Archive for the ‘Gambling’ Category

Ever wondered how a slot machine works?

February 10, 2008

I’ve heard many theories over the years about how slot machines work. I’ve never heard a layman’s description that was right. Not even once.  I’ve heard some awesome theories too.  My favorite was the cab driver who claimed that the machine had electronic scales in them to weigh the coin hopper (he didn’t use that term).  When the hopper is “heavy” it’s time to pay a few coins out.  When it’s “light” the machine goes into accumulation mode.  Simple.  Effective.  Completely wrong.

Here’s the real scoop.

The most confusing thing about slot machines is the question of how they control the payout so that the operator makes money. It seems intuitive that if a machine has been paying out, then something must be tweaked or manipulated to “cool it down” so that it doesn’t pay out too much. This is the fundamental flaw in the general understanding of slot machines.

In reality, every spin of a slot machine’s reels is independent of the spin that went before. There are some caveats to this regarding bonus games and special accumulating features, but for the sake of this discussion it’s easier to work without those extras.

A slot machine has many similarities to tossing a coin. If you toss a fair coin and get 10 heads in a row, surely you’re more likely to get a tail on the 11th throw, right? Actually, and as you probably realize, no. The throws are independent. The same is true of slot machines.

It is the math behind the design of a slot game that ensures, over the long run, an operator will make a profit. The simplest possible explanation is that if you paid a dollar for every possible combination of symbols and got paid prizes accordingly, you would have spent more than you won.

To go back to the example of tossing a coin, let’s imagine a game. The rules of the game are that, each time you play, I toss a coin. If the coin lands heads, you get paid $1.50. If it lands on tails, you get nothing. I charge you $1 to play this game.

The two possible outcomes are heads, for which you get $1.50 and tails for which you get nothing. So the total amount you get in return for purchasing all possible outcomes is $1.50 ($1.50 + $0). However, it would cost you $2 to buy all (both) the outcomes. So the game is a losing proposition. The return-to-player (RTP) of this game is $1.50 / $2.00 or 75%. Most slot machines have an RTP upwards of 85%. When Casinos in Vegas advertise the “loosest slots on the strip” they’re referring to machines that have a very high RTP.

Let’s extend this to a simple, single reel slot machine. This would obviously be a very boring game to play, but bear with me.  This should provide a foundation to explain more complex games. The game has three symbols: R, G and B. The reel has only one instance of each of these symbols, so it is three symbols long. The game is as follows. The reel is spun and comes to a stop, the player will be paid (or not) based on whatever symbol is shown on the middle position. If the symbol is R, the player gets paid $2, if it’s G they are paid $0.50 and if it’s B, they get nothing.

Working from our previous cost-per-play of $1, it will cost us $3.00 to purchase all possible outcomes and our total return from those purchases would be $2.50 (R:$2 + G:$.50 + B:$0). This game has an RTP of $2.50 / $3.00 or 83%.

Let’s step the game up another level and duplicate the first reel. We now have two reels, each with R, G and B in that order. We now consider the outcome of a game to be the two symbols that are show, side by side, on the middle position of each reel. In gaming parlance, this is usually known as a line. In this case, we’re talking about the center line.

On the first reel, the middle position can have any one of three outcomes (R, G and B) with equal likelihood. The same is true of the second reel. This, in combination, gives us 9 unique and equally like outcomes (RR, RG, RB, GR, GG, GB, BR, BG and BB). Let’s adjust our “pay table” and say that we’ll pay the player $5 for RR, $2 for GG and $1 for BB.

Once again, to calculate the RTP, we charge the player $1 for each possible outcome, for a total cost of $9. The total return is $8 (RR: $5 + GG: $2 + BB: $1). The RTP is $8/$9 or about 89%.

I’ll give one more example but I hope, by now, that the underlying mechanism is clear. The game is set up so that, probabilistically speaking, each spin you play is a losing proposition. The numbers aren’t adjusted as the game goes on, they’re set up well in advance at the desk of a mathematician in an office far from the bright lights and scantily clad cocktail waitresses (ah Maria … *sigh*)

As a final example, let’s look at a very simple three reel extension of the two reel game we designed above. Duplicate the R, G, B reel again to give us three reels, all with R, G and B symbols in that order. Again, we pay out depending on the combination of three symbols shown on the horizontal line through the center of each reel on the display.

In this game, each reel has three possible outcomes and there are three reels, so the total number of possible outcomes is 27 (3x3x3) or (RRR, RRG, RRB, RGR, RGG, RGB, RBR, RBG, RBB, GRR, GRG, GRB, GGR, GGG, GGB, GBR, GBG, GBB, BRR, BRG, BRB, BGR, BGG, BGB, BBG, BBG and BBB).

For simplicity let’s assume we pay $15 for RRR, $8 for GGG and $3 for BBB. This game will cost our imaginary player $27 to buy all possible outcomes and get them a return of $26 (RRR: $15 + GGG: $8 + BBB: $3). This comes out to an RTP of $26/$27 or 96.3%. That return is much higher than many (most?) Casino games out there, so we would probably have to lower the RTP so the Casino’s take is a bit higher. How would we do this? There are two ways to accomplish it either lower the amount paid for prizes or decrease the likelihood of those prizes. Decreasing the likelihood of prizes involves adjusting the distribution of symbols on the reels and is beyond the scope of this little rant. Lowering the payout for RRR from $15 to $14 would lower the RTP to $25/$27 or 92.6%.

The only difference between our really simple slot machine and one you would play in a Casino is complexity. Real slots have reel strips that are dozens of symbols long and have about 10 or so different symbols. The number of possible combinations are in the tens of millions. However, the fundamental slot principle still applies: if you purchased all possible outcomes and got paid prizes accordingly, you would have spent more than you won. Each spin is independent and a bad bet for you.