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Ask the Slot Expert: Relativity and the perception of time in the casino

8 January 2020

A century ago a solar eclipse proved one of the predictions of Einstein's General Theory of Relativity: the gravity of massive objects can bend light. Astronomers compared the positions of distant stars in the night sky with their positions during the eclipse, when the sun was between the Earth and the stars, and the stars moved the exact amount predicted by general relativity.

Einstein published two theories of relativity. Special relativity, which dealt with movement at a constant speed, in 1905, and general relativity, which dealt with acceleration and gravity, in 1916.

Special relativity is about the structure of spacetime -- the three dimensions we're used to dealing with plus time. We are constantly moving through spacetime, even when we are at rest. All of our movement is through time while we are at rest. Special relativity tells us, though, that when we move through space, we move a little more slowly through time.

Consider a car on a highway. At first the car is traveling due north. All of the car's motion is moving it farther north.

The car exits onto a highway going northeast. Now some of the car's motion is moving it farther east and some is moving it farther north. The car is making less progress northward because some of its motion is to the east.

When the car is traveling northward is like when we are at rest. All of our motion is through time. When the car is traveling northeast is like us in motion -- some of our movement through time is now used to move us through space.

This is known as time dilation in special relativity. Moving clocks tick more slowly than a stationary clock.

This may sound off the wall, but consider this scenario.

You and a friend are riding bicycles at the same speed directly across from one another. You toss a tennis ball to your friend. Both of you see the ball move in a straight line from one to the other.

There is a drone hovering overhead. The picture from the drone shows the ball moving diagonally from you to your friend.

All observers simultaneously see you through the ball and simultaneously see your friend catch the ball, but the ball travels a greater distance according to the stationary drone.

There are no forces acting on the ball to make it speed up, so the ball's speed has to be the same for all observers. We can't change the distance the ball traveled for the different vantage points. The only thing left to change is time. Time must be moving more slowly for the riders as compared to the drone to give the ball more time to cover the greater distance as observed by the drone.

General relativity describes how gravity affects time. Objects warp the spacetime around them and gravity is how we experience this curvature of spacetime.

General relativity also deals with the passage of time. Gravitational time dilation says that clocks run more slowly the closer one is to the object.

Experiments have proven both types of time dilation. In one experiment, two atomic clocks are synchronized. One is taken to the penthouse of a building and one remains on the ground floor. The clocks are brought together again after a few days and the time on the clock that was in the penthouse was later than that on the clock that remained on the ground floor. Time passed more quickly in the penthouse than on the ground floor.

In another experiment, two atomic clocks are synchronized and one is flown in an airplane for many hours. The time on the traveling clock differed from that on the stationary clock by the amount predicted by the gravitational time dilation due to the altitude of the plane and the time dilation due to the speed of the plane.

We experience both types of time dilation every day -- your head is actually aging a little bit faster than your feet -- but we're talking about nanoseconds (there are one billion nanoseconds in a second). The effect is miniscule.

There is a situation, however, in which you depend on relativity and time dilation. The Global Positioning System accounts for the effects of gravitational and velocity time dilation in its calculations that determine your position.

Einstein's theories of relativity deal with the actual passage of time. My theories of relativity in the casino deal with our perception of the passage of time. Just like an hour in class can seem to pass more slowly than an hour at the movies, time in the casino seems to pass more slowly or quickly based on our point of reference. Einstein had to use thought experiments to develop his theories because at the time we did not have clocks accurate enough to test his theories. I was able to develop my theories based on my actual experiences in the casino.

Time passes more quickly the higher your credit meter.

I frequently have to pass time waiting for a drawing. Time flies by when I don't have to feed the machine. When I run out of credits, though, I check the time whenever I have to put more money in the machine. How much longer until the drawing? I hope I won't have to put more money in. A few times my luck has been so bad that I found other ways to pass the time, like taking a few laps around the casino or finding a comfortable chair and reading the newspaper on my phone.

The passage of time is affected by how many points you've played.

This theory is more complicated than my first one because time slows down and then speeds up again.

I frequently set a goal for the number of hands I want to play that day. For this example, I'll play 2000 hands of dollar video poker at $1 = 1 point, so my point goal is 10,000 points.

The first 1000 points fly by and I think that I'll have my 10,000 points in no time at all. I check my point total at what seems like enough time to be almost halfway done, and I discover that I have only 3000 or so points. The point meter that had moved so quickly in the beginning has now slowed to a crawl.

