Assume this online casino promotion. A blackjack game with 0.5% house edge, $20,000 play thru required to get a $100 in free credits. Basically a break even promotion. Now assume the player has good luck and at the halfway point of $10,000 play thru he is $500 ahead. He then takes a hour for dinner and comes back to finish the promotion.

When he started the promotion his play was expected to yield a $100 loss. However, with only $10,000 to go can we assume his loss will only be $50, and he will end up with a $450 gain plus $100 in free credits. Or will he lose everything he won and his original $100 loss will prevail.