How does the house always win?

Question

If a gambler and the casino keep going forever, how come the casino is always the winner?

In: Mathematics

Answer 1

In the long run, the house has better odds.

In roulette, there are 38 slots. 16 red, 16 black, and 2 green (zero and double zero). You can place bets on individual numbers, on red vs black, odd vs even, high vs low, but never on the zeroes.

When the result is 0 or 00, the house takes all the bets. This is just enough to guarantee that in the long run, the house always comes out slightly better.

In slots, the casino literally controls the odds, and will set them so that the expected average payout is less than the cost of playing.

In poker, the house doesn’t even play. They just take what’s called a “rake”, which is a percentage of every pot. The house has zero risk on a poker table. The only way they could lose money is if they pay the dealer more than the rake is earning, but they can always just up the table minimum.

Blackjack is the only game where the player has the ability to track their odds over time and “beat the system”. Blackjack only goes through a few cards per hand, so instead of a single deck that gets reshuffled every hand to reset the odds, the dealer uses a “shoe” of 6 or more decks all shuffled together, and as cards are used they’re discarded to the side. The shoe is occasionally reshuffled, but not every hand.

If you were to pay attention to the cards that are drawn, you could know whether there are a lot of face cards (worth 10) left in the deck, or if more have been drawn already, and use that knowledge to hit or stand, impacting your odds. On a newly shuffled shoe, you don’t know much, but later in the shoe if you’ve kept track you can use that information to your advantage.

This is called “card counting”, and while not illegal, if a casino has any reason to believe you’re counting, they’ll start shuffling more often, or they’ll simply kick you out. Don’t try it, because you don’t want to find out the hard way whether they’re gentle about it or not.

The simple fact is that the house makes the rules, and they collect a lot of data on games. If a game isn’t profitable enough, they adjust the odds or remove it from the floor.