Vesuvio said:
Agreed. A does the least badly because he bets the least, and so on. They all lose the amount the house edge predicts overall. Whoever bets the most loses the most.
No-one should ever gamble at a casino
p.s. but who knows what their results will be on-line - this is one for the corrupt programmers among us to answer
Bingo
Imagine that A,B,C,D are all playing at the same table, and that the chance of winning the pass line bet is 49% (its a little lower).
When they lose one of the first 3 rolls, all brothers walk away with the same total. But when they win the first 3 rolls,
Brother A quits with $3 won
Brother B plays one more $1 bet, and walks away with $2 51% of the time, and $4 49% of the time .... therefore, he on average will lose more than A
Brother C plays one more $2 bet, and walks away with $1 51% of the time, and $5 49% of the time .... therefore, he on average will lose more than B
Brother D plays one more $2 bet, loses and walks away with $1 51% of the time
The other 49%, he plays $2 again, loses and walks away with $2 51% of the time
The other 49% he plays $2 again, loses and walks away with $3 51% of the time
The other 49% he plays $2 again, loses and walks away with $4 51% of the time.
etc etc etc
Its a little harder to see in the case of Brother D, but his expectation is worse than brother C, which is worse than B, which is worse than A.
As Vesuvio pointed out, your expectation is solely a result of the house advantage, and the amount that you wager. And the next wager you place, is the next wager you place. Doesn't matter if its today, tomorrow, next week, or next year. If you don't have the best of it, adjusting your betting won't do anything. You are going to lose in proportion to the amount of your total wagering.
What does this all mean? When you don't have the best of it, gamble for fun ... not profit. Online, bonus whoring is about the only way to have the best of it.