 2 bet 1 unit per pair spin 2 bet 1 unit per pair

spin 3 bet 2 units per pair spin 3 bet 2 units per pair

spin 4 bet 3 units per pair spin 4 bet 4 units per pair

spin 5 bet 5 units per pair spin 5 bet 7 units per pair

spin 6 bet 8 units per pair spin 6 bet 13 units per pair

spin 7 bet 13 units per pair spin 7 bet 24 units per pair

spin 8 bet 22 units per pair spin 8 bet 44 units per pair

spin 9 bet 36 units per pair [Total of 778 units required]

spin 10 bet 60 units per pair

[Total of 1057 units required]

Chasing 9 Pairs Chasing 10 Pairs

spin 1 bet 1 unit per pair Split the 10 into 2 sets of 5 pairs (high/low)

spin 2 bet 2 units per pair and follow the strategy above for each set

spin 3 bet 4 units per pair

spin 4 bet 8 units per pair Chasing 11 or 12 Pairs

spin 5 bet 16 units per pair Split them into sets of 5 & 6 pairs, or 6 & 6

spin 6 bet 36 units per pair pairs, and follow the strategy above

spin 7 bet 64 units per pair

[Total of 1143 units required]

As strong as this strategy is, it is not unbeatable by any means. I strongly suggest that you practice this strategy at home extensively before putting large amounts of money at risk. If the number of units required to play these strategies is alarming to you, then you may want to consider one of the following Variations of the strategy.

Variation A: The vast majority of your hits will occur within the first 3 or 4 spins into your chase. If you want to play a bit more conservatively than the betting sequences described on the previous page, it is easy to do. Just bet half as many spins as is listed. If you still do not have a hit, stop betting in that set of 20. Wait for the next set, then pick up your betting at or near the level you stopped at. If you do not get a quick hit the first time, chances are good you will the next. This slows down your win rate, but it is a more cautious way to protect your bankroll.

Variation B: After you have tracked a set of 20 spins and have 7 (in this variation, 7 not 5) or more unhit pairs, you are not supposed to bet on any of the pairs until you have a hit on one of them. However, once you go 5 spins into the new set of 20 and none of the 7 or more pairs has hit yet, you can go ahead and start betting on the pairs. The odds of 7 pairs going much more than 30 spins without a hit are extremely remote (less than 1 in 100,000), so you can get a double hit. Once as the pair (the Big X) finally wakes up in your new set of 20 spins, then bet again as you go for the pairs you are chasing to repeat. Do not try this unless you are at least 5 spins into the new set.

Variation C: You will notice with the suggested betting progressions above that there is a point where there is a rather sizable jump in the bet. With 6 pairs that happens when you go from 6 to 9 units, with 7 pairs it happens when you go from 5 to 8 units, and with 8 pairs it goes 4 to 7 units. You can stop the steep progression at these cut-off points to minimize the risk of a huge loss. Now, with Variation A you would pick up the steep progression in the next set of 20. With this variation, you shift the strategy to betting only on the pair that has hit. As you recall, you only start to bet on the "bunch" of pairs after one of them has hit. That is because you have now linked all of those pairs and are basically betting that one of the set will hit. If I do not want to chase them all, for any reason, then I will only bet on the pair that hit. This is a much less expensive route to go and it usually works. I should add that I only chase that pair in this case for no more than 13 to 20 spins (13 is the median, 19 is the mean frequency for pairs). If another one of the missing pairs hits, then I will start chasing it as well, and so forth. Now what you have done basically is to shift to chasing individual pairs instead of the whole bunch.

It is an economical way to take advantage of the reasoning behind this strategy without putting as much money at risk.

Variation D: Though I prefer to play "chasing bunches of pairs" while staying at one table for a length of time, you can play it as a table-hopping strategy if you like. Just go up to a table, check with the players that the results board is accurate, and within about 3 spins you should be ready to bet on a bunch of pairs. Most results boards list the past 17 spins, but some have less and some have more. So count them! This variation has the added advantage of keeping you moving and not under the watchful eye of a pit boss for a long time.

Variation E: You will notice while practicing this strategy that after one sleeping pair wakes up, the others often follow suit. While this happens a good deal, it does not happen with such predictability that I want to make it a set part of the strategy. But you might want to consider playing on a few of these still-sleeping pairs with the profit you just made from chasing the whole bunch. Don't get greedy and don't chase your losses from these pursuits. But if you are ahead and want to place a few bets on sleepers that may wake up while waiting out the remainder of the set of 20 you are on, you will generally come out ahead. I almost always stop this sort of betting if I have accumulated three hits within the set of 20 spins I am betting.

