13. Pattern Betting
While it is true that the LIVE Dealer roulette wheel has no memory, can't think or feel, and has no sense of time or space, table results often produce patterns that appear to be consistent or predictable. With even-money bets such as red or black or odd for roulette and the banker and player bets for LIVe Dealer baccarat, innumerable patterns routinely appear. Can we make any money trying to use these patterns for predictive purposes or are we just deluding ourselves?
Patterns and Probabilities
Many gambling systems are based on observing the outcome of casino wagers and then either betting with the trend or betting for the trend to end.
Assume that you and I are sitting at a roulette table and we observe that the wheel has landed on a red number for the last three spins. If we are of the school of thought that this signals that another red number is due, we will probably bet for red to repeat.
However, we may believe that any event occurring in a casino game is of limited duration and decide to wager that a black number shows, ending the streak of red numbers. Neither of these systems has any statistical validity, as the occurrences of red or black numbers on a roulette wheel are what statisticians call independent events.
In general, two or more events are said to be independent of each other if the occurrence of one in no way affects the probability of the occurrence of any of the others.
To give another illustration, let's determine the probability of drawing two kings in succession from a deck of 52 ordinary playing cards, without the first card being replaced before the second is drawn. Since there are four kings, the probability of getting a king on the first draw is 4/52. Given that the first card drawn is a king, the probability of getting a king on the second draw is 3/51, reflecting that we only have three kings left out of 51 cards. In this case, the probability of drawing the second king is dependent on the outcome of the first draw. We could calculate the probability of getting two kings in a row as 4/52 x 3/51 = 1/221.
If we had replaced the first card before the second was drawn, the probability of getting a king on the second draw would have been 4/52 (the same as getting a king on the first draw). We could then compute the probability of getting two kings in a row under these circumstances as 4/52 x 4/52 = 1/169. Since the probability of getting a king on the second draw is now 4/52 regardless of what happened on the first draw, these draws are independent. Generally speaking, two or more events are independent if the occurrence of one in no way affects the probability of the occurrence of any of the others.
If two events are independent, the probability that they will both occur is the product of their respective probabilities. With a balanced coin, the probability of getting heads is 1/2 and the probability of getting two heads in two flips is 1/2 x 1/2 = 1/4.
The probability of getting four heads in a row is 1/2 x 1/2 x 1/2 x 1/2 = 1/16.
Returning to our example of three red numbers in a row, if we assume that the probability of spinning a red or black number is 1/2, then the probability of the next spin being another red is 1/2.
Likewise, the probability of the next spin being a black number is also 1/2. Because the result of each spin is independent of each other spin, we find that the previous spins have no affect on the outcome of the next spin.
If we examine this problem from a difference angle, and ask what the probability is of getting four red numbers in a row, we find that it is 1/16, the same probability of flipping four heads in a row with a coin. If we ask what the probability is of spinning at least one black number in four spins, we find that probability is 15/16.
With the casino games of craps, roulette and baccarat, we are dealing with independent events, where the outcome of a previous decision does not affect the following decision. With LIVE blackjack, we are dealing with dependent events, for as we saw when drawing kings out of a deck, if we don't replace the drawn cards after each draw, the probability of the next draw will change.
This is the reason that blackjack is considered a game of skill while the other LIVE casino games are considered games of chance.
With skill, we can alter our strategy as the probabilities change in a blackjack deal, while with the games of chance, we should probably keep the same strategy throughout a game. (Technically, baccarat is also a game of skill as the probabilities change as cards are dealt, but because of the mechanics used for playing the game, it can for all practical purposes be treated as a game of chance, which we have done).
The Hunt for Pattern Recognition
Several years ago I was involved in a project using a computer program known as a neural network. Studying patterns which occur with even-money bets in several casino table games, I became fascinated with patterns occurring in these games and began to zero in on identifying and betting patterns of decisions.
In examining patterns, the program looked at and tested many different patterns, but zeroed in on just a few of the most important types of patterns that can be identified by observing the outcomes of just a few decisions.
As a result of using the neural net, several very powerful strategies were developed for winning at roulette, craps and baccarat. These strategies are just as powerful now as they were then, and if you would like to learn more about them, The Neural Strategy uses pattern theory as a means of winning at craps, roulette and baccarat.
Four major attributes of all patterns were examined:
- The types of patterns.
- The lengths of patterns
- The frequency of the patterns.
- Identifying patterns.
These are examined in greater detail below:
Types of Patterns
We all know that no matter how unlikely an event may be, there are times when it will occur. The program examined all patterns of decisions and identified repeating patterns of decisions, alternating patterns of decisions, and such unusual patterns as paired doublets as the most common patterns that we humans would recognize as a pattern. If we were recording decisions in a roulette game, with a "b" representing a black decision and a "r" representing a red decision, we could represent these patterns as follows:
REPEATING PATTERN b b b b b b
ALTERNATING PATTERN b r b r b r
PAIRED DOUBLETS bb rr bb rr
Incidentally, these patterns were also identified as the most common types of patterns occurring which will affect a player's wagering strategy.