The points continue to slowly accumulate until I reach 5000-6000 points. Then the points start to add up more quickly and the pace continues to increase as my point total climbs. The last few hundred points add up so quickly that I sometimes overshoot my point goal.

To sum up, points accumulate quickly in the beginning, then they accumulate more slowly until a little after the mid-point, and then they accumulate more and more quickly the closer you get to your goal.

Both theories operate at the same time. If I start with a big credit balance or hit a number of good hands and never have to feed the machine to reach my point goal, the slowdown in the middle of my point quest won't seem so bad. If I run out of credits, especially during the second quarter slowdown, I check to see how many points I've earned each time I feed the machine and it seems like it will take forever to reach my goal. Even running out of credits during the last 1000 or 2000 points will cause the point meter to lose its momentum and the points add up more slowly until I'm done.


Maybe you think my theories of relativity in the casino are a bit wonky. Coincidentally, here is an email I received while I was working on my theories. I'll comment only that in past columns I have addressed the fact that the Random Number Generator function in a slot machine is more accurately called a Pseudo-Random Number Generator because the numbers are not truly generated at random. The stream of numbers from the function pass many of the tests for randomness and are sufficient for use in a slot machine.

Your analogy although elaborate is not equal to what actually happens inside a slot machine.

There is a chip in there called an RNG or random number generator.

In the purest sense, computers can't generate truly random numbers. They generate pseudo random numbers based on a programed algorithm. because a pre-programmed algorithm is the basis upon which the random number is generated, there is no way it can be random. Additionally, computers are limited to a total of 36 numeric digits separated by a decimal point.

Because the slot machine is going to select a number that is pseudo random generated, and based on a pre-programmed algorithm, only 18 digits can be used. All of the digits past the decimal point are discarded. It is possible that prior to discarding the digits after the decimal point, that number is used to round up or down, the digit closest to the decimal point. It is also possible that rounding that one digit up or down, can affect every other digit to the left of that.

It is a fact that neither humans or computers can be random. We are both deterministic machines. in both cases this is due to our hardwiring and programming. Take a couple of hundred of leaps forward, and one can argue that nature isn't deterministic at a quantum level. At a quantum level we measure random events like atomic decay to get random seed numbers. Since quantum physics or mechanics is not involved concerning slot machines, this can be discarded.

Everything a computer or human does is predictable to some extent. Therefore neither can produce truly random numbers. Instead, produce pseudo or fake random numbers. In order to get truly random numbers, we have to look to nature and hope nature doesn't have a bias.

Although we are 100% sure that anything in the universe is truly random, scientists agree that when it comes to fluctuations of the smallest particles such as quarks or radioactive decay, randomness occurs. As we observe the events, a random seed number is derived. However, the split second we appoint a computer algorithm to the seed or get too involved as humans, we all but remove the true randomness from the result.

Randomness is important in everything from the lottery to security software, but in the practical sense, a pseudo random number with a truly random seed, typically gets the job done, sometimes even better than a truly random number. From here the discussion on determinism and randomness gets more philosophical and technical. In as much, it would not apply to slot machines.

Just for a little fun try this. If we could determine where every subatomic particle is and is going to be then we would be able to teleport or possibly time travel. At that point, nothing would be random.

John Robison
John Robison is an expert on slot machines and how to play them. John is a slot and video poker columnist and has written for many of gaming’s leading publications. He holds a master's degree in computer science from the prestigious Stevens Institute of Technology.

You may hear John give his slot and video poker tips live on The Good Times Show, hosted by Rudi Schiffer and Mike Schiffer, which is broadcast from Memphis on KXIQ 1180AM Friday afternoon from from 2PM to 5PM Central Time. John is on the show from 4:30 to 5. You can listen to archives of the show on the web anytime.

Books by John Robison:

The Slot Expert's Guide to Playing Slots
John Robison
John Robison is an expert on slot machines and how to play them. John is a slot and video poker columnist and has written for many of gaming’s leading publications. He holds a master's degree in computer science from the prestigious Stevens Institute of Technology.

You may hear John give his slot and video poker tips live on The Good Times Show, hosted by Rudi Schiffer and Mike Schiffer, which is broadcast from Memphis on KXIQ 1180AM Friday afternoon from from 2PM to 5PM Central Time. John is on the show from 4:30 to 5. You can listen to archives of the show on the web anytime.

Books by John Robison:

The Slot Expert's Guide to Playing Slots