Recently I’ve been receiving emails about beating craps by watching the table and tracking numbers until the player sees a trend or pattern. This practice is known as ‘charting.’
Here is my thought on charting at the craps table: it’s a complete and utter waste of time, as far as beating craps goes.
There is possibly one benefit to charting numbers, and it’s actually a very good benefit. Charting may lower your Average Daily Theoretical Loss (ADT), if you don’t play while charting.
If you are the type of charter that doesn’t play until you spot a potential pattern, then tracking numbers will potentially lower your Average Daily Theoretical Loss (ADT) because you won’t be playing as much while you are waiting. However, if you seek to obtain this benefit, you can save yourself the extra effort and obtain the same benefit by just playing every other hand, or every second or third shooter.
In other words, the benefit obtained by charting – namely, the lower ADT – isn’t derived from charting, rather it’s derived from sitting out. It’s a cause and effect issue.
If you’re the type of player who plays a standard game and then hammers the pattern with larger bets, then charting will increase your losses because you will be making bets larger than your normal play would warrant.
THE GAMBLER’S FALLACY
The gambler’s fallacy is the mistaken belief that past results have bearing on future results, when each trial or hand is independent.
Some games have trials that are not independent. Blackjack hands are not independent of each other because the next hand’s probability and expected values are dependent on the composition of the deck, and the composition of the deck depends on what was dealt in prior hands.
For example, if on hand number one out of the shoe, the players draw 24 aces, then for the remainder of the shoe, a blackjack is no longer possible. If a blackjack is not longer possible, the players no longer have the possibility of being paid 3-2 on any of their bets.
The gambler’s fallacy only applies to games where each trial or hand is independent of each other. What I mean is that in a standard game of craps, each roll is independent of the last roll. It doesn’t matter if the number 8 has rolled zero times or 100 times in a row. The probability of the next roll being an 8 is always 5 in 36.
Mathematically speaking, that’s why charting is a waste of time. No matter what has happened in the past, the probabilities and odds do not change.
However, you’re thinking, ‘but RoadGambler, I’ve seen it work with my own eyes.’
In that case, let’s continue the discussion…
WHY TRACKING NUMBERS WILL NOT HELP
Let’s discuss a situation that probably many of us have seen at the craps tables…
Assume that the number 8 has rolled four times in a row. Does that indicate a trend that is now worthy of a bet on the 8?
Let’s now assume that you make a place bet on the 8 because you saw it roll four times in a row. What is the probability that you will win the 8 place bet? 5 to 6, meaning you will have 5 ways to win and 6 ways to lose.
If you haven’t spotted the trend, what would your probability of winning the same place bet have been? The same 5 to 6.
What if the 8 hasn’t rolled at all in the last 10 rolls, and then you decide to make a place bet on the 8? It’s still…you guessed it…five ways to win, and six ways to lose.
Visualize yourself in that moment. It’s easy to think in hindsight and say, ‘I should have done this or done that’, but it’s much more difficult in the heat of the moment. Actually, I argue that it’s beyond ‘difficult’, it’s impossible, unless you own a genuine crystal ball.
Selective Memory and Hindsight Judgement
Let’s stay with our prior example that the number 8 has rolled four times in a row.
While it may seem like a trend has come to life, once you have made that bet, what guarantee do you have that the trend will continue? You don’t.
If you now make the place bet on the 8 and the 7 rolls, some will say that you waited too long. The trend was already over.
However, if you make the bet and win, then you will be congratulated for spotting the trend.
It’s a pure case of Monday morning quarterbacking for believers of charting.
When Does the Pattern or Trend Begin?
This question of spotting patterns also begs the question: when does the pattern or trend begin?
In our previous example of the 8, does the trend begin when the 8 rolled one time, two times, three times, or four times? How about five times?
There’s just no way to know because the moment this alleged pattern starts, there’s no guarantee that it’ll either continue or be over.
The reason why there’s no way to know is because, as I stated before, no matter how many times a number has rolled, the probability of that number rolling again does not change.
