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Slot machines are the most popular game in any casino. Sure, people bet more on the lottery, and the worldwide sports betting market is huge. But slot machines are the game du jour in most casinos, especially in the United States. Sadly, slot machines games also offer the worst odds in the casino except maybe for keno. The compounding effect of. The best paying slot machines take you from hero to zero even with a small bet. Finding which slot machines pay the best involves looking at RTP, bonus features, paylines and the minimum bet amounts amongst other things. To get the highest payout, you must play slots with the best odds of winning.
Additional information: My wife cannot afford to play the maximum bet, but when she hits the jackpot combinations, she thinks she missed out. I keep telling her that I believe the odds of hitting those combinations would significantly decrease if she paid the maximum, but she doesn’t believe me. In statistics terminology, it would make sense to maintain the same expected return (payout multiplied by probability), in order to obtain the same overall percent payback for different players (although I doubt they are required to maintain such consistency). Using this assumption, if the payout increases disproportionately relative to the size of the bet, the probability would have to decrease. This would also be a good way for the casino to dupe players into increasing their bets to the maximum.
Slot machines are pegged to payout at a certain % by a computer chip. This percentage does not alter due to bet size at any time, so increasing your bet is essentially just losing your money faster. Higher denomination machines are typically programmed to payback a higher % than lower denomination ones, so that a $.25 machine will pay better than a $.05 machine which will pay better than a $.01 machine.
Regardless of bet size, even with the inflated jackpots for max bet, the expected payback remains the same on slot machines to the best of my knowledge. I don't think it's like video poker where betting max bet inflates jackpot size and increases expected value, but i'm not 100% sure.
As to MAX COIN... Most, but not all, slot machines offer inducements for players to play max coin but read the payout table to be sure that final coin actually buys you something. However, whether you put in Minimum Coin, Maximum Coin or Something in between, once you hit that little red button... its all up to the random number generator and the random number generator just goes along and does its thing with no knowledge at all about how many coins are in there or whose player card it is or if they've been tipping the waitress or not. So the EVENT is not influenced by the number of coins, only the payment for that event.
Expected payback? You mean each and every press of the little red button has to be a certain expectation?
The general rule is that a higher denomination machine returns a greater percentage, yes, but going to max coin on a lower denomination has to be compared. Its amount bet times expectation.
The odds do not change when you bet max. I believe that some jurisdictions require identical odds. I've never, out of hundreds of games, seen a game that behaves differently.
There would be no advantage for a gamemaker to do that kind of manipulation. The probability of hitting the jackpot is so low, that the manufacturer is free to riase the payout without changing the EV of the game very much.
It is very popular for the machines to be designed so that the player to be denied an entire class of high payouts if he does not put in max coin. Even though the house edge may not be that much worse, the player will eventually see hit a case where he would have been paid a much higher payout if he had more coins.
But every machine design can honestly say it has a lower house edge if you play more coins. It doesn't say how much lower.
An example from a real machine is 8.04% HA for 1 coin, and 7.48% and 7.30% for 2 or 3 coins.
One thing I will say now is that I think more of the average payout is related to the jackpots than you might think. For example, one local casino (Hollywood, FL) states that it pays out 94% of the bets wagered (i.e. a house advantage of 6%). I would conjecture that 5% or 10% if that payout is related to the jackpots. If it was really small – say 1% – then you would expect that, on the average, your credits would decrease by only $7 for every $100 you wager (such as 100 pulls on a $1 machine). But I will bet your average losses are much higher than that, unless of course, you hit a big win. This is because a significant portion of the 94% payback is related to the big wins.
I may be confusing the issue by using the word “jackpot”. I am not talking about the huge progressive jackpots of 100’s of thousands or millions that are rarely ever paid, but rather the smaller payouts of $1,000 to $10,000 that you might find on nickel and quarter machines. My wife, who only plays slots 5 to 10 hours a week, hits 3 or 4 of these “jackpots” every year. I know because I have to claim them on our tax return. Maybe I should call them 'big wins' rather than 'jackpots'?
Our next casino trip is later this week, so I should have a decent example to post sometime this weekend. If I am right about this, it is very important for players (such as my wife) to understand, so they don’t get duped into losing a lot of money, especially mine!
Question: Many slot machines offer a disproportionately higher return on the jackpot combination when the maximum size bet is played. Do they also decrease the odds of hitting the jackpot combination when the maximum bet is played?
Additional information: My wife cannot afford to play the maximum bet, but when she hits the jackpot combinations, she thinks she missed out. I keep telling her that I believe the odds of hitting those combinations would significantly decrease if she paid the maximum, but she doesn’t believe me. In statistics terminology, it would make sense to maintain the same expected return (payout multiplied by probability), in order to obtain the same overall percent payback for different players (although I doubt they are required to maintain such consistency). Using this assumption, if the payout increases disproportionately relative to the size of the bet, the probability would have to decrease. This would also be a good way for the casino to dupe players into increasing their bets to the maximum.
