am pleased. ]]>

I once again find myself spending a lot of time both reading and

commenting. But so what, it was still worth it!

A quick observation: I don’t think the solution presented in the link (The Grey Labyrinth) is incorrect – it seems the issue is that you are analysing slightly different games. The rules of the game in that link state that in the event of a draw (all three players select the same number), each player has his dollar returned. So in that game a draw is better than a straight loss, and is in fact 1/3 as good as a win.

In contrast, the game you analyse counts a draw as a loss for everyone. So it makes sense that the optimal strategies are slightly different.

]]>For Geometric, lets say I have 100 timesteps between inception till maturity of the option, instead of taking the 100.root(S1.S2.S3.etc…S100), I simulate the stock price in each timesetp by taking the Ln of the Black Scholes:

LnS1 = LnS0 +(r – 0.5sigma.sq)dt + sigma*sqrt(dt)*x

Now if if were to code this in excel, technically I would only have to take Ln on S0??? and the rest of the stock prices from S1 to S100 should be just based on:

Let S0 = Ln100 (Ln of stock price at S0),

therefore, S1 = S0 +(r – 0.5sigma.sq)dt + sigma*sqrt(dt)*x ]]>