Victory in the Pacific

Battles of Numbers
Case #5

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:

US Retreat: 1:1, 2:2, 3:3, 5:4

 

 

IJN Retreat: Impossible

 

 

US

IJN

US Win

US Surv

IJN Surv

LR

2

1

67.56%

1.375

0.324

1.082

3

1

93.24%

2.310

0.068

1.351

4

1

99.06%

3.383

0.009

1.606

5

1

99.91%

4.446

0.001

1.802

6

1

99.99%

5.484

0.000

1.938

3

2

49.64%

1.705

0.797

0.929

4

2

81.41%

2.486

0.287

1.132

5

2

95.09%

3.520

0.071

1.303

6

2

99.01%

4.652

0.014

1.473

4

3

39.40%

2.075

1.344

0.86

5

3

69.59%

2.674

0.637

1.016

6

3

88.66%

3.613

0.220

1.164

6

4

58.15%

3.025

1.171

0.951

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