Reader Darrell Q sent me this email, and with his permission, I’ve published it here. This is a topic of relevance to many gamblers, whether recreational or professional.
Can you write an article about dealing with losing, whether it be one session, one trip or 3 months or longer?
If the house always has the advantage, am I a sucker for playing craps 2x a month?
Out of your last 10 trips, how many were winning sessions and how many were losing? For me 7 were losing and 3 were winning…..
Do you ever have regrets after a losing session? How do you mentally deal with it?
There are multiple aspects from which one could approach the question. I’ve decided to approach the question holistically and look at why players have severe losses that question their desire to pursue gambling as a continuing hobby.
It’s true that casino gambling if played straight up, is a negative expectation proposition. Gambling, as a form of entertainment, comes with expenses, which manifests itself in the form of losses.
It’s my theory that the vast majority of losses that devastate bankrolls, and subsequently question a gambler’s desire to gamble, comes from one main culprit: tilt.
Tilt is simply the process whereby a gambler no longer employs optimal strategy due to psychological stimulus. Tilt will cause you to bet more and play in a way that is not optimal. Tilt will cause you to start betting more than you would normally bet or it will cause you to deviate from your normal betting patterns or strategies. Most gamblers have heard of tilt and immediately associate tilt with ‘loser’s tilt’, where a player changes their play due to losing. Winner’s tilt is just as dangerous to your bankroll, and I will demonstrate this in Part 2.
While it’s true that the house edge is certainly what gives most casino games their negative expectation, the house edge alone does not explain why so many bankrolls are destroyed and left at zero or near zero, thus spurring the gambler to consider quitting. The house edge is the grindstone that grinds down your bankroll, while tilt is the hammer that finishes off your bankroll.
In part 1 of this 3 part series, I am going to explain why you must understand that the math applies to everyone. Saying that the math ‘is only theoretical’ is a dangerous way to gamble. Part 1 lays the foundation for understanding why you, too, are susceptible to the laws of statistics. Part 1 will make the case for why you are not exempt from the premise in Part 2.
Then in Part 2, I will pull away the illusion of your losses and show how the house edge grinds away at your bankroll, but show you how tilt brings the hammer to your bankroll. Casinos make it hard to understand variance. Human beings have a hard time perceiving the effect of a 5% house edge, much less a 1% house edge. So I am going to break it down in Part 2. Again, if you think the breakdown in Part 2 doesn’t apply to you, then read Part 1. Too many players think that it’s only ‘math’ and that the math doesn’t apply to them.
In Part 3, I will attempt to show how you can teach and condition yourself to avoid tilt. I can’t teach you how to avoid tilt. Some of the best gamblers in the world admit to being susceptible to tilt. It’s human to want to tilt. I can only show you the process and information so that you can control tilt. You will never ever completely rid yourself of the desire to tilt, but if you can control tilt, you can limit the affect that it has on your bankroll.
To control your desire to tilt, you should be equipped with the understanding of ‘why’ and ‘how’ tilt destroys your bankroll. Just have an amorphous understanding is not enough.
As they say, knowledge is power.
IT’S ONLY HUMAN: THE INABILITY TO PERCEIVE STATISTICAL REALITY
Many players lose and then blame many different factors, such as not walking away when they were up, for example. But such factors do not fully explain the presence of severe losses.
Excuses such as ‘not walking away while up’ ignore the fact that all play is statistically continuous. If during your vacation, you play 20 hours straight or 20 hours broken up into ten different 2-hour sessions, the dice do not know how you partitioned your sessions. The dice also do not know if you left each session up or down. When the player returns to the table, his likelihood of winning or losing is no different if he had remained at the table earlier.
It’s easy to blame everything and everyone except the real culprits who are the twin destroyer of all bankrolls: the criminal mastermind known as the ‘house edge’, and his accomplice ’tilt’. Because players have a hard time comprehending how a small theoretical house edge can damage a bankroll so badly, they tend to blame other factors than the house edge; and when they take their entire bankroll to ruin, they conveniently ignore that tilt may have had a hand in the destruction.
