If a gambler and the casino keep going forever, how come the casino is always the winner?
In: Mathematics
A house that does not win goes out of business and therefore all you are left with is houses that do win.
Let’s say that you and I decide to play a game. I’m going to put 51 red balls and 49 green balls into a bag. You draw a ball out without looking, then you look at it and put it back in the bag. If it’s a red ball, you give me a dollar. If it’s a green ball, I give you a dollar.
That means that after we play 100 times, on average, I’m going to win 2 more times than you did, so you’re going to have $2 less.
Now let’s stretch that out into 100,000 games. On average, you’re going to lose $2000 to me. Now, you’re going to hit lucky streaks here and there, and at certain times you’ll probably have more money than you started with. But if you don’t have the good sense to stop playing at that point and walk away with your winnings, eventually, odds dictate that you’re going to continually lose money over time until you eventually run out of money and can’t play anymore.
That’s how casinos work. Pretty much every game at the casino (where you play against the casino, we’re not talking about games where you compete against other players like poker) is designed to give the house (the casino) a very slight advantage. In slots, it’s because the machines are programmed that way. In roulette, it’s the 0 (and often 00) spaces on the wheel. In blackjack, it’s that the players are forced to play first (and possibly bust) before they see what the dealer does, including losing their bets even if the dealer busts as well (there are a few other things as well, like insurance bets and the dealer automatically winning if they deal themselves blackjack).
It’s absolutely possible to walk out of a casino with more money than you went in with. If it wasn’t, people would never play. The problem is that when you play long enough, eventually statistics dictate that you’ll lose all of your money (which is something that the casino can’t really do). That’s why it’s so important to stop while you’re ahead.
We had a preacher once who had lived in Vegas in the 80’s or 90’s. He said while he was there a new casino was featured on the front page of the paper for their grand opening. He said that in one week, 7 days, there were again on front page of the paper showing them in the bank to completely pay their mortgage off. It was $750 million dollars.
They didn’t do this by letting everybody win.
We had a preacher once who had lived in Vegas in the 80’s or 90’s. He said while he was there a new casino was featured on the front page of the paper for their grand opening. He said that in one week, 7 days, there were again on front page of the paper showing them in the bank to completely pay their mortgage off. It was $750 million dollars.
They didn’t do this by letting everybody win.
We had a preacher once who had lived in Vegas in the 80’s or 90’s. He said while he was there a new casino was featured on the front page of the paper for their grand opening. He said that in one week, 7 days, there were again on front page of the paper showing them in the bank to completely pay their mortgage off. It was $750 million dollars.
They didn’t do this by letting everybody win.
Because expected return for player is negative and expected return for house is positive. In practice this means that more games gambler and casino play less likely gambler is to be on winning. Going into more detail kinda takes it away from ELI5 territory.
Theoretically house can lose only if it runs out of money. While in practice casion could theoretically run out of money with very unlucky streak, but bigger buffer of money casion has the more unlikely scenario this is. Casions have big enough buffers of money that odds of string of victory to cause casino to run out of money are extreamly unlikely.
Additionally there tends to be win limits etc. To limit gains individual people can get from getting from finding glitch in the system. After winning enough generally casino refuses to play with you for limited period. In case of continued success they’ll set people to investigate your winning streak, in case it’s luck, cheating or abusing mistake done by casino.
Anyway the potential buffers of money casions have access to are wast compared to even biggest jackpots. And usually the biggest jackpots are grow over time, so you can’t win them multiple times in row.
When you win, the house pays out a small percentage less than the “fair” payout for the actual odds. Simple as that.
In roulette, for example, an American wheel has 38 pockets; payout for a single number bet should be 37:1. The actual payout is 35:1. On average, in 38 bets of 1 dollar (say), you lose $37 and win $35 – that’s a 5% profit to the house. Other bets (and games) have similarly biased payouts.
Keep playing roulette long enough, betting on single numbers, the house takes 5% of all the bets you make. And if you keep winning and losing, you’ll likely pass your money across the table quite a few times. (Say you start with $100 dollars. After a few bets, you’ve bet it all, but maybe you won once or twice, so on average you still have $95. So you keep playing. A little later, you’ve bet another $95 dollars, but on average you still have about $90. So you keep playing. And so on.) Sure, you *could* win, and walk away. But the house is taking its cut of every single bet, and there are plenty of punters – statistics are in the house’s favour. It’s not in the game of losing money.
On top of the odds based stuff others have discussed, there is also the fairly simple fact that they kick you out if you do too well against them.
For example, blackjack is a beatable game in that you can count cards and push your odds against the house into favorable territory, but you can’t do that if they won’t let you play, which is why (good) card counters regularly get banned…
Say you have a single die (one of a pair of dice). It has 6 sides, right?
Let’s invent a game where a player can bet $5 that a throw of the die will be either 3 or 6. If it’s one of those numbers, they get to keep their $5, and the house pays them another $5. But if it lands on 1, 2, 4, or 5, they lose, and their $5 goes to the house.
A player can easily double their money in a single roll. How exciting!
But it’s not a good bet, because their odds of winning are only 2 in 6 (one third). So a third of the time they will win $5, but two thirds of the time they’ll lose $5.
An individual throw of the die is random. It can land on any of the 6 sides. But over time, the ratio will look closer and closer to what you expect based on the die having six sides, 1/6th of the rolls l will be a “1”, 1/6th will be a “2”, and so on.
The gambler (irrationally) hopes to get lucky on a few rolls. But the house is playing a long game. As long as there are enough rolls of the die, they are guaranteed to win 2/3rds of them.
The House doesn’t literally win *every single time*; this just means that the odds are weighted in the House’s favor. Even if it’s just 49.9 to 50.1, in the long run the House will always come out ahead. Individual gamblers might have a good night, win some money, and have the sense to stop & cash out while they’re ahead, but the odds say that more people will push their luck & wind up losing to the House.
*You* might not gamble every single day, but the House does. And over the course of a year, or 10 years, or whatever, that small percentage in the House’s favor adds up to major $$$.
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