by John Grochowski
At first glance, there's a large gap – or is it a gaping chasm? – between slot machines and table games.
Probability Slot Machine
Slot machines use a random selection process to achieve a set of theoretical odds. Then the probability of hitting this jackpot is 1/20 x 1/20 x 1/20 or one in. For example, let us take that the odds are 4 to 1. Then, the probability would be found by using the following equation: 1 / (1+4) = 1/5. In other words, the probability in this case would equal to 1/5, or 20%. What players need to know is the fact that the so-called 'evens' are odds of 1 to 1. They are always paid even money.
You can see cards being dealt and dice being rolled, but you can't see random numbers being generated. That leads to the impression that slots can adjust on the fly, making sure players can't win too much in ways that can't be done with cards, dice or roulette wheels.
Nonetheless, slots and tables share common ground that makes them more similar than players realize. Both give the house an edge by paying less than true odds on winning bets. The casino share comes from losing bets, of course, but the winners don't quite offset the losers because they're paid at less than the true odds.
Not only that. Slots and table games both arrive at expected results through normal probability.
It's that last part that gives many slot players trouble. They see that a slot game has an expected payback percentage – usually less than 90 percent on penny slots but more on higher denominations. And they hear that results are random.
That leads to the question, 'How can slot results be both programmed and random? If there are big wins, doesn't it take cold streaks to get back to the programmed percentage? That doesn't sound very random to me.'
Some answers:
Slot Machines Don't Work Like That
Game designers set the odds so that normal results will lead toward an expected average payback percentage.
Probability Slot Machine Random Games
That's the same situation you face on a table game.
Take roulette. On an American double-zero wheel, the game is 'programmed' with 38 possible results — 1 through 36 plus 0 and 00.The numbers come up randomly, and when you win on a single number, you're paid at 35- 1 odds, a bit less than the true odds of 37-1. That gives the house an edge of 5.26 percent. That's the same as saying a payback percentage of 94.74 percent.
There is nothing to keep your number from coming up two or three times in a row, and nothing that says it has to come up within several dozen spins or more. But given enough trials, the random results and the odds of the game will lead to something very close to roulette's expected percentage.
Probability Slot Machine Random Wheel Spinner
Slots work the same way, except there are thousands of possibilities instead of 38. For regular play on the reels, randomly occurring numbers are programmed, each corresponding to a reel symbol. To make up an example, the programmer might write it so that every time the random number one shows up, the reel shows a jackpot symbol; with numbers two, three or four, it shows a seven, with numbers five through nine, a triple bar, and so on. The possibilities are programmed, but when they turn up is random, just as it's random when a 17 turns up in roulette.
After a big win, the machine doesn't go into makeup mode. Over a long period of time, normal results according to the odds of the game will yield a normal payback percentage, and your big win fades into statistical insignificance.
Just as when a table games designer sets the rules of a card, dice or wheel game, the slot programmer sets the possible outcomes, and the pay table gives you back a little less than the true odds of hitting the winners. You can hit several winners in a row, or none, for a number of spins.
Results are random, but over hundreds of thousands of plays they will lead to something very close to the programmed payback percentage.
Cold Streaks After Jackpots Are a Myth
Casinos are there for the long haul, and they know that normal results in line with the odds of the game will take care of the percentages.
Imagine you're betting three coins at a time at a dollar machine with a top jackpot of 10,000 coins, and that the machine is programmed to pay 95 percent in the long run. We hit the jackpot on our first pull. How low must the payback be over the next 999,999 spins to bring the overall percentage back to 95 percent for 1 million reel spins?
Would you believe a drop to 94.7 percent would do it? And if those 999,999 spins brought 95 percent, the overall payback including that first jackpot would be only 95.3 percent.
Normal results bring the overall payback percentage into normal range. The game doesn't have to force any cold streaks.