Variation F: Betting on streets. Credit for this idea must go to a Connecticut colleague. He suggested I map out this strategy for those folks who like to bet on streets. A "street" is a set of 3 numbers that are in a line on the betting area. The streets are 1 2 3, 4 5 6, 7 8 9, 10 11 12, etc. If you prefer to track the spins using sets of three to match up with the streets instead of pairs as I have described above, the basic strategy can still work. In this case you will only want to bet when there are 4, 5, or 6 different streets that have not hit in the previous 20 spins.

That magic number of 20 stays the same. Since 4 streets covers 12 numbers, the odds of success are the same as for betting on 6 pairs. Five streets cover 15 numbers, and six streets cover 18 numbers. The betting progressions would be as follows:

Chasing 4 Streets Chasing 5 Streets

spin 1 bet 1 unit per street spin 1 bet 1 unit per street

spin 2 bet 1 unit per street spin 2 bet 1 unit per street

spin 3 bet 2 units per street spin 3 bet 2 units per street

spin 4 bet 4 units per street spin 4 bet 3 units per street

spin 5 bet 7 units per street spin 5 bet 6 units per street

spin 6 bet 12 units per street spin 6 bet 10 units per street

spin 7 bet 18 units per street spin 7 bet 17 units per street

spin 8 bet 27 units per street spin 8 bet 30 units per street

spin 9 bet 40 units per street spin 9 bet 51 units per street

spin 10 bet 60 units per street [Total of 605 units required]

[Total of 716 units required]

Chasing 6 Streets

spin 1 bet 1 unit per street

spin 2 bet 2 units per street

spin 3 bet 4 units per street

spin 4 bet 8 units per street

spin 5 bet 16 units per street

spin 6 bet 32 units per street

spin 7 bet 64 units per street

[Total of 762 units required]

#3: Chasing the Sleeper Pair

This strategy works well with the "chasing bunches of pairs" strategy. Let's go back to the X 60, Y 51, Z 31 formula. The idea is to play for a repeat on a pair that has been asleep for at least 40 spins. This is an easy strategy to use and you will have plenty of pairs to bet on in any given 2- or 3-hour session. But you need to be careful how hot and heavy you pursue any given pair. So here are the ground rules.

First, never bet on a pair to repeat with this strategy unless it has been "asleep" for at least 40 spins. You will know this in an instant by looking at your chart. If a pair has a big 0 marked in it for two or more spaces in a row, it is a sleeper. On average each pair should hit once during each set of 20. The standard deviation of this average is a bit over 18. So by waiting for a minimum of 40 spins, we can be sure that the pair was asleep for one full standard deviation above the mean. That means we may be about to encounter what I have been describing as the correction effect.

Look at the 35/36 pair on the chart on page 9 of this kit. The 3 straights indicate it has been at least 60 spins since that pair has hit. Accordingly, once this pair hits, I would start betting on it. I would bet on it for no more than 50 spins (the Y sequence). Then I would wait for the pair to "wake up" and hit again before trying it another sequence of 30 spins (the Z sequence). That is the "chasing the sleeper pair" strategy in a nutshell.

A few words of warning. First, do not assume that a pair that has been asleep for a long time will always be followed by a short sequence. The last time I played I saw a pair go over 70, it promptly fell asleep again and stayed asleep for over 120 spins. That is why I stop at 50 spins. Now, I waited around long enough to see it finally wake up, and this time I was prepared to chase it for 30 spins. I did not need to wait that long. It hit twice in the next 8 spins.

Second, you do not have to chase every single possible pair. Often you will be chasing 2 pairs that have been asleep, or maybe 3 that have finally hit after a long sleep. You can form these 2 or 3 pairs into a medium-sized bunch and progress your bet accordingly. That way you only need to hit one of them. Keep in mind that each spin counts as two spins if you are betting on 2 pairs and 3 spins if you are betting on 3 pair (for the purposes of the X 60, Y 51, Z 31 formula). So if you are betting on 2 pairs, just bet for 25 spins on the both of them before quitting the Y series. Walk away once you hit your win goal. Do not feel compelled to chase down every single pair you think is overdue. That is a good way to crash and burn.