Your wife is right she did miss out on a bigger jackpot for not playing the maximum coins. The odds of hitting the jackpot do not change weather if she bets 1 coin or 2 but the payout changes. Casinos offer better payouts for max coins because they want to encourage people to bet the max. The odds could go from 96% payback to a 97 or 98% payback from minimum to max coins.
The EPROM chips, which control the theoretical return percentages on slots, are generally changed very rarely. It would be bad business to loosen and tighten the slots according to the day of the week. For any given casino there is some optimal return to maximize profit. Wherever that is, a smart slot manager would find that point and then just leave the EPROMS set to that return.
Michael V.
Sure. There are lots of ways. Putting in fake coins just to name a simple one. Be warned that in Nevada cheating in a casino carries the same kind of penalty as bank robbery, or so I hear. Let the record show that I disapprove of all forms of cheating.
Thanks for the kind words. I always enjoy hearing from high school math teachers out there because I almost became one myself. Based on seeing par sheets and speaking to industry insiders I can confidently say that if the alternative choices are shown at the conclusion of a bonus round then the game is honest about them. In other words the prizes were randomly determined and what you see at the end is truly how they were hidden. However in games where the alternative choices are not shown the odds are likely similar to a prize wheel, with lower probabilities for the higher wins. I played Price is Right enough to see the Showcase Showdown twice. As you said, the values behind the price tags are revealed at the end. So I maintain that the game is indeed truthful and speculate that you have just been unlucky.
Your girlfriend is right. Nevada Gaming Control Board regulation 14.040.2(b) states...
'For gaming devices that are representative of live gambling games, the mathematical probability of a symbol or other element appearing in a game outcome must be equal to the mathematical probability of that symbol or element occurring in the live gambling game. For other gaming devices, the mathematical probability of a symbol appearing in a position in any game outcome must be constant.'
In other words a representation of dice must have the same odds as real dice. Thus there would be no way to predestine an outcome because the player could roll anything during the course of the game.
I asked three casino executives about this hypothetical situation. They all said that you can’t win a bet if you don’t make a bet. In the case where betting somebody else’s money is consensual then they will pay the person pressing the buttons. However in the case where it is not consensual they will not pay the person who pressed the button. A more difficult question is whether they will pay the person who did put money in the machine. That seems to be taken on a case by case basis. Considerations include whether the player was vigilant in guarding his machine, how much the player was playing for, and if he is a known good customer. Basically a player should follow the McDonald’s rule of 'keep an eye on your fries.' However even if the player was remiss in guarding his machine the casino may not want to anger a good customer. It also helps to be playing a high denomination game.
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It depends. If the slot play may be used in any machine in the casino, including video poker, then it can be worth 99 cents on the dollar or more, depending on the video poker offerings. For example, the MGM Mirage casinos award $1 in free slot play for every one point earned. It can be used in any machine in any casino connected to the MGM Mirage player card. Most MGM Mirage properties offer 9/6 Jacks or better, so the value of $1 in free slot play is worth 99.54 cents, with correct strategy.
However, sometimes free slot play must be done on particular promotional machines that don’t accept money. The value of this kind of free play is hard to estimate closely, but generally very little. For example, the Las Vegas World used to sell “$1000” vacation packages for $400. Of the alleged $1000 value $600 was in promotional slot machine play. In his book “Million Dollar Video Poker,” Bob Dancer writes that he did this deal numerous times over, and estimates the value of the free slot play to be about ten cents on the dollar.
Thanks. As I say about machine jackpots, 0.5% to 1% of the jackpot amount after taxes is good. Whether the dealers pool their tips or not should not make a difference.
I asked a source of mine who works at one of the casinos that utilize this technology. Besides the Treasure Island, this technology is also used at casinos in California, Michigan, and Mississippi. Here is what he said,
'Nothing can be changed if there are credits on the game. The slot machine will always reject any changes sent when there are credits on the meter. In Nevada, the machine also has to be idle for four minutes prior to and following any changes. It’s also not completely transparent to anyone standing in front of the slot machine. A black window pops up that says ’Remote Configuration In Progress’ (or something like that).
We mainly use ours to change the available denominations on our games. Similar to how table games will raise minimum bets on when the casino is busier, we will remove lower denominations on Friday morning and return them on Monday morning.'
So, rest assured, that the slot manager can not tighten up a game on you just because he doesn’t like you. As long as you have credit in the game, nothing can be changed.
Let:
p = Number of Party Poopers.
w = Number of wins.
e = Party Poopers needed to end bonus.
Imagine the w wins in a row, like a loaf of bread. Then place the p Party Poopers like raisins equaly along the bread, creating the same distance between consecutive raisins as well as from each end. For example, if the bread was 12' long, and you had 3 raisins, you would place the raisins at the 3', 6', and 9' points, creating 4 segments of 3' each.
The expected number of wins picked is the product of the length of each segment and the number of Party Poopers needed to end the bonus, or e × (w/(p+1)). Let's look at an example.
