Slot Machine Probability Distribution
Results that have already happened are no longer probabilities, and cannot be counted in probability distributions. What happened prior to you walking into the casino? It doesn't matter, does it? And the reason is that you are looking forward, not backward. So as soon as you get a result, you can no longer use it to make probability distribution calculations.
I never said it did. The probability distribution of winnings is measured at the time you being playing, and the observed results occur when you either walk away broke or press the cash out button. In between, you are just playing the game.
The probability of winning on a slot machine is 5%. If a person plays the machine 500 times, find the probability of winning 30 times. Use the normal approximation to the binomial distribution. Find the area under the normal curve over the interval (29.5,30.5). Probability: Odds of Winning at Slot Machines The Odds of Hitting it Big The number of possible combinations is fairly easy to calculate. You multiply the number symbols each slot has together. The features of the game, the design of slot-machines itself, and the probability trace and pay-out percentage were inspired by real slot machines in Swiss casinos, and allowed players significant freedom to express different types of gambling behavior (Figure (Figure1). To increase engagement in the task, participants gambled with real.
If you need to go pee, hit cash out, put the voucher in your pocket, use the restroom, and then put the voucher back in the machine and pick up where you left off. You could cash out, go home, return three months later, and put the same amount of cash in the machine and pick up where you left off (hopefully it's $18.00, a ten, a five, and three ones, not $18.26, but that's a minor thing). The probability distribution of winnings from the point that you begin playing has nothing to do with how much time elapses between spins. It can be a second, 5 seconds, 10 minutes, or 3 months. It matters not.
When you're done playing, you could write down the results, and then do it again, over and over and over, until you have lots and lots of data points, and then plot them on a graph, with winnings on the x-axis and frequency on the y-axis. That's a probability distribution. It tells you the probability of winning a certain amount or within a certain range.
Obviously playing a slot machine with a +EV is ideal but I have no idea how to identify those machines. I can still win on a -EV machine as long as I'm on the right side of the probability distribution curve. Likewise, at a +EV machine, you can still lose if you're on the left side of the probability distribution curve (unless you play long enough to get into law of large numbers land). The same applies to BJ AP. Even with perfect counting and changing your bet from $5 to $50 (and a dumbass pit boss apparently), you can be unlucky and still lose. Likewise, with flat betting, you can still win by being lucky and landing on the right side of the probability distribution curve for blackjack.
Just so everyone knows... I never win on reels. It's all been a sham. All the jackpot pictures I have posted aren't even mine. I found them on the internet. I don't even live in Vegas... I was only vacationing when I met AxelWolf and ZK.
..I was wrong you were right. I'm stupid ... your smart. Your good looking... I'm not so attractive...
'God damn alligator bit my hand off! ...cut me down in ma prime!'I have a question for you, and it goes right along with the topic of the OP, stop loss!
I understand that a significant amount of your knowledge on slot AP has been acquired from banging away on these machines for several years over millions of coin-in. You must have quite a few -EV pulls under your belt while scouting profitable plays. Do you budget a certain percentage of your winnings to go towards 'research and development', so to speak? At what point do you realize a particular game/jackpot/slot club/promotion just isn't beatable and move on?
I didn't realize that it was you who posted this question... since it is you I will help you understand somewhat. I've been in town a long time. Over 25 years on and off but mostly on. Some of the information is passed down or by word of mouth. Other information is through Employees. I don't just go around looking at machines and testing. Although like today I was at a Casino because my wife's card got locked out. So low and behold I was looking at these Double Jackpot 777 Machines last night at the same place and I noticed that they had three machines. 2200... 2700... and 5800. I am not sure what the Jackpot starts at but I was thinking 1000 and after talking to a slot attendant they said it was 2000 but I still am not sure. What I can tell you is all of a sudden the meters were something like 2700... 11,750... and 5800. This kind of thing sparks my interest. Obviously they moved some money from one machine to that one. Most likely because it isn't very common to hit the jackpot or those machines aren't getting any play. I didn't investigate any further but I did fire off 1000 dollars at it and it is 5 dollars a spin and they are the newer reels that you can stop immediately. They kinda seem like video reels but look like mechanical reels. That doesn't matter. On average will I be able to spin off the top jackpot of 11,750 before I lose 12,000 is the question I ask myself? If the jackpot starts at 1k I would without a doubt believe I can. If it starts at 2k I still like my chances. I really didn't have the time to hammer it long. I ended up losing the 1k and had to do other things but it is on my radar now. I most likely will take 10k and see what happens. This is an example of pure speculation and scouting that I might do.
Most of what I do is on machines I have known for many years. I know the hold not only from Employees but over time I have played so much that I know that I lose so much per hour or per how much coin I put it. I am not out there testing machines. I do what I can to find out what the hold is. I stay away from new machines... I like the older type of reels and it is a smaller loop than you might think. I'm not out there in every casino testing every machine. I think I have said enough. The information is free and you can either understand what I am saying and choose to believe it or not. I am just sharing some of what or how I do things.
