Pennies - challenge The Game is not fair ! Here is why: Player A needs Head followed by Tail or HT to win. Player B needs Head followed by Head or HH to win. Let's examine the results after K trials. (2**K total possibilities). What is the number of possibilities for Player A NOT to win. versus the number of possibilites of Player B NOT to win. Case 1: no heads at all Player A and B have one such possibility Case 2: 1 head found Player A and B have the same K possibilities. Case 3: 2 heads found Player A must have the Heads at the end which is a single possibility. and it looks like: T T T T ..... T T H H Player B has much more  For him not to win he need the construct .... H T H but also ... H T T H in fact in this case he as (K-1)*(K-2)/2 possibilites In fact for the case of 3 heads Player has one possibility over the K trial ..... T T T H H H however Player B has number of possibilities in the order of O(3) or K**3 compared to Player A. And so on and so forth ... Therefore clearly Player A has an advantage. Aharon Tam Wednesday, July 16, 2003 I think the correct solution is that there is no advantage to either player. The two published solutions seems to miss that the game ends as soon as one player wins. A needs HT, B needs HH 2 Tosses: HH B Wins HT A Wins TH No winner TT No winner A and B have same odds of winning. Only TH and TT play on. 3rd toss: THH B Wins THT A Wins TTH No winner TTT No winner A and B have same odds of winning. Only TTH and TTT play on. 4th toss: TTHH B Wins TTHT A Wins TTTH No winner TTTT No winner A and B have same odds of winning. Only TTTH and TTTT play on. 5th toss: TTTHH TTTHT TTTTH TTTTT etc, etc. Lars Thursday, September 18, 2003   Fog Creek Home