Suppose there is a field of 40 icons with 8 Party Poopers. It takes three Party Poopers to end the bonus. That would leave 32 wins. So, p = 8, w = 32, and e = 3. The expected number of successful picks is 3 × (32/(8+1)) = 32/3 = 10.67.
'Anonymous' .
Community, or group, bonuses is a popular new concept in slot machines. While the bonus can be earned in different ways, depending on the game, the concept is that more than one player can play the same bonus round at the same time. Usually the outcome is shown on a large video screen visible to all players. One exception is the Wheel of Fortune community bonus, where an enormous wheel sits between the individual machines.
From what I can tell, the Wheel of Fortune community bonus is earned by an individual player achieving the initiating event on his own. It then starts a 10-second countdown, to give other players a chance to trigger a bonus. Usually this doesn't happen, so the player who earned the bonus plays by himself.
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In contrast, on the American Idol slot machine, all active players play the community bonus. It is also triggered independently of where the reels stop, so no matter how many players are playing, or how fast they play, the odds of a bonus at any given time are always the same. The rest of this answer shall focus on how specifically the American Idol community bonus works.
It would be unfair if there were two players in a bank of community bonus machines, in which one was betting $1 a minute, and one was betting $10 a minute, if they both had the same expected value in the community bonus. To avoid such injustice, a multiplier is applied to the final bonus win, roughly according to the amount the individual player was betting at the time the bonus was initiated, factoring in both average bet and speed of play. How the game determines each player's multiplier is a bit complicated. Here is what I could figure out:
- The game keeps track of the players' last 40 seconds of betting activity for each player, in the form of a queue.
- Each 20 cents the player bets at one time buys him 10 seconds of 1x multipliers. So, a $1 bet would buy 10 seconds of 5x multipliers. This multiplier is added to the end of the player's queue.
- If the player plays at a faster rate than one bet per ten seconds, causing there to not be enough space in the queue to add 10 seconds of multipliers, then it will cram any excess multipliers onto the last few seconds. How exactly it does this, I'm not sure.
- As the player sits at the machine, the game will drop off from the stack the highest multipliers in the queue. Kind of like how in a queue for a Vegas nightclub it doesn't matter your position in line for girls, but how pretty you are; the most attractive girls are removed from the queue first.
- As multipliers are dropped off the queue they are also the eligible multiplier should the community bonus be triggered at that moment.
- At any given microsecond, except if a community bonus is already in progress, there is a fixed probability that the bonus will be triggered. So the time between bonuses would follow an exponential distribution. In other words, a bonus has a memoryless property and is never overdue, much like a royal flush in video poker.
Example: Let's say the player has 35 seconds of 1x multipliers in his queue. He then makes a $1 bet. Normally this would buy 10 seconds of a 5x multiplier. However, in this case there isn't enough room in his queue to add ten seconds. What the game would likely do is add four seconds of 1x multipliers, and one second of a 6x multiplier. I'm not saying it would do exactly this, but something along these lines, where the total time × average multiplier still equals 10.
Besides community bonuses, there are also 'local bonuses' that are earned by each individual player and played only by that player. If a community bonus hits during a local bonus then that local bonus will be put on hold during the community bonus. To keep the local bonus player eligible for community bonus the game will give the player 60 seconds of multipliers. This is an exception to the usual 40-second queue. I am not sure how the multiplier during this time is determined. If the player finishes the local bonus in less than 60 seconds then the multipliers for the remaining time are somehow added to his queue.
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One thing I have no idea about is what happens if a player sits down and starts playing during an ongoing community bonus, which the game will let him do. It would be unfair if the player were playing during this time without any chance to trigger another community bonus. I'm told that the machine somehow compensates the player in this situation, but I have no idea how.
This question was raised and discussed in the forum of my companion site Wizard of Vegas.
If you can shed any light on the unanswered questions in my answer, please feel free to write to me or post your comments in my forum.
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She was playing a 5¢ machine and the alleged win was $8,588,749.65. This number looked familiar to me as a power of 2. To be specific, 2^33 = 8,589,934,592. If this were a count of tenths of pennies, it would equal $8,589,934.592. The difference between that and the jackpot is $1,184.942.
What I think happened is the machine declared the win as an unsigned integer, meaning a number that could never go negative. However, through some programming error, it wanted to. When you try to put a negative number into an unsigned integer, the computer will wrap around the other end. In this case, I think something bizarre happened and through whatever programming error, the game thought the player had a loss of $1,184.942. When it tried to display this number as an unsigned integer, it wrapped around the maximum value and displayed the win of $8,588,749.65.
Every slot machine I've ever seen says somewhere 'malfunction voids all pays and plays.' If I were the judge, I would have to say that this was indeed a malfunction and side with the casino. This was, of course, what the casino argued. Nevertheless, their $80 compensation offer strikes me as very stingy.
More information at KATU.
For more discussion on this question, please see my forum at Wizard of Vegas.
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'Anonymous' .
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As a rule of thumb, the location makes no difference.