question about house edge....

[witchdr]

Hello everybody! I have a question regarding the house edge: how is it obtained by the...well..house ? I mean for example let's say you are playing European Roulette in a casino where the min bet is 1$ and the maximum is ..I don't know...300$ and you decide to use the Martingale system. Everybody says that the system is good but in the long run you'll lose because of the house edge. Now what is this "long run" how is it calculated? I mean if you play and play and play without stopping, eventually you won't be able to double your last bet (either you'll run out of money, or you'll be restricted by the max bet), and the longer you'll play the bigger the chance for this to happen. But if you were to play it safe...if you were to make each day let's say 30$ (so 30 successful runs) and then stop (eventually withdraw these 30 bucks) and start again tomorrow? I guess what I'm trying to ask you is: the chances to loose increase the longer you play a game without stopping or according to the total time you've played it today and tomorrow and the day after....thanks

[maphesto]

House edge means that in every single game of roulette the house have bigger chance to win than the player.

Even if red comes up 21 times in a row, it's equal chance for red and black the spin after.

Even if you have unlimited bankroll, and no betsize limit at all at the table, the House have bigger chance than you to win on next game.

Of course, we realize that one color in very rare occasions comes up more than 15 times in a row. But remember:

1
2
4
8
16
32
64
128
256
512
1024
2048
4096
8192
16384
32768

The last time you bet 32768$ to win one, I repeat one single dollar..

Roulette is a perfect entertainment game, but there is absolotely no system that could beat it.

If someone invent a system and wins with it, it's only luck. But I enjoy lotteries and entertainment.

[takethemoney]

With an unlimited bankroll you could beat it..........IF there were no table limits. The casinos are kind of smart and know what they are doing.

[Eliot Jacobson]

Hello everybody! I have a question regarding the house edge: how is it obtained by the...well..house ? I mean for example let's say you are playing European Roulette in a casino where the min bet is 1$ and the maximum is ..I don't know...300$ and you decide to use the Martingale system. Everybody says that the system is good but in the long run you'll lose because of the house edge. Now what is this "long run" how is it calculated? I mean if you play and play and play without stopping, eventually you won't be able to double your last bet (either you'll run out of money, or you'll be restricted by the max bet), and the longer you'll play the bigger the chance for this to happen. But if you were to play it safe...if you were to make each day let's say 30$ (so 30 successful runs) and then stop (eventually withdraw these 30 bucks) and start again tomorrow? I guess what I'm trying to ask you is: the chances to loose increase the longer you play a game without stopping or according to the total time you've played it today and tomorrow and the day after....thanks

Let
N = number of rounds
E = expected winnings
A = actual winnings

The "Long run" is the statement that:

limit (N -> infinity) E/A = 1.

The rate of convergence of the limit depends on the variance of the game.

A common misunderstanding is to believe that E and A get close to each other. That is not necessarily the case. Limits can converge to a value even as the numerator and denominator diverge:

10/9, 101/99, 1002/998, 10003/9997, 100004/99996 --> 1

--Eliot