THE ‘TREND’ IS NOT REALLY A TREND, EXPLAINED
The alleged trend that you see? That’s just normal probability distribution. Seeing the 8 roll x number of times in 10 rolls is no more special, trendy, or pattern-like, than seeing the 8 roll zero times or one time.
I’ll explain using a coin flip analogy. Coin flips are easier to use for illustration purposes because there are only two sides to a coin. The same concept applies if we are talking about two sides, six sides like a casino die, 36 sides like a pair of dice, or a die with 120 sides.
If you flipped a coin 10 times, and heads appeared twice in a row, very few people would say there’s now a trend for heads, or that something unusual happened. However, if you saw a cluster of 10 heads in a row, most people would now say that something trendy has happened.
But what if I told you that 10 heads in a row is no more special or trendy than two heads in a row?
If you do anything enough, eventually you’ll see 10 heads in a row. That’s not really a trend. That’s just normal probability distribution.
Let’s go back to that ‘cluster’ of 10 heads in a row. Let’s say that heads has flipped 9 times in a row. Is there a trend? At that very moment, you don’t know. If you decide to call the next flip as heads, in the long run, you’ll be right half the time and wrong half the time, statistically.
That means that for every cluster of 10 heads in a row, you’ll see two clusters of 9 heads in a row. That’s because once you’ve reached 9 heads in a row, the probability of heads again (on the 10th flip) is 1 in 2.
Similarly, for every one cluster of 10 heads in a row, you’ll see a cluster of 8 heads in a row four times, in the long run. Once you reach 8 heads in a row, the probability of getting 10 heads in a row is 1 in 4. So you’ll see four times more clusters of 8 heads in a row than you will be clusters of 10 heads in a row.
Going on, for every cluster of heads 10 times in a row, you’ll statistically see a cluster of 7 heads in a row eight times. Why? Again, because once you reach 7 heads in a row, your probability of reaching ten heads in a row are now 1 in 8, so you will see eight clusters of 7 heads in a row for every cluster of 10 heads in a row.
In other words, it’s normal distribution to see any cluster; be it 10, 9, 8, 7, etc, and they’re all going to appear in proportion to their probability of happening. You don’t know if you’ll be part of the 10, 9, 8, 7, 6, 5, 4, 3, or 2 cluster.
The exact same thing applies to craps. While it appears that a cluster or a trend is happening, you don’t know which cluster you will be a part of.
In the end, there is no cluster, trend, or pattern because it’s all normal distribution.
Just think of it this way: 10 heads in a row is no more unusual or no more of a trend than 1 head because the probability of heads happening 10 times in a row is directly proportional to one heads happening. You won’t know which trend or cluster that you will be a part of.
The same concept applies to dice. Going back to the box number of 8 that started this article…
If you see the 8 roll six times in a row, you’ll also see the 8 roll five times in a row, four times in a row, three times in a row, two times in a row, etc.
The cluster of six in a row will be way more common than five times in a row, which will be proportionately more common than four times in a row…and so on and so forth.
You just won’t know which cluster you’ll be a part of.
That’s why, in the end, charting is a waste of time: You never know which cluster you’ll be a part of because these clusters are nothing more than your mind telling you that there are clusters.
Humans have a propensity to see patterns where patterns don’t exist. It’s a concept known as pareidolia, which is the reason why people see Jesus in their toast and faces on the sands of Mars.
Pareidolia is a strong force at play when you are gambling. All those alleged patterns you see are nothing more than your mind trying to make sense of something that is completely nonsensical. If you let your mind fool you, it may cost you money in the form of larger bets, when larger bets are no warranted.
At the end of the day, I’m not telling you how to play. If you enjoy looking for trends or patterns, then by all means, do it. Just be aware of your reality.
All those patterns and trends you see are nothing more than a mirage in the desert.
Let me know your thoughts, questions, or criticisms in the comments section below. FYI, I just got back from a four day trip, so I’m catching up to your comments. Thanks for everyone’s thoughtful input on the prior topic of tipping. I think it’s an important topic to anyone who cares about this wonderful game.
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