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two sides, America and Russia, are facing off in a deadly game.

america has the technological advantage, they have more missile silos, a total of 12.

however america only has 10 primary cities.

russia has the people advantage, they have 14 primary cities, but only 10 missile silos.

both sides want to disable each other's missile silos while causing maximum damage to the population, in order to win. both sides have an agreement that they will only fire 1/2 of their missile silos every "round" until one side has won or the other. there two ways to win, are either destroy all missile silos or destroy all the primary cities.

as an example game, in the first round, russia uses 2 missiles on the missile silos, and 3 missiles on the primary cities; while america uses 4 missiles on the missile silos and 2 missiles on the primary cities.

russia now has 6 missile silos and 12 primary cities while america has 10 missile silos and 7 primary cities.

in round 2, russia uses all 3 missiles on the primary cities, and america splits its attack again , using 2 missiles on the missile silos, and 3 missiles on the primary cities.

russia now has 4 missile silos and 9 primary cities, while america has 10 missile silos and 4 primary cities.

in the final round, russia trying for the knock out uses both missiles on the primary cities. america splits its attack and ends the game, using 4 missiles on the missile silos and 1 missile on the primary cities.

final result america wins, with 2 primary cities left and 10 missile silos while russia has 0 missile silos and 8 primary cities.

now, assume both sides use a random number generator to determine how many missiles they'll use on cities and on missile silos. what is russia's chances of winning?

(if a player has an odd number of missile silos he'll round up when firing.)

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America; 12M 10C

Russia; 10M 14C

Common logic says that America would win, because it it America. Observant logic says that Russia would win, as they have more targets to take fire. While military logic argues that America would win, because they have more weapons. Numerical logic would agree that America would win, because they are able to emiminate more targets.

As weaponry is the only active variable, variable logic would say that America would win.

With my number generator, I got Russia winning 21.6%, Ties 2.3% and America winning 60%. Out of 1,000 trials.

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America; 12M 10C

Russia; 10M 14C

Common logic says that America would win, because it it America. Observant logic says that Russia would win, as they have more targets to take fire. While military logic argues that America would win, because they have more weapons. Numerical logic would agree that America would win, because they are able to emiminate more targets.

As weaponry is the only active variable, variable logic would say that America would win.

With my number generator, I got Russia winning 21.6%, Ties 2.3% and America winning 60%. Out of 1,000 trials.

Something's wrong with your numbers: They don't add up to 100%.

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Something's wrong with your numbers: They don't add up to 100%.

Thanks. Typo...

Russia is 27.6, Ties are 2.3% and America is 70% (was looking between screens, with a lack of sleep)

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I wrote a quick weighted graph search. I may have a bug in it but I got the following (hard to think there's a bug in the method, the computations give me a total probability of 1):

America win probability: 0.644241

Russia win probability: 0.265916

Ties probability: 0.0898429

My trial examination results, over 10,000,000 iterations were:

America win %: 76.80274

Russia win %: 15.8927

Ties %: 7.30456

I'm a little frustrated that my predicted results don't match the trial results. The one thing that i didn't do was keep track of each the win probability at each vertex for each team and propogate them up so that i can see the predicted probability (I just searched and totalled them - quick-and-dirty). Maybe if i did that, I would be able to see if there are any branches, that if taken, drastically skew the results. (and given the disparity between 4 different people...maybe that's the case)

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I wrote a quick weighted graph search. I may have a bug in it but I got the following (hard to think there's a bug in the method, the computations give me a total probability of 1):

America win probability: 0.644241

Russia win probability: 0.265916

Ties probability: 0.0898429

My trial examination results, over 10,000,000 iterations were:

America win %: 76.80274

Russia win %: 15.8927

Ties %: 7.30456

I'm a little frustrated that my predicted results don't match the trial results. The one thing that i didn't do was keep track of each the win probability at each vertex for each team and propogate them up so that i can see the predicted probability (I just searched and totalled them - quick-and-dirty). Maybe if i did that, I would be able to see if there are any branches, that if taken, drastically skew the results. (and given the disparity between 4 different people...maybe that's the case)

Well, i am an idiot:

my edge calculations computed the same probability for traversal to each child..(each child ended up being 1 in missiles fired instead of (missiles_fired choose r) * 1/2^missiles fired)

Here are the fixed graph traversal predicted probabilities:

America win probability: 0.767924

Russia win probability: 0.159057

Ties probability: 0.0730187

Which is MUCH MUCH better (and closer to the trial method).

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