Actually, a player being ahead after 100 or 1,000, or even 10,000 (non-pushed) hands of baccarat is hardly unrealistic.
Assuming he's playing bank at 5% commission, and is playing out of an 8-deck shoe, then his probability of winning a single hand (conditioned on not pushing) would be about 45.860% / (1-9.516%) ≈ 50.682%.
To be ahead after 100 non-pushed hands he'd need to win at least 52 of those hands.
To be ahead after 1,000 non-pushed hands he'd need to win at least 513 of those hands.
To be ahead after 10,000 non-pushed hands he'd need to win at least 5,129 of those hands.
To be ahead after 100,000 non-pushed hands he'd need to win at least 51,283 of those hands.
Hence:
Probability of being ahead after 100 hands would be 43.528%
Excel formula =1-BINOMDIST(52-1,100,50.68244%,1)
Probability of being ahead after 1,000 hands would be 35.986%
Excel formula =1-BINOMDIST(513-1,1000,50.68244%,1)
Probability of being ahead after 10,000 hands would be 11.405%
Excel formula =1-BINOMDIST(5129-1,10000,50.68244%,1)
Probability of being ahead after 100,000 hands would be 0.007%
Excel formula =1-BINOMDIST(51283-1,100000,50.68244%,1)