Problem gambling & Science: chapter #1

Motivation

Problem gambling aka ludomania is (according to Wikipedia) “an urge to gamble continuously despite harmful negative consequences or a desire to stop”. I’m definitely not a psychologist but after 15 years behind casino systems and slot machine math (while having obtained the casino industry’s top certifications), I can certainly provide you with a few insights:

• The addiction can take time to develop, remaining unnoticeable for a long time or until the financial consequences can’t be hidden anymore.
• Magical thinking (like relying on faith, luck, or esoteric energy) makes vulnerable individuals even more vulnerable. Sometimes this is hard to argue without invading a very private and intimate zone.
• Many problem gamblers use pseudo-science for justifying their behavior. They think and even state to know something special. Sometimes it’s about knowing a “reliable” method for obtaining a positive balance. Sometimes they state to have the skill of predicting when a prize is going to be awarded.
• Government authorities warning the people about the existence of ludopathy is good a start but not everything. People need to be aware of the risk but more effective preventive actions can be taken. Ie: A basic course on math foundations, especially on probability, can become an effective vaccine for the most common biases related to magical thinking.

This series of articles aims to contribute by explaining a few technical and mathematical aspects of casino games and to debunk some frequent misconceptions and urban myths.

NOTE: I welcome your feedback, especially from math teachers that would help me to make these concepts easier to assimilate.

Fact #1: What really happens when you hit the slot machine “Spin” button

No matter what your previous idea was, trust me, this is what really happens:

1. The game software calls a subsystem (sometimes it’s a separate hardware device) called Random Number Generator (RNG) to obtain an Integer number between X and Y. This will be used to determine the reel stop position.
2. The game software takes the resulting integer number and uses it as an index for looking for a symbol contained in a list of symbols called “virtual reel“.

Steps #1 and #2 are repeated one time per each reel (usually 3 or 5 reels) until the stop position (a symbol ) for each reel gets determined.

3. All the reels stop. The game software builds an ordered sequence of symbols by taking one symbol per reel from the central line. (simplifying to one line game)
4. The game software compares the sequence of symbols with all the entries from a table called “Pay Table”, which maps winning combinations with the prize amount.
5. If the sequence of symbols matches a winning combination, the prize gets awarded. You get instant visual and audible positive feedback.
6. The information from your bet and the prize, if any, gets stored in the game’s persistent memory for accounting and control purposes.
7. Well…there’s no #7, and here is where most people fail to understand how a slot machine works. Absolutely nothing from this spin will influence the next spin.

Myth #1 “Cold and Hot slot machines”

Ok, let’s expand on #7 as this is one of the most common superstitions. The player thinks that the result of the next spin is somehow influenced by previous results. If the machine hasn’t paid a prize for a long time then it will do it soon. Then this “soon” becomes “maybe in next spin” and so.

The cognitive bias resides in the act of attributing certain subjectiveness to inanimated objects. In the case of slot machines, the player is attributing certain aspects of a human personality to them. If human, the machine will implicitly hold the desire of returning to a certain (economic) balance by taking a steering decision (locus of control). Of course, this is totally wrong as the machine, and especially its software does not take any decision based on the previous results or future events.

Let’s say that you have the capacity of completely deleting the machine’s persistent memory (RAM Clear) and that the odds of getting a “bar-bar-bar” combination is 1 in 1000. So you spin one time, without success, a then clear the memory. The odds for the “bar-bar-bar” remain the same: 1 in 1000. Just like when you flip a coin and both sides have 50% of chances on every round.

You may be thinking about how does the casino hold a predictable revenue and business model if everything seems to be left to chance. The reality is that the economic balance is already there, but instead of being determined by algorithmic decisions during the gameplay, it has been guaranteed at game math design time. This work is done by a mathematician who crafts a Probability & Accounting Report (PAR) sheet precisely describing the virtual reels and the paytable. In the long run, after tens of thousands of spins, the theoretical earnings stated in the PAR sheet will match the actual earnings in the game accounting meters.

Again, in the long run, a casino will usually hold between 15% and 7% of what has been bet on the slot machine (coin-in). This “long-run” usually translates into a few months or more on an average gaming floor.

This is the base of probability and statistics. What happens to the population happens to the sample as the sample size increases. Theoretical earnings which were estimated based on a population of millions of spins will become the actual earnings after a significant number of spins. This profit predictability is the cornerstone of the slot machines industry.

This article is dedicated to a casino manager who used to arrive several hours before the opening just to put tons of money in those “cold” slot machines to get them “stabilized” ( I won’t give names)

Play safe!