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Author Topic: Taking risks & driving the P2 seat  (Read 28677 times)

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Insomniac

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Re: Taking risks & driving the P2 seat
« Reply #50 on: August 29, 2012, 01:52:38 pm »
0

BTW: Forager has a heavy heavy player 2 advantage. (Assuming both players go forager)
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rrwoods

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Re: Taking risks & driving the P2 seat
« Reply #51 on: September 11, 2012, 09:59:31 pm »
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I'm starting to get convinced the optimal strategy is actually quite complex. I think it uses all 3 options, and also includes the 'turns to go' and 'actual point difference' (not just 'am I behind or ahead'). But I won't go into that - I didn't name it Borinion for nothing.
Well I will :-P

I've attached linked a spreadsheet I used to solve the game.  With optimal play, Player 1 wins 59% of games.

Solving the game is a simple matter of backward induction.  Evaluate turn 9 first; based on the P1 win percentages in turn 9, we can solve P2's optimal play on turn 8, and so forth.

Something interesting:  Not only does the optimal strategy involve all three options, and not only does it involve "turns to go" and "how far ahead/behind am I" (of course it would!)... the strategy is non-monotonic!  As a simple example, in turn three, if player 1 is 2 points behind or 6 points behind, he should choose option A.  But if he's 5 points behind he should choose option B.  (It's impossible for him to be 3 or 4 points behind, so the sheet ignores those possibilities; something it doesn't do beyond turn 3.)

There's a "pocket" at the 5-point deficit mark where player 1 should choose the riskier option, despite that at some higher deficits, he should choose the safer option!  Don't know about you, but to me this is fascinating.  "Borinion" -- maybe to play, but analysis is extremely interesting :-)

In the later turns more pockets appear.  In turn 8 (might as well choose the last player 2 turn since we are talking about taking risks in the player 2 seat), there are two such pockets; one from +5 to +7, and one from -2 to -1.  At -6 to -7 we choose B as well, but at -8 to -13 we choose option C and at -14 or worse it is hopeless.

Is it possible there is something to be learned about Dominion (or games in general) from the non-monotonic nature of this strategy?  Can this revelation be put to any practical use?


EDIT: looks like I was beaten to this by Gamer-man, but our results differ a bit.
« Last Edit: September 11, 2012, 10:19:34 pm by rrwoods »
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