I had a friend of mine recently involved in an interesting proposition and he asked me for my advice which unfortunately is more limited now that I do not spend any time teaching math's or stat's.
The proposition evolved from a disagreement with an obnoxious player who was convinced that soft 18 should never be hit against 9,10 or Ace.
I told my friend that a hit on soft 18 was more advantageous against a 9 and to use this upcard for the following scenario :-
200 hands are dealt with soft 18 verses dealer 9 and the total of hands won is tallied, for hitting and standing. The method which wins the most hands gets paid a fixed amount.
The question I have is that after 200 hands what is the probability that the 'Hit soft 18' will be ahead of the 'stand 18'. I also managed to work out that you would expect to win 90 hands by hitting and 82 hands by standing but I could not calculate what chance my friend had of losing the bet over 200 hands.

Any ideas gratefully received.

Best regards

Geoff Hall