Originally posted by: akshatp
Originally posted by: DrPizza
not watching the video... (dialup) However, unless you're playing for entertainment, mathematically speaking, the smartest gamble IS to bet it all on the first spin.
Explain.
Without going to the extent of providing a mathematical proof, I'll just point out a few things. First, lets assume that you have an equal chance to win as to lose; a 50/50 proposition at the casino. And, you keep playing that game until either you're broke, or the house is broke. Well, after you play 2 hands, there's a 50% chance that you'll break even, a 25% chance that the house is ahead, and a 25% chance that you're ahead. Sure, there is a 1 in 8 chance that you'll win 3 times in a row, but there's also a 1 in 8 chance the house will win 3 times in a row. Winning 3 times in a row is far more likely than winning 10 times in a row. However, it's equally likely to win 10 times in a row for both the house and for you. Sometimes you'll be a little ahead, sometimes the casino will be a little ahead. Sometimes you'll be a lot ahead, sometimes the casino will be a lot ahead. Unfortunately, it is far more likely for the "a lot ahead" for the casino to be more money than you have than it is for you to be "a lot ahead" of the casino by the amount they have available to them (assuming the casino has a MUCH bigger bank roll than you.)
A simpler way to express this: "Vegas wasn't built on winners." Over the long run, the odds heavily favor the house. Sure, people have short term winnings, but the longer people play, the more likely it is that the house ends up ahead. This is simply because while I used 50/50 above, every game in a casino favors the casino.