To: jeevacation©gmail.com[jeevacation@gmail.cont Jeffrey Epsteinfieevacationegmail.comj From: Nowak, Martin Sent Mon 9/10/2012 12:28:34 AM Subject: Re: harmonic function, n=9, decimal version he wrote an algorithm that calculates the winning probabilities in the alliance game this algorithm will also allow us to prove what we observe in the simulations we start from all players as singletons then they form alliances the larger alliance wins over the smaller one if two alliances have the same size the one with the highest ranked player wins when the number of players is odd then 1 loses often i am so happy that mike likes this problem so much he discusses it with the greatest mathematicians it is totally amazing to work with him the three of us must get together when you visit next! On Sep 9, 2012, at 11:56 AM, Jeffrey Epstein wrote: what dos this represent On Sun, Sep 9, 2012 at 7:46 AM, Nowak, Martin a wrote: the project with mike is going well!!! Begin forwarded message: From: Michael Hopkins < Date: August 30, 2012 9:46:46 PM EDT To: "Nowak, Martin" < > Subject: harmonic function, n=9, decimal version e[e[1, x, x, x], e[x, x, x, x, x]] -> 0. e[e[x, x, x, x], eft x, x, x, x]] -> 1. EFTA_R1_02203227 EFTA02720152 e[e[1], e[x, x, x, x], e[x, x, x, x]] -> 0.25925925925925924 e[e[x], e[1, x, x, x], e[x, x, x, x]] -> 0. e[e[1, x], e[x, x, x], e[x, x, x, x]] -> 0.07407407407407407 e[e[x, x], e[1, x, x], e[x, x, x, x]] -> 0.037037037037037035 e[e[x, x], e[x, x, x], e[1, x, x, x]] -> 0. e[e[1], e[x], e[x, x, x], e[x, x, x, x]] -> 0.07994261867501304 e[e[1], e[x, x], e[x, x], e[x, x, x, x]] -> 0.06311945748565467 e[c[x], e[x], e[1, x, x], e[x, x, x, x]] -> 0.03312467396974439 e[e[x], e[x], e[x, x, x], e[1, x, x, x]] -> 0. e[e[x], e[1, x], e[x, x], e[x, x, x, x]] -> 0.04903495044340115 e[e[x], e[x, x], e[x, x], e[], x, x, x]] -> 0. e[e[1, x, x], e[x, x, x], e[x, x, x]] -> 0.03703703703703704 e[c[1], c[x, x], c[x, x, x], c[x, x, x]] -> 0.048751769878530436 e[e[x], e[1, x], e[x, x, x], e[x, x, x]] -> 0.041769878530441916 e[e[x], e[x, x], e[1, x, x], e[x, x, x]] -> 0.03468961919666145 e[e[1, x], e[x, x], e[x, x], e[x, x, x]] -> 0.03939339742156644 e[e[x, x], e[x, x], e[x, x], e[1, x, x]] -> 0.034689619196661456 e[e[1], e[x], e[x], e[x, x, x], e[x, x, x]] -> 0.045247880994745755 e[e[1], e[x], e[x, x], e[x, x], e[x, x, x]] -> 0.0422351092858521 e[e[x], e[x], e[x], e[1, x, x], e[x, x, x]] -> 0.034063641105894625 c[e[x], e[x], e[1, x], c[x, x], c[x, x, x]] -> 0.038169314210988924 e[e[x], e[x], e[x, x], e[x, x], e[1, x, x]] -> 0.034376630151278044 c[c[1], c[x], c[x], c[x], c[x, x], c[x, x, x]] -> 0.04068614541360055 e[e[x], e[x], e[x], e[x], e[1, x], e[x, x, x]] -> 0.03735886505788107 e[e[x], e[x], c[x], c[x], e[x, x], e[1, x, x]] -> 0.03425143453312468 e[e[1], e[x, x], e[x, x], e[x, x], e[x, x]] -> 0.04049636848817573 e[e[x], e[1, x], e[x, x], e[x, x], e[x, x]] -> 0.03838036304039884 e[e[1], e[x], e[x], e[x, x], e[x, x], e[x, x]] -> 0.039585444918585365 e[e[x], e[x], e[x], e[1, x], e[x, x], e[x, x]] -> 0.03793329903369269 e[e[1], e[x], e[x], e[x], e[x], e[x, x], e[x, x]] -> 0.038983460931105954 e[c[x], e[x], e[x], e[x], e[x], e[1, x], e[x, x]] -> 0.03774182104175548 e[e[1], e[x], e[x], e[x], e[x], e[x], e[x], e[x, x]] -> 0.038628706677005825 e[e[x], e[x], e[x], e[x], e[x], e[x], e[x], e[1, x]] -> 0.03774182104175548 EFTA_R1_02203228 EFTA02720153 e[e[1], e[x], e[x], e[x], e[x], e[x], e[x], e[x], e[x]] -> 0.038628706677005825 *********************************************************** The information contained in this communication is confidential, may be attorney-client privileged, may constitute inside information, and is intended only for the use of the addressee. It is the property of Jeffrey Epstein Unauthorized use, disclosure or copying of this communication or any part thereof is strictly prohibited and may be unlawful. If you have received this communication in error, please notify us immediately by return e-mail or by e-mail to jecvacation@smail.com and destroy this communication and all copies thereof, including all attachments. copyright -all rights reserved EFTA_R1_02203229 EFTA02720154