The Lengths of Patterns
Having zeroed in on the patterns that it found significant, the program next explored the length or duration of each pattern. This is important, because if each of the identified patterns was of extremely short duration, then it would be of little use in attempting to "bet the pattern" and gain an advantage in the game.
Analysis showed that for a significant amount of the time, an identified pattern would be of five to seven decisions in duration, with the exception of Paired Doublets. The computer "threw up its electronic hands" on this pattern and refused to find any optimal length for this pattern.
The Frequency of the patterns.
If patterns occur very infrequently, then they are of little use in attempting to overcome the house advantage. On the other hand, if the identified patterns occur fairly frequently, then gearing our betting to a recognized pattern can be an enormous benefit. In checking for pattern frequency, the neural network concluded the following:
- A great deal of reliance can be placed on a Repeating Pattern or an Alternating Pattern in the games of roulette and baccarat. Only a moderate level of reliability was found for these patterns with craps.
- The Paired Doublet Pattern could be treated the same as a Repeating Pattern for all of the casino games. In other words, if the Paired Pattern is recognized, then we may treat it the same way as the Repeating one.
- The reliability of betting these patterns is highest in roulette, followed by baccarat, with craps coming in last.
It is one thing for a computer program to tell us that it has found patterns; it is quite another to translate this information into a practical and useable form. If, for example, the software is identifying patterns using hindsight, then this information has little applicability in casinos, as anyone can beat these casinos if "hindsight betting" was allowing. We asked the system to give us a reliable way of identifying these patterns so that this information would be of real use in a casino setting. After much hemming and hawing (our neural net had a mind of its own and didn't want to be limited in the number of decisions it was allowed to observe before pronouncing that a pattern was in progress), our system decided that only two decisions need be observed for a pattern to be identified on a slightly higher than random basis.
Using Patterns to Select Bets
The ability to recognize and exploit patterns gives us a powerful edge in attempting to beat these casino games. Does this mean that the laws of probability have been repealed? Of course not. What has occurred is that we have identified a situation wherein certain patterns, once they begin, are slightly more likely to continue for a limited number of decisions than pure randomness would indicate.
We will use an extreme example to illustrate this. We know that by using an unbiased pair of dice the number of pass and don't pass decisions in a craps game will approach fifty percent each if we have a large enough number of decisions. By "large", we mean hundreds of thousands or even millions of decisions. Does this mean that the pass and don't pass decisions have to be distributed evenly? It doesn't. It the course of reviewing our million or so dice decisions, we will find all kinds of unusual patterns, such as pass line decisions repeating 10, 11 or even 12 times consecutively. This is to be expected. What will surprise us is that certain patterns of dice decisions will appear at a higher rate than we would expect to find on a random basis.
Suppose that we have ten dice decisions where the color black (b) shows 50% of the time, and the color red (r) also occurs exactly 50% of the time. A purely random pattern might look like this: b r b b r b r r b r
A less than random pattern would look like this: b b b b b r r r r r
In each of these examples, there are five black and five red decisions. What our research has shown us is that when a non random pattern such as the strings of consecutive passes and don't passes in the second pattern above occurs, there is a slightly greater chance that the series will continue for up to seven decisions than pure randomness would indicate.
This does not refute the laws of probability. What it does show is that certain patterns of casino decisions, such as a repeating pattern, have slightly greater durability than we would expect if such a pattern was purely random. Quite frankly, we really don't have an explanation for this. But we have confirmed that it can be exploited most profitably in the casino games of roulette, craps and baccarat.
If this sounds a little strange to you, consider the results of a seasonality study of the stock market, conducted by The Institute of Econometric Research. Their study spanned 64 years of market data and showed that the first trading day of the week (except for holidays, always a Monday) was the loser of the week. In contrast, the last trading day of the week produced the most dramatic profit.
If you had owned stocks only on the first trading day of the week for a 64-year period, you would have lost more than 99% of your investment. If you had invested $10,000 in 1927, by 1990 it would be worth a mere $50.
In contrast, if you invested only on the last trading day of the week, then your $10,000 investment made in 1927 would have mushroomed to $2.77 million by 1990.
We offer no explanation for this phenomenon either. For our purposes we really don't care why there are certain aberrations in patterns of casino decisions, or why this pattern of daily seasonality occurred in the stock market. This is not a theoretical exercise. Our purpose is to find and exploit any phenomena which will give us an additional edge in making more money.
Randomized Pattern Selection
The Neural Strategy, which I mentioned earlier, goes much beyond the introduction to patterns I presented here. Using simple ways to identify patterns, a very powerful betting strategy was developed for the games of craps, roulette and baccarat. I have not found a more consistent way of selecting "even money" bets at roulette until now.