That's the same situation table players face. If I'm playing craps, betting on 12 and collect 30-1 payoffs several rolls in a row as the shooter rolls an unusual number of boxcars, does the casino have to force other numbers to come up for a while to make up for my streak? Of course not.
Someone might congratulate me on a nice win, but operators know that the 35-1 odds against rolling 12 coupled with day after day after day of play and normal probability will lead my streak to fade into statistical insignificance.
Slot Machines Don't Work Like That
Game designers set the odds so that normal results will lead toward an expected average payback percentage.
Probability Slot Machine Random Games
That's the same situation you face on a table game.
Take roulette. On an American double-zero wheel, the game is 'programmed' with 38 possible results — 1 through 36 plus 0 and 00.The numbers come up randomly, and when you win on a single number, you're paid at 35- 1 odds, a bit less than the true odds of 37-1. That gives the house an edge of 5.26 percent. That's the same as saying a payback percentage of 94.74 percent.
There is nothing to keep your number from coming up two or three times in a row, and nothing that says it has to come up within several dozen spins or more. But given enough trials, the random results and the odds of the game will lead to something very close to roulette's expected percentage.
Probability Slot Machine Random Wheel Spinner
Slots work the same way, except there are thousands of possibilities instead of 38. For regular play on the reels, randomly occurring numbers are programmed, each corresponding to a reel symbol. To make up an example, the programmer might write it so that every time the random number one shows up, the reel shows a jackpot symbol; with numbers two, three or four, it shows a seven, with numbers five through nine, a triple bar, and so on. The possibilities are programmed, but when they turn up is random, just as it's random when a 17 turns up in roulette.
After a big win, the machine doesn't go into makeup mode. Over a long period of time, normal results according to the odds of the game will yield a normal payback percentage, and your big win fades into statistical insignificance.
Just as when a table games designer sets the rules of a card, dice or wheel game, the slot programmer sets the possible outcomes, and the pay table gives you back a little less than the true odds of hitting the winners. You can hit several winners in a row, or none, for a number of spins.
Results are random, but over hundreds of thousands of plays they will lead to something very close to the programmed payback percentage.
Cold Streaks After Jackpots Are a Myth
Casinos are there for the long haul, and they know that normal results in line with the odds of the game will take care of the percentages.
Imagine you're betting three coins at a time at a dollar machine with a top jackpot of 10,000 coins, and that the machine is programmed to pay 95 percent in the long run. We hit the jackpot on our first pull. How low must the payback be over the next 999,999 spins to bring the overall percentage back to 95 percent for 1 million reel spins?
Would you believe a drop to 94.7 percent would do it? And if those 999,999 spins brought 95 percent, the overall payback including that first jackpot would be only 95.3 percent.
Normal results bring the overall payback percentage into normal range. The game doesn't have to force any cold streaks.
That's the same situation table players face. If I'm playing craps, betting on 12 and collect 30-1 payoffs several rolls in a row as the shooter rolls an unusual number of boxcars, does the casino have to force other numbers to come up for a while to make up for my streak? Of course not.
Someone might congratulate me on a nice win, but operators know that the 35-1 odds against rolling 12 coupled with day after day after day of play and normal probability will lead my streak to fade into statistical insignificance.
On a roulette wheel, if red numbers come up half a dozen or more times in a row and the whole table is betting with the streak, does the casino panic? No, because normal probability will lead the streak to fade into statistical insignificance and the game will pay something close to its normal percentage.
There is no mechanism to force cold streaks after big wins on tables, nor is there any such mechanism on slots. Forced results on slots are illegal in all American jurisdictions. Results have to be random, just as they are on tables.
But odds of the game can be set so that winners are less frequent than losers, and winners pay at less than true odds. Slots work that way, and so do table games. That's enough for random results to give the house its edge.
Netbet casino slots rtp. John Grochowski has been covering casinos and casino games for nearly 40 years. He is the author of six books and his work appears in newspapers, magazines and websites around the world.
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