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Sep 18, 2012 at 15:48 comment added Douglas Zare I don't know what you mean by a transcendental value for the integers $n_1$ and $n_2$. However, your formula says you only need the banker to have a nonnegative expected return, and it is easy to ensure that. Set $M$ so that betting on Pass has a nonpositive return for the player, and set $N$ so that betting on Don't Pass has a nonpositive return. That said, I'm voting to close since I don't think the question is on the level of this site.
Sep 18, 2012 at 15:15 answer added Arthur B timeline score: 1
Sep 18, 2012 at 13:34 answer added Noah Stein timeline score: 2
Sep 18, 2012 at 13:13 comment added l4rmbr The profit(M or N) and the risk(p) will influence how people bet
Sep 18, 2012 at 12:44 comment added Colin Reid I'm struggling to see a mathematical question here. How are $n_1$ and $n_2$ influenced by $M$, $N$ and $P$?
Sep 18, 2012 at 12:26 history edited Gerry Myerson CC BY-SA 3.0
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Sep 18, 2012 at 8:16 history edited l4rmbr CC BY-SA 3.0
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Sep 18, 2012 at 8:08 history edited l4rmbr CC BY-SA 3.0
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Sep 18, 2012 at 8:03 history edited l4rmbr CC BY-SA 3.0
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Sep 18, 2012 at 7:56 history asked l4rmbr CC BY-SA 3.0