If you have $10 or $20 or even $100 to put into a slot machine, my system works great. If you want to have a 99+% chance of losing your entire bankroll instead of just 1/3, go with monet0412's system where you shove in the cash and keep hitting spin until you win the jackpot. Obviously the more cash you shove in, the better your chances of winning the jackpot. $100 is low chances, $10 is even worse, but $1000 is better. $10,000 better still. Personally I don't like that system, because a) I don't have thousands of dollars laying around for this; and b) I'm perfectly happy with an even-steven win of zero (net zero), or a small win, and I still have a chance to win the jackpot. Jackpot or nothing is extremely risky. Your money will last much longer with a stop-loss/stop-win method. If you have an unlimited amount of money and time to throw at slot machines, then ignore my method and go with monet0412's method.
Slot Machine Probabilities
Honestly if you do not have a large Bankroll you should not even think about messing with Reels. A player should play Video Poker with smaller Bankrolls. You need to be able to put massive amount of time and money through Reels for it to pay off in the end and you need to know what reels to play and what number the jackpots have to be to turn the game into a positive. Even though you don't have to lock a machine down till you spin off the jackpot... I find that it is the best way to play. You only have to play that Reel machine when the Progressive is over a certain number but if you don't take the time to spin them off you shouldn't even bother. Some Vision Machines are different like Rock around the Clock or Aladdin or that Zombie game yelling play play play at you ever two seconds. Many others but why even bother explaining all this to everyone. Play VP... much less headache and you really can't lose.I like to mix Reels into my play because it looks like I'm a maniac :)
Slot Machine Probability Distribution Calculator
Honestly if you do not have a large Bankroll you should not even think about messing with Reels. A player should play Video Poker with smaller Bankrolls. You need to be able to put massive amount of time and money through Reels for it to pay off in the end and you need to know what reels to play and what number the jackpots have to be to turn the game into a positive. Some Vision Machines are different like Rock around the Clock or Aladdin or that Zombie game yelling play play play at you ever two seconds. Many others but why even bother explaining all this to everyone. Play VP... much less headache and you really can't lose.
I usually play video poker, but after a while I get bored and want to do something else. I don't have thousands of dollars laying around, and the nearest casino is 5 hours away. I really do not care if a slot machine takes 8% of my bet, because the amount I'm wagering is something like $500 a YEAR.
A couple of months ago I put $60 into a Double Diamond $1 5 line slot machine with a jackpot of 5,000 coins, and my balance fell to $47 and then I got jackpot symbols on line 5 -- $5,000! That was great! Of course the IRS got 25% of that, leaving me with $3,750, but given how much I've gambled at slot machines my entire life, I'm pretty sure I'm up now (by at least $1,000).
I'm not going to stop just to say 'I'm up, life-to-date, on slot machines'. I'm still going to play occasionally just like I did before. Losing $100 a year to the casino at the slot machines isn't going to break me. It provides many hours of entertainment.
Results that have already happened are no longer probabilities, and cannot be counted in probability distributions. What happened prior to you walking into the casino? It doesn't matter, does it? And the reason is that you are looking forward, not backward. So as soon as you get a result, you can no longer use it to make probability distribution calculations.
TWEEEEET! (Referee's whistle stopping play)
Is that true also from the view of Bayesian statistics? Where your assumed 'prior' is refined by data as you collect it?
For example, at Lucky's Casino there is one game. You dip your hand into a large container holding red and green marbles. It costs $1 each time you retrieve a marble. Red marbles pay you nothing. Geen marbles pay $100.
On your first visit, you buy 1000 'plays,' and you get 2 green marbles.On your next visit you buy 1000 'plays,' and you get 5 green marbles.
Others who do this kind of analysis for a living may disagree. However, I think those results -- if they were mine -- would affect my probability calculations going forward. I'm not sure that differs significantly from earlier discussions about the OP's suggested play. Just my 2 cents...
TWEEEEET! (Referee's whistle stopping play)
Is that true also from the view of Bayesian statistics? Where your assumed 'prior' is refined by data as you collect it?
For example, at Lucky's Casino there is one game. You dip your hand into a large container holding red and green marbles. It costs $1 each time you retrieve a marble. Red marbles pay you nothing. Geen marbles pay $100.
On your first visit, you buy 1000 'plays,' and you get 2 green marbles.
On your next visit you buy 1000 'plays,' and you get 5 green marbles.
Others who do this kind of analysis for a living may disagree. However, I think those results -- if they were mine -- would affect my probability calculations going forward. I'm not sure that differs significantly from earlier discussions about the OP's suggested play. Just my 2 cents...
If you know how many green marbles there are, then you know the probability of winning, and your results of 2 and 5 are just data points.
