Is there any benefit to the house from a probability perspective that a gambler tends to gamble until he loses?
Let me clarify with an example:
In a video poker game I play on my pda, if you win a hand, the game allows you to double your bet by picking if the next card drawn is red or black. If you win that you can double again the same way and then again until you lose. You can also stop any time and walk away.
Theoretically each time you play there should be no benefit to the house because the odds are even. So it shouldn’t matter to the house how many times you double or don’t double - it should all even out.
On the other hand, there’s the psychological propensity to keep going until you lose. Which I’d think would benefit the house. Is there any mathematical truth to this?
No. The house’s profit is determined by how many plays are made, multiplied by the house’s profit per play. If a casino gets 2 billion plays a year, it doesn’t matter if those plays came from hundreds of thousands of people who all went broke, or from one guy with a lot of free time and a ten billion dollar bankroll.
But it can sure affect the players!
OK - then I’m thinking about it, explain to me why this logic is wrong:
Suppose EVERY player kept playing until they lost. Then the house would never lose, and would often win. Suppose only 1 player walked away at some point when they were still winning, if there are many players, then theoretically the house should still be up. At what point does that effect vanish?
You’re thinking that, at some point in time, every gambler is “ahead”, which is false.
Here’s a better way of thinking about it. At any moment in time, 100,000 bets are being placed by various gamblers in the casino. Due to the way that the casino has set the odds, between 51% and 70% of them are going to lose that bet, depending on the game that they are playing. As long as the bets keep coming, the casino keeps making money, the casino doesn’t have to care if the same gambler is making consecutive bets.
-lv
I agree with Mr. Stone, and would like to add that adding the concept of “credits” to slot machines (and video poker, naturally) helped the casino industry - before, you could run a roll of quarters through a machine and bucket whatever was in your tray when you were done, and walk. Now, after 40 quarters are played, you have maybe on average 36 “credit quarters” on the machine, and they don’t seem so much like real money leaving your fingers when you play those off.
To answer your second question - if I have $20 and fifteen minutes to play quarter video poker, I’m really there to shoot for the $1000 royal flush, or maybe the $100 four of a kind (certain variations of machine). If I don’t get those, I’m probably leaving all my $20 in the machine. And even if I get a four of a kind, I might play $20 or $40 more of the $100 win, before taking my $80 or $60 and walking.
If I hit the royal, I’m toking (tipping out) the changeperson or bartender and leaving happy.
Now, I haven’t played video poker for money in two years, and possibly never will play for money again, seeing as how my current employment involves creating the machines. But I’ve seen foreign, tourist, recreational, and degenerate (addicted, problem) gamblers at play - and they all play a little differently.
uglybeech
The fault in your gambling logic is that the pda does not play the same way a casino does.
Don’t forget, a casino always has a percentage. Your pda takes no percentage whatsoever. (To simulate real gambling, they should have programmed it that way).
To make it simple, let’s talk about roulette which has 38 numbers (1-36 and zero and double zero). If you play a particular number for $1, and it comes up, you’d think that you should keep your bet and get $37 more right? Actually, casinos pay you back only $35 for each dollar bet. Unlike your pda, casinos do NOT give you 50/50 odds.
Still you think, “okay, if I keep doubling my bet, eventually I’ll come out a winner.” Well do you have the financial resources to do this? 10 or 12 losses in a row would require a phenomenal amount of money to keep pace. Your pda gives you unlimited funds but this isn’t so in the real world.
Also, casinos place limits on bets. So, even if you had unlimited funds, eventually your bet doubling would require a situation in which you must place a bet which is larger than the house will take. Again, your pda allows this - casinos don’t.
Hope ths has been helpful.