Scenario: there is a machine at a casino that hits jackpot 1/100 times it is used. The probability that one does NOT hit jackpot on their first spin is .99^1, the second .99^2, and on their nth .99^n (hoping my math is right). As the number of non-winning spins increases, many people would say the machine is “due” because the probability of the losing streak continuing gets lower and lower, but AFAIK that is not valid. Why is that?
In: 0
Even using what you said, you could do the math and see that with a 1/100 chance of hitting the jackpot, doing 100 spins gives you a 36.6% chance of not hitting. Hell, you could put in 200 and see that there’s still a 13.3% chance you win nothing after 200 spins.
Long story short a 1 in 100 chance at something random and independent DOES not mean that if you do something 100 (or even 200 or 500) you are guaranteed to win.
Also, many people are using coin flips as an example. Many slot players mistakenly believe that slot machine spins are different than flipping a coin, and are not independent events (meaning previous events do not impact future events). These players believe that slot machines do keep a history, and change odds positively or negatively based on how much the machine has paid out. This is patently false though. Slot machines have the same odds of winning any prize whether it is your first pull or your hundredth. You have the same odds of winning a jackpot after losing on 100 straight pulls as you would if you just hit the jackpot. Slot machines are just random number generators with glitzy front ends and noises.
Sometimes it is, and sometimes it isn’t. It depends upon the gamble.
Look at it this way.
You put 10 stones into a bag, one of them blue, the others white.
If you pull out a stone and it isn’t blue, set it aside, and keep going, then eventually you will get the blue stone. Eventually, you will run out of white stones.
However, if you get the blue stone and set it aside, your chance of getting the blue stone on the next draw is zero.
The odds of you getting the blue stone are dependent upon what stones you previously drew and how many.
However, if you put the stone back every time you draw, then the later odds are independent of the earlier ones. If you put back the white stone, then there are always 9 white and one blue, and the odds are the same. Similarly, the odds of getting the blue stone do not change if you got the blue stone last time if you put it back. Still one chance in ten.
In the first case, it matters how many stones have been taken out and not returned, and what color they are. In the second case, it is always the same as the first draw: there are always 9 white and one blue, and your chances of getting the one blue are always 1-in-10.
The hard part is figuring out whether or not the number of previous tries changes the odds, i.e. the odds are dependent or independent.
Counting cards is an example of correctly seeing that the odds of each card in the next deal is dependent upon what is played. The next card cannot be an ace if all aces in the deck have been played, for example. Another example is pull tabs. If there are five $50 pull tabs in a stack of one thousand, no one has gotten one, and there are only 5 left, you cannot fail.
A lottery where the ball is drawn from a properly functioning randomizer or spinning on a properly functioning roulette wheel, not so much. Hitting the number 23 once doesn’t remove 23 from play, nor is there anything forcing the wheel to hit one number more than the others.
In some cases, it is a bit of both. For example, slot machines are designed to hit more the longer they are played, or at least used to be. This was intended to get people thinking that if they just kept playing they would come out ahead. They were, of course, designed to do this so little that it almost never was better to just sit there and play. However, watching a slot machine fail to hit over and over until other people had given up meant your odds on that machine improved.
a gambler who plays 1000 games will be more likely to have a win at any point than someone who only plays one game, but the odds of winning in that specific game are the same for each gambler
To maybe give you a more intuitive example instead of just rehashing the same “gambler’s fallacy” comment, think about every other instance of probability that we interact with.
Every time you drive to work, you have some probability of getting in a car accident. Do you get more and more frightened every time you get in your car because you’re “due” for a car accident? It’s the same principle for gambling.
Each time you spin the machine it’s a separate go from the last time with all the parameters reset.
Think of it this way: We can play a simple game where we put 99 of white marbles in a bag with one black ones. A group o people draw the black one, you win, otherwise you loose.
If each person reveals their draw but holds onto it then the number of loosing options goes down with each draw so the 5th person has a 1/96 chance of winning instead of a 1/100. This is not how gambling machines work however.
Now you put the marble you took out of the bag back in each time then shake it around, then there’s always a 1/100 chance of winning because there’s 100 marbles in there to choose from. It doesn’t matter how many times you have drawn before, so long as you always have 99 white and 1 black the odds are the same. This is how the machine works which is why the odds don’t improve with each attempt.
It depends on how the machine works but typically the probabilities are independent, meaning every time you play the machine the odds of winning are the same. In which case, as others have mentioned, this is an instance of the “Gambler’s fallacy”.
What *does* happen is that every time you play, some of the money you put into the machine is added to the jackpot. So there is in fact a benefit to playing a machine that hasn’t had a payout for a long time, not because you’ll have a better chance of winning, but because when you do win, your payout will be larger.
For instance, say we take your example of a machine with a 1-in-100 jackpot probability. On average, you have to play 100 turns on the machine to get a single jackpot, but much longer losing streaks are possible. Now let’s say someone who used the machine before you played for 200 turns without success. They put a quarter in the machine every time and 20 cts of each quarter was added to the jackpot, so the jackpot is now at $40. This means you can now afford to play 800 turns, and as long as you win the jackpot somewhere in those 800 turns, you make a profit or at least break even.
(You can afford 800 turns because as long as you win, each turn actually has a net cost of 5 cts and you start with $40 “in the bank”. $40/0.05 = 800.)
Because each new event in random things is unconnected to the previous event, i.e. “the dice don’t know which roll it is”
Really easy experiment, if you flip a coin a bunch of times you should get a 50/50 distribution of heads and tails. Go flip a coin and then count how often you get the opposite side you did last time. You’ll notice you get the “expected” result only about half the time.
Putting it simply, it’s unlikely you’ll have flipped a coin and gotten 10 heads in a row but once you have you have a 50/50 shot of getting the 11th
It’s called the gambler’s fallacy for quite obvious reasons. Basically there is no reason it should be “due” from the results of a previous attempt, because the next result is completely independent of all others.
If I flip a fair coin and it gets heads 100 times in a row, there’s no reason that the next flip isn’t still a 50/50
The example of a slot machine at a casino isn’t a good one because *by law* they must payout based on their listed probabilities within a certain period of time.
So while most of the statistic arguments on this topic will say things like…. “a coin has no memory of the previous flips so each flip is a totally independent event” …..slot machines quite literally *do* have a memory and the outcome of the next spin is actually dependent on the previous spins.
The probability of the losing streak continuing is *identical* on the 100th spin as it is on the first.
The probability is only .99^n that, *starting now* you will lose the next n times. But the probability, after n-1 times? Still .99 that the nth spin loses.
You’re conflating “the odds of starting now and experiencing a streak of n losses” with “the odds of continuing a streak for one more spin”. The former is .99^n, the latter is *always* 0.99, regardless of how big the current streak is.
Latest Answers