On his website, John Patrick advocates that if it is allowed, the player should surrender a hard 17 against the dealer's face card. The expected value for this play is to lose approx. 42% of your money. I challenged Patrick to the following wager which he of course has declined to accept.
I'll play the above hand out for 2000 games. If I am down more than 1000 units, I owe him $10,000., if I am down less than 1000 units he owes me $10,000. Taking standard deviation into account, what are the chances that after 2000 games, that I could be down more than 1000 units? My guess would be about a 5% chance that I could lose this bet. Does anyone know how to figure it out exactly?