Regardless of how small the house edge, eventually, the theoretical house edge will almost always becomes reality and manifest itself in the form of real losses. Once the gambler’s bankroll has been grounded down, tilt then finishes the job. Before we talk about tilt, let’s turn our attention to the house edge. We will get to tilt in Part 2.
Let’s explore why the theoretical probabilities are ultimately unavoidable.
Poisson and Binomial Distribution: the explanation for why the theoretical becomes reality
This question is often asked: when does the theoretical become the reality? The short answer is that it can become reality at any time, but the more you play, the more probable that the theoretical becomes the reality.
To keep things simple, first, let’s talk about a fair coin toss (I used binomial distribution in this article, in case someone wants to check my math). To keep things simple for the calculations below, when I refer to an event as a ‘not heads’ equivalent, I am just referring to a flip that resulted in tails (so five flips with 0% heads means that five tails won the flip)
In any fair coin toss, the odds of heads appearing is 50%. Obviously, that doesn’t mean that if you flip the coin 10 times, that heads will appear 5 times, like clockwork. If we flip the coin 10 times, heads could appear 0% of the time, 100% of the time, or any probability in between 0% and 100%.
There is usually a deviation from the expected result that 50% of the flips will be heads.
The more trials are executed, the more probable that the expected result will become a closer reality. In other words, it’s all relative. If you only flip the coin 10 times, your results will deviate from the 50% result more than if you flipped the coin 100 times. If you flip the coin 100 times, the results will probably deviate more than if you flipped the coin 1000 times. If you flipped the coin 1000 times, your results will probably deviate more than if you flipped the coin 1 million times.
Eventually, with enough trials, the expected result will eventually become a nearly unavoidable reality, and any significant deviation from the expected result becomes more improbable.
How this applies to craps (or really any game)
Let’s now apply the above analysis to the game of craps.
In craps, the house has an edge on every single bet that is not an odds bet.
On the pass line bet, the house will have an edge of 1.41%. This means that if the gambler places $100,000 worth of action on the pass line, then he is expected to lose $1410.
If the gambler only plays 10 hands, at $10,000 per pass line, the gambler’s final result will deviate from the $1410 expected loss wildly. The gambler may lose every pass line bet or he may win every pass line bet. There are so few hands, that it’s not unrealistic that he wins everything or loses everything.
If the gambler plays 100 hands at $10 per pass line, then the deviations in his result will most likely be less wild than if he only played 10 hands. It’s less likely that he wins every hand or loses every hand. Also, it’s more probable that the actual result is closer to the expected loss of $1410.
Finally, if he plays 10,000 hands at $10 a hand, it’s exceedingly and astronomically unlikely that he loses every hand or wins all the hands.
Just like how the extreme possibilities (of losing every hand or winning every hand) become less likely with more trials, the possibilities in between the extremes become closer to reality, and any significant deviation from the expected results becomes more improbable with more trials.
So if you roll the dice only 36 times, you may win a lot of money because the seven appeared only once or twice, and not the expected 6 times. But if you roll the dice 100 million times, the probability of the 7 appearing somewhere in the neighborhood of 16.66% (1 in 6) of the time becomes nearly unavoidable. You might get a little deviation, like 16.5% or 16.75%, but it’s highly improbable – on a galactic scale – that the 7 will only appear 14.2% of the time (1 in 7) over 100 million random rolls. We’ll get to that below.
DIFFICULTY OF COMPREHENDING THE PROBABILITIES, DEMONSTRATED
When I refer to the probabilities in between the extreme events, I am referring to the possible events in between 0% and 100%.
With the coin flip example, it’s usually easier to comprehend concepts if illustrated from the extreme positions. As an example that you yourself can test…
First, most people will understand that it’s extraordinarily unlikely that in 400 coin flips that heads will never appear or appear all 400 times. People may not know the numbers involved, but they have an intuitive sense that it’s highly improbable.
Secondly, the average person also understands that while either extreme event is highly unlikely, both are still statistically possible events, no matter how unlikely.
