What are the odds?

[deeter]

In a recent battle, both side's CnCs died simultaneously in an otherwise bloodless melee involving on both sides. It was the impact phase if that matters. I'm hoping someone with math skills can tell me the odds of that happening. Thanks in advance.

Deeter

[Ray552]

From an earlier thread where RBS mentioned the odds (https://www.slitherine.com/forum/viewtopic.php?t=101187):

If the general's unit is being pursued, he has a 1 in 12 chance of being incapacitated per test.

If his unit loses a close combat he has a 1 in 30 chance of being incapacitated per test. But this test may be taken several times in a turn if his unit is fighting multiple enemy units.

If his unit draws or wins a close combat he has a 1 in 90 chance of being incapacitated per test. But this test may be taken several times in a turn if his unit is fighting multiple enemy units.

Converting those odds into percentages:

Probability of a general dying/being incapacitated while with a routing unit that is being pursued: 1 in 12 = 0.0833 = 8.33% (checked each turn for every enemy unit that is pursuing.)

Probability of a general dying/being incapacitated when he is with a unit that loses a close combat (impact or melee): 1 in 30 = 0.0333 = 3.33% (checked each turn for each enemy unit that is fighting with his unit.)

Probability of a general dying/being incapacitated when he is with a unit that draws or wins close combat (impact or melee): 1 in 90 = 0.0111 = 1.11% (checked each turn for each enemy unit that is fighting with his unit.)

In your particular situation, I'm assuming "an otherwise bloodless melee" means the combat was a draw, so the combined probability of *both* generals dying is 0.0111 x 0.0111 = 0.000123 = 0.0123%

So yes, it was extremely unlikely to happen

[Edit] Did the units pass their respective cohesion tests from the loss of the generals? It would be even weirder if they both failed to pass...

[deeter]

Thanks for crunching the numbers. So 1 in a million? Neither unit lost cohesion, although two of my nearby units when fragged.

[Ray552]

Converting 0.000123 to a fraction = 123/1,000,000