Slot machines are the workhorse of the modern casino. They take up less space than blackjack tables, don't take breaks, and allow for up to 600 spins per hour.
- [Instructor] I'd like to start this movie with an image of the workhorse of the modern casino, the slot machine. The slot machine has a very simple design. The original design concept was to have a slot at the top to accept the coin the player puts in, a secure box at the bottom to hold the coin, and something to look at in the middle. Sometimes people win, but most of the times they don't. This is a great story, I have no idea if it's true, but I don't care.
Slot machines are efficient moneymaking devices and they have many advantages, of which I'll highlight three. The first is they don't take breaks. They take up less space than a blackjack table and certainly less than a roulette or craps table. And they don't want to steal from the house. Most individuals in the casino industry are honest, believe it or not, but there are a few who are not. Slot machines by themselves are neutral workers and they will keep going for as long as you'd like them to. Another thing to note with slot machines is that profit per square foot is much higher than it is on other games.
If we take a look a the four basic games that you'll find in most casinos, and those are blackjacks, craps, roulette and slots, you'll see that by far there are more slot machines than any other unit. However the win per unit per day is much lower. And you can see that the daily unit revenue per square foot is also quite low. In fact it's only really in close comparison to blackjack, whereas craps and roulette are significantly higher. But if you look in the final column to the right you'll see that the daily unit profit per square foot for slot machines is double that of craps which is its nearest competitor.
Blackjack is lowest and roulette is a little bit below craps. So you can see that if you are looking for bang for your buck, daily unit profit per square foot, that slot machines are the way to go even though individual slot machines don't win as much as other units of other games. Let's break down slot machine revenue a little bit more. All the numbers I show you here are in thousands, so add three zeros to the end of each of the numbers for the win amount. I'll start by highlighting a couple of denominations.
The first is the penny slots. Now penny slots are kind of a misnomer because most players don't bet one penny at a time. You can bet anywhere from one up to 100 pennies. So you can play for one penny all the way up to a dollar. And take a look at the win amount. This is for Las Vega strip casinos in the year ending September 30, 2017. Penny slots won over $1.2 billion. And as a percentage of the total win that was 11.52%.
That is a lot of money won by slots that are listed as only costing one cent to play. Compare that to Megabucks, which has a win percentage that is the amount of money that is kept by the casino of 13.3%. Megabucks is listed as a $1 slot, but in fact if you don't play for $3 per spin then you're not eligible for the main jackpot, which is the reason to play the game in the first place.
Where do slot machines fit in overall. Well the total gaming win for the year ending September 30, 2017, for Nevada strip casinos was $6.55 billion. The total slot machine win was $3.2 billion. You can see that that's close to 50%. And the actual total is 48.85%. So slot machines make up almost half of the gaming win for Las Vegas strip casinos for the year ending September 30, 2017.
They are good workers. How do slots work? Well first you have to make the game entertaining to play. You can have a cool theme and there are a lot of really neat themes out there. Blues Brothers Wheel of Fortune is extremely popular. Also Elvira the former late night horror movie host has some slot machines designed with her as the main image. You can have multi-line pays. So instead of just looking at three symbols across the middle and you want to line them up, instead you can have different lines that go through and you can get paid on any of them.
The more you play for each round, the more lines are activated. And also multiple denominations. If you want to play for a quarter, you can. If you want to play for a penny, you can. Next, you do it a lot. If you play roulette by yourself, you can get in about 100 decisions per hour. Spins of the wheel. If you're playing at an empty blackjack table you can play about 200 hands per hour. However if you're playing a slot machine, you can play up to 600 spins per hour. And remember the house advantage is grinding away each time you play.
So the frequency of play makes even very small advantages pay off. Slot machines have an internal pay table and they're based on probabilities for how much money to return to the payer under what circumstances. I've created a very simple slot machine. So let's say that you generate a pseudo-random number using a computer algorithm from 1 to 10,000. You then dispense the rewards based on an internal pay table. It might look something like this. This is a very bad design. I do not recommend anyone in the industry take this seriously.
