[RocketManJames]

I have a question about expectation and independence with regards to tipping (perhaps to a BJ dealer).

I have a friend who is a card counter. Let's assume for the sake of my question that he's a successful/profitable card counter. Let's assume that his expected return is 2% per dollar wagered.

From any session to the next his future expected return should be independent of the events from previous sessions. So, if he lost $500 in one session, his expected return is still 2% per dollar wagered.

Now, let's say he plays through $5000 and he nets $200. He is $100 ahead of schedule. So, what if he tips the dealer $50 (say he's feeling ultra-generous, or it was the holidays and he felt like giving). In my opinion (again, I am NOT a mathematician, but I like to think about this stuff from time to time), it makes no real difference that he does that this one time. But what if he repeatedly gives these large tips a lot more than once. This is where my logic confuses me.

How will this affect his long run? Assume that he will give up 50% of anything in excess of his normal 2%. If he is at the expected 2% or less (win or lose), he tips nothing. My questions:

1) How does this affect his overall expectation?
2) Will he go broke, or better yet is there some tipping strategy such that he will go broke so long as he does not tip more than his expected return for any session?

Interested to hear your analyses.

Much appreciated,
RMJ