Also, if you are on a regular (not video) roulette table and you think a wheel may be biased, then be careful about chasing just one pair for any length of time. The pair may be about to correct, but there could be mechanical reasons why it will not appear or repeat when it should. The very cool thing is that chasing pairs and bunches of pairs as described a bit earlier work really well together. After gathering data for that first 20 spins (less if you have a reliable results board), you will be betting pretty regularly for the rest of your session--I would estimate 15 of 20 spins--either on a big bunch or on 1 or more sleeper pairs. It is fun and typically you roll up steady profits.

Here is the progression to follow if you end up chasing a single pair for as many as 80 spins (Y series of 50, Z series of 30). Remember: You do not need to chase every single sleeper pair. The smaller the numbers you bet on, the greater the possible variance and room for the Variance Demon to do mischief.

Set a goal for your session and when you reach it, leave. Don't stay to bet on just "one more pair" because that could be the unlikely one that causes a large loss.

First 50 Spins

spins 1 - 16, bet 1 unit

spins 17-24, bet 2 units

spins 25-29, bet 3 units

spins 30-33, bet 4 units

spins 35-37, bet 5 units

spins 38-39, bet 6 units

spins 40-42, bet 7 units

spins 43-44, bet 8 units

spins 45-46, bet 9 units

spin 47, bet 10 units

spins 48-49, bet 11 units

spin 50, bet 12 units

[Total of 195 units required]

Next 30 Spins

spin 51, bet 13 units

spin 52, bet 14 units

spins 53-54, bet 15 units

spin 55, bet 16 units

spin 56, bet 17 units

spin 57, bet 18 units

spin 58, bet 19 units

spin 59, bet 21 units

spin 60, bet 22 units

spin 61, bet 24 units

spin 62, bet 25 units

spin 63, bet 26 units

spin 64, bet 28 units

spin 65, bet 30 units

spin 66, bet 32 units

spin 67, bet 34 units

spin 68, bet 36 units

spin 69, bet 38 units

spin 70, bet 40 units

spin 71, bet 43 units

spin 72, bet 46 units

spin 73, bet 48 units

spin 74, bet 51 units

spin 75, bet 55 units

spin 76, bet 58 units

spin 77, bet 62 units

spin 78, bet 66 units

spin 79, bet 70 units

spin 80, bet 74 units

[For all 80 spins, a total of 1250 units are required]

Modifying the Chasing Pairs Strategies

I am making the majority of my profit now doing a combination of "chasing bunches of pairs" and "chasing sleeper pairs." However, I only play "chasing bunches of pairs" with the variations described above. I also vary the way I play "chasing sleeper pairs." Those variations are as follows:

Variation A: I often add two "insurance" bets. This has made a significant difference in levelling out the roller coaster of wins and losses. The first insurance bet is to always have something on the green (0/00), whether it seems "due" or not. Now, you could pick any pair for insurance, but there is a little added psychological rush from hitting on the green. This side bet has come in quite handy for me, especially when I have been having a rough time catching sleeper pairs to repeat.

The second insurance bet is to always bet on the last pair to hit. Now lots of folk will bet on the last number, but you will double your pleasure by always betting on the last pair. I have found that especially when the table is giving weird, skewed results that are killing me on the "chasing sleeper pairs" strategy that this insurance bet really can save my butt.

Variation B: I seldom chase pairs for as long as I used to. There is nothing wrong with chasing them precisely as I have described above, but one can limit the needed bankroll and potentially save yourself some time by limiting your chase to between 13 and 20 spins. Why these numbers? The median frequency for repeats is 13. That is, half of the time a pair will repeat within 13 spins. The mean frequency is, of course, 19 spins and 66% of the time a pair will repeat by the 20th spin. The marginal benefit of chasing a pair after that number of spins decreases significantly, as indicated in the Probability Chart based on Bernoulli Trials you will find in the appendix.

This concludes the inside betting strategies. As I said at the outset of this kit, I am not giving you a set formula or rote lesson in memorization for playing roulette. I am trying to improve your understanding of the game and provide a new set of ways of thinking about playing roulette that are more statistically sound than playing by guesswork or with the vast majority of systems out there on the market.

So you should feel free to play. Use my strategies but if you get a sudden instinct to bet on the zeros for a spin, go ahead. Or if you think a pair is really hot and you want to bet on it a few extra times, go for it. Don't let me stop you. I am merely a coach, not your boss. The nine strategies described so far are now added to your menu of options. Whether you decide to stick to them, adapt and modify them, or ignore them altogether is wholly up to you.

Strategies #7 through 9, then, are Chasing Zeros (with three versions), Chasing Bunches of Pairs (or Streets) and Chasing the Sleeper Pair. You now have 9 different strategies in your menu of options.

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