But if you don't know how many green marbles there are, then you need those results in order to estimate the probability of winning. The estimated probability of winning would be 7/2000 (really bad since a zero house edge probability would be 20 in 2000).
Either way, once you have an estimated or exactly right probability of winning, you can construct a probability distribution of winning based on how many plays you buy.
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Remember the movie National Lampoon’s Vegas Vacation, when gambling fever consumes Chevy Chase’s character, Clark W. Griswold? He goes on a losing streak to beat all losing streaks while his son, Rusty, wins four cars by playing the slot machines. Maybe Clark would have done better if he had read Probability For Dummies! In this article, you discover the basic ideas behind slot machines and how they work, so that you can get past the myths and develop a strategy based on sound probability.
Understanding average payout
When casinos advertise that their slot machines pay out an average of 90 percent, the fine print they don’t want you to read says that you lose 10 cents from each dollar you put into the machines in the long term. (In probability terms, this advertisement means that your expected winnings are minus 10 cents on every dollar you spend every time the money goes through the machines.)
Suppose you start with $100 and bet a dollar at a time, for example. After inserting all $100 into the slot, 100 pulls later you’ll end up on average with $90, because you lose 10 percent of your money. If you run the $90 back through the machine, you’ll end up with 90 percent of it back, which is 0.90 x 90 = $81. If you run that amount through in 81 pulls, you’ll have $72.90 afterward (0.90 x 81 = 72.90). If you keep going for 44 rounds, on average, the money will be gone, unless you have the luck of Rusty Griswold!
How many pulls on the machine does your $100 give you at this rate? Each time you have less money to run through the machine, so you have fewer pulls left. If you insert $1 at a time, you can expect 972 total pulls in the long term with these average payouts (that’s the total pulls in 44 rounds). But keep in mind that casinos are designing slot machines to go faster and faster between spins. Some are even doing away with the handles and tokens by using digital readouts on gaming cards that you put into the machines. The faster machines can play up to 25 spins per hour, and 972 spins divided by 25 spins per minute is 38.88 minutes. You don’t have a very long time to enjoy your $100 before it’s gone!
The worst part? Casinos often advertise that their “average payouts” are even as high as 95 percent. But beware: That number applies only to certain machines, and the casinos don’t rush to tell you which ones. You really need to read or ask about the fine print before playing. You can also try to check the information on the machine to see if it lists its payouts. (Don’t expect this information to be front and center.)
Implementing a simple strategy for slots
Advice varies regarding whether you should play nickel, quarter, or dollar slot machines and whether you should max out the number of coins you bet or not (you usually get to choose between one and five coins to bet on a standard slot machine). In this section, you’ll find a few tips for getting the most bang for your buck (or nickel) when playing slot machines.
Basically, when it comes to slot machines, strategy boils down to this: Know the rules, your probability of winning, and the expected payouts; dispel any myths; and quit while you’re ahead. If you win $100, cash out $50 and play with the rest, for example. After you lose a certain amount (determined by you in advance), don’t hesitate to quit. Go to the all-you-can-eat buffet and try your luck with the casino food; odds are it’s pretty good!
Choosing among nickel, quarter, and dollar machines
The machines that have the higher denominations usually give the best payouts. So, between the nickel and quarter slots, for example, the quarter slots generally give better payouts. However, you run the risk of getting in way over your head in a hurry, so don’t bet more than you can afford to lose. The bottom line: Always choose a level that you have fun playing at and that allows you to play for your full set time limit.
Deciding how many coins to play at a time
When deciding on the number of coins you should play per spin, keep in mind that more is sometimes better. If the slot machine gives you more than two times the payout when you put in two times the number of coins, for example, you should max it out instead of playing single coins because you increase your chances of winning a bigger pot, and the expected value is higher. If the machine just gives you k times the payout for k coins, it doesn’t matter if you use the maximum number of coins. You may as well play one at a time until you can make some money and leave so your money lasts a little longer.
For example, say a quarter machine pays 10 credits for the outcome 777 when you play only a single quarter, but if you play two quarters, it gives you 25 credits for the same outcome. And if you play the maximum number of quarters (say, four), a 777 results in 1,000 credits. You can see that playing four quarters at a time gives you a better chance of winning a bigger pot in the long run (if you win, that is) compared to playing a single quarter at a time for four consecutive tries.
The latest slot machine sweeping the nation is the so-called “penny slot machine.” Although it professes to require only a penny for a spin, you get this rate only if you want to bet one penny at a time. The machines entice you to bet way more than one penny at a time; in fact, on some machines, you can bet more than 1,000 coins (called lines) on each spin — $10 a shot here, folks. Because these machines take any denomination of paper bill, as well as credit cards, your money can go faster on penny machines than on dollar machines because you can quickly lose track of your spendings. Pinching pennies may not be worth it after all!