Tuesday, March 30, 2010

Why everyone always loses at gambling

You always hear about people coming back from Vegas having lost big. A small percentage of people win big. However, you may also know that, if you make smart bets*, the house edge is only, say, 1 or 2%. So you'd imagine, if you had 100 friends, maybe 49 would go to Vegas and win and 51 would lose.

Ah, but here's the trick: if your friends each took $1000 to Vegas, bet it all at once on one of these low-house-edge bets, and stopped there, you'd have 49 friends who won and 51 friends who lost. But that's not how we gamble. I might sit down at a table with $100 and bet $5 until I lose, in which case I'm trivially guaranteed to lose.

Or you might play like me. I thought "aha, I am a clever one. I will sit down at a table with $x, and if I double my $x, I will shrewdly leave the table. Thus my two exit points are $2x and $0; I have a 49% chance of hitting the first and a 51% chance of hitting the second, so I will likely not lose all the time."

But that's not how things work! If the house edge is 2%, like in this example, you basically lose 2% of your money on every bet! The longer you play, the less likely you are to hit $2x, and the more likely you are to hit $0.

How much more likely? You could probably math it out. But I gave up math for programming, so here's a bit of python you can copy and paste:


import random

startingMoney = 50
bet = 5
wins = 0
losses = 0

for i in range(10000):
money = startingMoney
while 1:
result = random.randint(0,99)
if result >= 49:
money -= bet
money += bet

if money <= 0:
losses += 1
elif money >= 100:
wins += 1

print "wins: " + str(wins)
print "losses: " + str(losses)

Run it a few times. The house edge here is set to about 2%, corresponding to the 49/51 thing we discussed earlier. You'll find that you win about 40% of the time, though. Ratchet the house edge up to 4% (change that 49 to a 48), and you'll win only 30% of the time! Terrible! And this is not even counting the fools who play slots or those goofy table games or whatever.

Or, you could just accept the folk wisdom that "everyone always loses in Vegas", and you wouldn't be too far off.

* AFAIK, the "good bets" are the pass line and odds in craps and 3-2 blackjack with solid basic strategy. And poker, if you're good. But that's a whole different story...

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