Allied Cruisers 1-1-7
vs. Japanese
Cruisers 1+2-7
“To pursue or not, that is the question”. I wrote this Case as a response to William Burch’s claim that pursuit is not worthwhile below 2.5 : 1 (or 2.18 : 1 for a 1+1-* light Japanese cruiser). That ratio is actually the ratio of expected sunk ships in one salvo, starting with 1:1. But at the point where ships shoot (and dice are rolled :-) the forces can only be 1:1, 2:1, 3:1 etc. As the inferior side cannot evade the battle, they will be overwhelmed with little cost in further rounds. So while I may be cautious to pursue with 2:1, I would certainly do so with 6:3. Randomness helps here the superior side, because they can always stop pursuing if the situation worsens.
Starting data:
1 IJN vs. 1 Allied: 44.44%
1 Allied vs. 1 IJN: 27.78%
2 Allied vs. 1 IJN: 48.07%
3 Allied vs. 1 IJN: 62.81%
4 Allied vs. 1 IJN: 73.46%
5 Allied vs. 1 IJN: 81.12%
6 Allied vs. 1 IJN: 86.60%
Lanchester Equivalent Value LEV = sqrt(0.4444/0.2778) = 1.26 Allied cruisers equal one Japanese cruiser.
Results:
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US Retreat: 1:1, 2:2, 3:3, 5:4 |
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IJN Retreat: Impossible |
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US |
IJN |
US Win |
US Surv |
IJN Surv |
LR |
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2 |
1 |
67.56% |
1.375 |
0.324 |
1.082 |
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3 |
1 |
93.24% |
2.310 |
0.068 |
1.351 |
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4 |
1 |
99.06% |
3.383 |
0.009 |
1.606 |
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5 |
1 |
99.91% |
4.446 |
0.001 |
1.802 |
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6 |
1 |
99.99% |
5.484 |
0.000 |
1.938 |
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3 |
2 |
49.64% |
1.705 |
0.797 |
0.929 |
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4 |
2 |
81.41% |
2.486 |
0.287 |
1.132 |
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5 |
2 |
95.09% |
3.520 |
0.071 |
1.303 |
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6 |
2 |
99.01% |
4.652 |
0.014 |
1.473 |
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4 |
3 |
39.40% |
2.075 |
1.344 |
0.86 |
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5 |
3 |
69.59% |
2.674 |
0.637 |
1.016 |
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6 |
3 |
88.66% |
3.613 |
0.220 |
1.164 |
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6 |
4 |
58.15% |
3.025 |
1.171 |
0.951 |