Thirdly, most people can understand that both extreme events are in direct proportion to each other. Even without knowing the actual probability, most people will intuitively know what both extremes have the same probability of appearing. This just means that the unlikely probability of heads appearing 400 out of 400 times is the same as tails appearing 400 out of 400 times.
But the average person has a much more difficult time comprehending the relationship between the possibilities that lie within those two extreme events. This is how casinos are able to market games which have horrible payouts, but yet people still play those games.
This is also why most gamblers are slow to blame statistics for their losses.
If you would like to test my hypothesis, ask the average person, who you know, about the following coin flip game. Or test it on yourself. How well do you understand the following statistical relationships?
Virtual coin flip that is fair, with the chance of heads at 50% and the chance of tails at 50%.
- Bet One
- Coin is flipped 1 time.
- Bet that heads will appear.
- If the casino wanted to offer true odds (100% return), what should the casino offer as payout that heads will appear on a single flip?
- Answer: even money, a.k.a. 1-1
- Bet Two
- Coin is flipped 40 times
- Bet that heads will appear 22 or more times in the 40 flips.
- What payout is needed to make this game have almost a fair payback that would be comparable to most casinos games?
- Answer: Probability of 22 or more heads in 40 flips is 31.7%, so a 2-1 payout would be like most casino games, leaving the casino a nice edge, but not out of the norm for new casino games.
- Bet Three
- Coin is flipped 400 times.
- Bet that heads will appear 220 or more times in the 400 flips
- What payout is needed to make this game have almost a fair payback, comparable to most casino games?
- Answer: 38-1
Most people will understand Bet one. It’s a simple 50/50 proposition, and even money offered would be a true payout.
Bet Two is a set up for Bet Three.
Bet Two typically conditions the person into grossly underestimating the probability presented in Bet Three. In 400 flips, the realistic probability of more than a mere 20 more heads appearing seems to be not that difficult. It’s only 20 more heads, after all, and we’ve already established that the probability of winning Bet Two is roughly 31.7%.
However, the expansion from 40 trials to 400 trials deceives most people into not realizing that as the trials grow, so does the difficulty of ‘hitting’ the bet, if the same proportions are applied (22 out of 40).
The probability of 220 or more heads appearing is roughly 2.55%, which justifies a payout of around 38-1.
Most people to whom I asked the above questions stated numbers far lower than 38 – 1, with most in the single digits.
This is how casinos can offer games that have extraordinarily high house edges and people will still play. Without mathematical training, the average person not not comprehend the statistical realities that lie within the extreme events; those statistical realities are somewhat invisible to most people.
Then add in nearly imperceptible factors – such a 1% house edge – and the understanding of the probabilities becomes even murkier for most people. This is how casinos make money. To the uninitiated, it appears that the casino could make more money by having games with a 40% house edge, or even a 80% house edge. But the casino would actually make less money if it used a bizarrely high house edge. The reason is that the house edge would be immediately perceptible and understood. That would be an easily recognizable extreme. People would gamble less or not at all.
With a 1%, 5%, or even a 10% house edge, it’s rather difficult to comprehend that a house edge is taking a bite out of the gambler’s bankroll.
If you can’t perceive the unavoidable statistical reality of the game, then you will continue to gamble as if the house edge did not exist. You will blame – and subsequently be on guard – against the wrong enemy. The practical manifestation of this false accusation is that you increase chances of losing and you increase the amount that you lose.
The problem as it relates to craps
Casting aside all arguments of dice control or influence, the 7 will appear 1 in 6 times, on average. All house edges in craps are based off the 7 appearing 1 in 6 times.
Most craps players hope to have a good 7 to rolls ratio that is better than 1 in 6, meaning that the 7 is less like to appear 1 in 6 times. If this happens, the player will most likely win.
Let’s apply this hope – that the 7 will appear fewer than 1 in 6 – times to a craps game. Let’s also say that the player likes to play for about 20 minutes and so will roll the dice 36 times. I also coincidentally play sessions for an average of 20 minutes.
