How dose the house always win? Are they simply cheating?
In: Mathematics
Let’s take a slot machine. Let’s say that you have to have 3 equal symbols of one type in the middle position to win money. That’s the only real winning condition.
Let’s say we only have 3 symbols on the roulette in each position. O,X and T and to win you need to make a line of X’s
Winning conditions:
XXX
Losing conditions:
XXO
XXT
OXO
OXT
TXO
TXT
OOX
OTX
TOX
TTX
OOO
OTO
OOT
OTT
TTT
TOT
TTO
You have 1/27 probabilities to win. So if you are lucky and the machine is not tricked, then you will have to play 27 times to play. If you don’t play that many times the house is already wining.
This is ofcourse too simple. Each casino has several games with complex rules and different wining conditions that can give more or less money. This make that your chance of winning are way lower.
So the house will always win because most of the players won’t win anything and playing with probabilities they can make profit as they wish. They don’t really need to trick anything, just design the player loop to make him/her play without realizing how much they are spending. If they want to tweak the chances of winning just because they want to make a weekend where it’s easy to win prices or just make a month harder for players, they just need to block or open more tables or slots, or just change the winning conditions and prizes a bit.
The only way for the player to win would be if probabilistically each time you play you win.
People just can’t calculate that risk is *the same* as loss
…in the same way as
magnetism is the same as electricity. (Electromagnetism)
If you can lower risk then you profit.
It’s clear at the roulette table with the zero on which only the house wins.
It’s also clear on the back of a lottery ticket where they’ve done the maths for you with (approximately)
“This ticket is worth $0.0000000000001”
Q: Why would you exchange $1 for $0.0000000001?
A: Because you’re an addict with mush brains. You know it’s wrong. You know there are better odds elsewhere and yet you can’t stop because dopamine has hijacked everything.
Odds are alway in the favor of the House. Take Roulette: playing single numbers the payout is 35/1, so for a $1 bet you get $35. But there are 38 numbers to bet (1-36, 0 and 00). So, if there is $1 on every number, someone is guaranteed to win $35, but the house made $38 on that roll. (And as it’s seldom every number is bet, many times the House wins without having to pay out.). The payout of 35/1 but the odds of losing 38/1.
Now say you’re the only person playing and you place $1 on one number and win. For that hand the House lost money. But over time it averages out to the odds and the House makes more than it pays out.
Let’s play a game. We’ll shuffle a deck of cards, and you randomly draw a card. If you draw a black card, I give you a dollar. If you draw a red card, you give me a dollar. If you pull a joker, you give me a dollar.
If we play this game according to the rules, what do you think will happen? If I set these rules, and these are the only rules I will agree to play by, am I cheating? Are these rules fair?
If we play this game, it’s possible that you will only draw black cards, and I will have to give you all my money. But that would be very unlikely. There are just as many black cards as red cards, so you will also pull red cards and have to give me money. In addition, there are also jokers. That means that there are slightly more cards where you pay me. What that means is that over time, if we play many, many rounds, I will win slightly more often than you, and will slowly get all your money.
This is why “the house always wins”. The house makes the rules, and they carefully make the rules such that they win slightly more often than the customer. The house doesn’t win every bet, but they win more bets than they lose, because the rules of the game are always tipped slightly in their favor.
Is that cheating? Is that fair? Well, in general, casinos have to publish their odds. As long as their games stick to those odds, they’re not “cheating”. Is it fair? Well, by gambling in the casino, you agreed to the rules they set. Even if the chances are in their favor, you agreed to it, so that’s “fair” (in some sense).
That said, stay away from casinos. They’ll just suck up your money. If you do go to casinos, set a budget, assume you will lose the entire budget, stop when your budget is depleted, and consider the money spent as your admission fee to play the games.
There is a discrepancy between the payouts and the odds of winning.
Roulette is the simplest example. In Roulette there’s 38 numbers on the wheel (1-36, plus a 0 and a 00), each of these numbers is equally likely to be the winning number. You can bet on *one* number, and if you win, you get 36 times your bet. So you bet ten dollars, if you win you get $360. So, your *success* ratio is 1:38, but your *earnings* ratio is 1:36. There’s that discrepancy. If you play 38 times, you’ll expect to win once. But the earnings for that one win is only 36 times what one play costs, not 38 times, which would make you come out even. Basically, if it costs $10 to play, and you played 38 times, you would spend $380 dollars, and win $360 dollars, a $20 profit for the house, therefore a $20 loss for you.
Let’s say we bet on the result of a coin flip. You will give me $1 for every tails and I will give you 98 cents for every heads.
Statistically, I’m going to win every second game, which means you will give me a dollar and I will give you back 98 cents. If we play a very large number of games, each of them will be worth 1 cent to me.
The key misnomer in “The house always wins” is the word “always”. The house always wins, statistically, after a very large number of games.
remember that most casino games are not games of skill, but games of chance, and that there is a chance element even in the games that can be influenced by some skill, like blackjack or poker. Blackjack is more-or-less a solved game; depending on the particular rules, there are charts out for the ideal action (hit, stay, double, split) for any given hand you have versus the dealer’s up-card, but in the end the odds of ending up with a hand that is greater than the dealer’s is still not greater than the odds of losing to the dealer even with perfect play by just the odds of what information you have from the current board-state; to push the odds in your favor, you have to also take into account information about the games before, and what cards are currently not in the deck (this is card counting), and know when you have an overall better chance of getting a winning hand, and thus should bet more, to come out overall ahead.
This is also why casinos will absolutely kick you out if you’re counting cards.
The house doesn’t need to cheat. The house sets the rules.
Lets do a simple game. Heads or tails. Heads you win, tails house wins. Both heads and tails are 50/50. Nobody has advantage.
Let’s do another. 3 sided die. 1, you win, 2 house win, 3 house win. Obviously house advantage.
House gets to choose which games are on the floor. So they get home court advantage.
The house doesn’t always win per se. They win the majority of the time due to chance. Black Jack for example is 6/5 against the player. The house may takes some hits but over time they will win more than they lose. If they won everytime then no one would play. They need the player to THINK they have a slight advantage (knowledge,skill etc) but they dont. The house always wins IN THE END.
The odds are always in the houses favor. Roulette has black spaces and red spaces. So the odds of winning (assuming you bet on a color) would be 50/50. House would break even. But wait… there are two green spaces as well. So those odds drop to 18/38 of winning. So the house has the statistical advantage.
Same thing with slot machines. They are programmed to pay out at a certain rate. Overall they are programmed to pay out less than they take in.
Blackjack is similar. The dealer hits or stays based on the number they have (17 is where they stay). The odds of getting a card combination higher than 17 but less than or equal to 21 is less likely than busting.
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