Victory in the Pacific

The Dice Got Me Again!
by Brad Solberg

Download the odds charts in Microsoft Excel format!

Please feel free to reprint this article and charts in any other medium, including journals like The Boardgamer. I see no reason why people without net access can't get the benefit of this work.

Following this article are some charts useful to anyone who plays WAS or VITP. I was motivated to make the charts after one too many comments by experienced players of VITP that went something like this:

"I had an 83% chance to succeed with my suicide CV" or "If Brad had not beaten my 72% chance for day/day night I would have held CPO."

In WAS similar statements apply to U-Boat probabilities, LBA/Air shots and the like. In VITP it usually refers to the Day/Night probabilities.

As most people who play VITP a lot know, the probabilities for day/night are:

Day/Night Probabilities

Day
Day/Night
Night

No Bonus or Split Bonus

42%

16%

42%

+1 (Day with no Flag)

58%

14%

28%

+2 (Day with Flag)

72%

11%

17%

It is important to understand that the probability of two events happening is the product of their individual probabilities. So in order to prevent a target such as a Marine from getting through in one salvo, you must multiply the probability of day or day/night (58%, 72%, 83%) by the chances of your available firepower doing the job if day arrives. So if you can send a Marine home 75% of the time, and have the Flag, you only have a .75*.83=.5865 chance. The odds get worse very fast if you have to send two ships home or three.

The problem is that none of us can agree on what the real chance of sinking or disabling a ship might be. My first attempt to combine Disable odds with Sinking odds was too pessimistic and was challenged by Alan Applebaum. When I showed my equations, David Finberg started an off-line discussion, presenting his own (overly optimistic) incorporation of disable. We attacked the problem differently and by comparing our attempts, David realized what we were doing wrong and left the math as an exercise for me to do.

Straight binomial expansions that consider armor and disables are too ugly even for my spreadsheet. But I was able to consider "odds to sink vs armor given x hits", "odds of getting exactly x hits with y shots", "odds to disable with x shots" and was able to apply those terms to an easier binomial expansion that included all of it.

The following tables show chances of disabling, sinking (useful vs LBA or to estimate casualties from a salvo) and removal (disable or sink). If you want to know the odds of getting disabled without getting sunk you can subtract the sunk odds from the disable odds.

I included armor values up to 6, and, because of certain very large BB's, also worked it out for armor = 9. If those BB's are damaged to 7 or 8 you can interpolate between the 6 and 9 figures for a pretty good estimate -- the math gets harder and harder as the armor value goes up.

As a final check of the numbers, Ed Menzel mailed me the results of an old General article which estimated chances to get "at least X damage" with "Y shots". The results matched my "sunk" table, except that the General article stripped off fractions on all numbers instead of rounding. This caused errors of up to 1% on smaller armor factors. On the 9 factor armor there are enough terms in the equation that their numbers were off by 2-3% in some cases. Still it was a good validation of the technique, and I have confidence in the numbers.

One last word about probabilities. We are not rolling enough dice in these games to use these as anything more than a guideline to choose between strategies. If something is 25% likely to happen you can't count on it happening in four attempts. But it can be used to reject the 25% strategy against one that accomplishes about the same goals but has a 50% chance of succeeding.

Going back to the original statements that caused all this (see Brad's game as IJN vs. John Pack on Consimworld)... The probability of a suicide CV sinking a SNLF with the flag turns out to be 70% -- not 83%. Good but hardly anything to count on all the time. Chance to prevent two SNLF from taking Midway in CPO vs. 5 LBA and no control of flag is 42% -- not 72%.

Thanks to everyone who motivated me and assisted me in making these charts. I hope you all find them as useful as I do.

Probability of Disable in X shots

Shots

1
2
3
4
5
6
7
8
9
10
11
12

Disable

17%

31%

42%

52%

60%

67%

72%

77%

81%

84%

87%

89%

Probability of Sinking in X Normal shots vs Y armor

Armor/Shots
1
2
3
4
5
6
7
8
9
10
11
12
0

17%

31%

42%

52%

60%

67%

72%

77%

81%

84%

87%

89%

1

14%

26%

36%

45%

53%

60%

66%

71%

75%

78%

82%

84%

2

11%

21%

30%

39%

46%

53%

58%

64%

68%

72%

76%

79%

3

8%

16%

24%

32%

38%

45%

51%

56%

61%

65%

69%

73%

4

6%

12%

18%

24%

30%

36%

42%

47%

53%

57%

62%

66%

5

3%

7%

11%

16%

22%

27%

33%

38%

43%

48%

53%

57%

6

0%

2%

4%

8%

13%

18%

23%

28%

33%

38%

43%

48%

9

0%

0%

1%

3%

5%

8%

11%

14%

18%

22%

26%

30%

Probability of Sinking in X Bonus shots vs Y armor

Armor/Shots
1
2
3
4
5
6
7
8
9
10
11
12
0

33%

56%

70%

80%

87%

91%

94%

96%

97%

98%

99%

99%

1

28%

48%

63%

74%

81%

87%

91%

93%

95%

97%

98%

98%

2

22%

40%

55%

66%

75%

82%

86%

90%

93%

95%

96%

97%

3

17%

32%

46%

58%

68%

75%

81%

86%

90%

92%

94%

96%

4

11%

24%

37%

49%

59%

68%

75%

81%

85%

89%

92%

94%

5

6%

15%

27%

39%

50%

59%

68%

74%

80%

85%

88%

91%

6

0%

6%

16%

28%

39%

49%

59%

67%

74%

79%

84%

87%

9

0%

2%

6%

13%

21%

30%

39%

47%

56%

63%

69%

75%

Probability of Removal in X Normal shots vs Y Armor

Armor/Shots
1
2
3
4
5
6
7
8
9
10
11
12
0

33%

56%

70%

80%

87%

91%

94%

96%

97%

98%

99%

99%

1

31%

52%

67%

77%

84%

89%

92%

95%

96%

98%

98%

99%

2

28%

48%

63%

73%

81%

87%

91%

93%

95%

97%

98%

98%

3

25%

44%

59%

70%

78%

84%

88%

92%

94%

96%

97%

98%

4

22%

40%

55%

66%

74%

81%

86%

90%

92%

95%

96%

97%

5

19%

36%

50%

62%

71%

78%

83%

88%

91%

93%

95%

96%

6

17%

32%

46%

57%

67%

74%

80%

85%

89%

92%

94%

95%

9

17%

31%

43%

54%

63%

70%

76%

81%

85%

89%

91%

93%

Probability of Removal in X Bonus shots vs Y armor

Armor/Shots
1
2
3
4
5
6
7
8
9
10
11
12
0

50%

75%

88%

94%

97%

98%

99%

100%

100%

100%

100%

100%

1

44%

69%

83%

91%

95%

97%

99%

99%

100%

100%

100%

100%

2

39%

64%

79%

88%

93%

96%

98%

99%

99%

100%

100%

100%

3

33%

57%

74%

84%

91%

94%

97%

98%

99%

99%

100%

100%

4

28%

51%

68%

80%

87%

92%

95%

97%

98%

99%

99%

100%

5

22%

44%

62%

76%

84%

90%

94%

96%

98%

99%

99%

100%

6

17%

37%

55%

71%

80%

87%

92%

95%

97%

98%

99%

99%

9

17%

32%

47%

63%

72%

80%

86%

91%

94%

96%

98%

98%


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