Victory in the Pacific

One Allied Cruiser 1-1-7
vs. One Japanese cruiser 1+2-7

This is actually the first case I tested – to compare the Markov chain approach to that used by William Burch. No simplifying approximations are needed for this simple case – so all 35 possible battle states are recorded: 

7 for the Japanese {Intact, 1 Damage, 2 Damage, Disabled, 1D+Dis, 2D+Dis, Sunk}
5 for the Allied {Intact, 1 Damage, Disabled, 1 Damage+Disabled, Sunk}

Our results are the same, so either we’re both right or both wrong but for the same reasons :-).  But these Markov chain calculations are more compact and easier to generalize.

Starting data:

IJN vs. Allied (both intact):
10/36 = 27.78% to sink it
6/36 = 16.67% to disable it

Allied vs. IJN (both intact):
4/36 = 11.11% to sink it
6/36 = 16.67% to disable it

… and corresponding values if the target is already damaged. The Japanese cruiser also loses the attack bonus if having any damage.

Lanchester Equivalent Value LEV = sqrt(0.4444/0.2778) = 1.26 Allied cruisers equal one Japanese cruiser.

Probability Distribution of Battle-Ending States

Green = battle continues; nothing should remain here at the end.
Blue = Allied Victory (control of area)
Purple = Japanese Victory
Grey = Draw (both knocked out of the area)

Summary of results

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