It's just something I put together. So let's say that half the time the player plays one coin and there's no payoff, they lose. Then 33.5% of the time, they get their coin back. And the other payoffs as you see here. The contribution is actually the amount that's returned to the player so I created this table from the perspective of the player as opposed to the casino. As you can see the total contribution for the player is .962, which means that they have a house advantage of 3.8%.
Next over time, you can calculate expected win. But first you need to calculate a volatility index to estimate the win. And I have these calculations in a separate spreadsheet so I'll just sort of gloss over them here. But I do want you to see them. The details are also in Casino Operations Management, second edition, on page 128. The formula is that your volatility index is the z score of your confidence interval multiplied by the standard deviation of your pay table.
For 90% confidence, you need to have a z score of 1.65. That's the number of standard deviations plus and minus the average. The standard deviation for my game, and again I don't go into the calculations in depth here, but it's 10.23, which means that the volatility index is 1.65, again this is my z score for 90%, times 10.23, which equals 16.88 rounding to two decimals. Also, on the course site, I have included a sample file called slot machine emulator dot xlsm.
And in there I break down these calculations in an Excel spreadsheet. So they're easier to understand there. Now let's talk about expected win. The expected win is the payback, which is 96.2% plus or minus the volatility index divided by the square root of the number of spins. So, what that tells you is that as the number of spins gets higher that means that the volatility index minus number of spins number goes closer to zero, as you approach infinity, and it comes closer to the actual payback.
Here's what the calculations look like with a number of spins. At 100 spins, you actually do have a good chance of losing, of paying back more than you take in. As you can see you might end up paying back more than you take in with 100 spins, but with 90% confidence after 500 spins, 1,000 spins, and especially 10,000 spins, you are much more likely to win an amount that is closer to the theoretical payback. I did a number of simulations that returned the results that back up these particular numbers, again, the file slot machine emulator dot xlsm, and in it is a macro that simulates 1,000 players making 1,000 spins each.
And if we take a look at the results we can see that the average bankroll for the players who started with $1,000 was $947 and about 75 cents. The maximum was $2,851. The minimum after 1,000 spins was $707. And there were 118 winners. And because gamblers will tell you that breaking even is not a bad thing I assumed that anyone who broke even was a winner. Let's see what a typical loser would look like.
In this case we had 506 loses. And then we had wins of varying amounts. We didn't have any 50s and we also only had one 100 and no 1,000. At the end of the 1,000 spins the player ended up with $936, which was in fact their lowest. But at one point they were actually winning. They had the highest total of $10,085 before they lost back to $936. Now let's take a look at the typical winner. And I'm sure that you will see the component of a winning player very quickly.
Win about the same number of payoffs for zero and one. But if you look down at the bottom, you'll see that this player hit the 1,000. They hit the one out of 10,000 shot to get a $1,000 jackpot. And what that meant was that their bankroll at the end was $1,853. Now at their lowest they were at $983 before they started winning back. And at their highest they were at $1,986, which means that even though they hit the jackpot they lost after that to the tune of about $133.
Last, I'd like to talk about video poker. Individuals tend to think of video poker as something separate because you're making choices about which cards to keep. However video poker machines are a type of slot machine. They have pay tables that let you calculate the maximum possible payback. But bad decisions can reduce that payback. Expert players don't make mistakes. But casual players like myself certainly do. What's dangerous about video poker is that it gives you the illusion of control.
In fact, you are only going to win a certain amount of the time. There is a built-in house advantage here too. So the lesson about video poker is that the occasional big wins for hitting a royal flush or for deuces and the illusion of control can be very dangerous. So if you're going to play slot machines or video poker be aware of the techniques to get you to keep playing. And when you're done, and you've lost your limit for the day, by all means get up and go do something else.