If anyone wants to check my math, I used binomial distribution. In each of the 36 rolls, I am referencing all rolls. The math below would be applicable regardless if one considers the come out roll or not. I am just stating the probability of the 7 appearing. So if one wanted to just count the post-come out rolls, the same math applies for all the post-come out rolls (the dice do not know if you are on a come out roll or post-come out roll).
For disclosure, I used, as a percentage, the probability of the 7 appearing to be 16.66%, while all combinations of non 7s to be 83.34%.
- Player Bob of expected luck
- The player will be able to roll 30 or more times without a 7 approximately 60.7% of the time.
- This is the same as saying that Bob will roll six 7s in 36 rolls.
- This is the expected result of most craps games, with the 7 appearing 6 times in 36 rolls. Most players might refer to this as a ‘choppy’ table.
- Player Mary, who has good moderate luck
- The player hopes to get lucky and have a good night. The player is hoping that the 7 appears only 5 times in 36 rolls, for a modest reduction in the number of 7s appearing.
- The probability of the 7 appearing 5 times or fewer in 36 rolls is a reasonable 43.1%.
- This is a mildly lucky table
- Player George is hot!
- This is a hot player and in 36 post rolls, only rolls the dreaded 7 one time.
- This is going to happen 1.15% of the time.
Let’s now say that Mary, the moderate luck player above, is on vacation. So let’s expand those 36 rolls to 3600 rolls, which is very possible over the course of a vacation. Let’s now apply the math and see what happens.
- Player Mary on vacation
- Using the same situation as above, where Mary hopes to have the same 7s ratio of being able to roll a modest 31 times or more without the 7 appearing.
- However, she is now playing over the course of a vacation, so she will roll or bet on the 3600 rolls of the dice.
- Mary hopes to roll the dice 3100 times or more without the 7 appearing in 3600 rolls.
- This is the same 7’s to roll ratio as 31 times or more without a 7 in 36 rolls, meaning she hopes the 7 appears only 5 times per 36 rolls on average.
- The probability of this 3100 rolls or more without the 7 appearing in 3600 rolls is now a staggeringly low .000280311%.
- In 3600 rolls over the course of a vacation, the odds of Mary seeing more than 3100 rolls without a 7 is 1 in 357,150 approximately.
While the ratio of 7s is not unreasonably improbable with fewer rolls, once the gambler starts with more rolls, a ratio of 7s that seemed probable at first, all of a sudden becomes a distant long shot.
Any deviation from the expected result is improbable that ‘luck’, as it’s commonly understood, is not much of a factor anymore.
In Mary’s vacation case, if she were to expand her vacation to a month and play at the same pace (or factor in her lifetime play), any significant deviation from the expected result becomes so unlikely that Mary’s losses become practically similar to what she does when she goes to the supermarket and pays a fixed price for her groceries. The theoretical house edge has become so unavoidable that, if there was a way, Mary may as well have just added up her total action, deducted the overall average percentage house edge from her total action, and written a check to the casino.
This is an important lesson to be learned if you are playing craps or any game for any amount of time. Once you start playing more, the probabilities become more and more unavoidable, and you are less and less likely to be even moderately ‘lucky’ over the entire trip.
This is why the house edge is unavoidable.
Indeed, most gamblers, when they lose, do not blame the house edge. I do not recall the last conversation with a gambler who blamed the house edge for his losses.
In the end, your results at the table are a natural product of unavoidable statistics.
No human is exempt from the laws of statistics, no matter where on the probability spectrum your results lay.
The player must understand that your losses come primarily from the house edge, and that the house edge is unavoidable. However, as I stated in the beginning, the house edge, while responsible for grinding away at your bankroll, does not entirely explain why a large bankroll can go to ruin.
In Part 2, I will show you how the house edge grinds away at your bankroll, and then apply tilt to the whole party.
It’s important to understand these concepts because then you can turn the information around and use it against your opponent. Ultimately, what is unavoidable for you is also unavoidable for the casino. You just have to be on guard against the correct enemy.