Did you know nr. 37 – Phoenix Rebirth

One Phoenix have a 20% chance to raise one unit with rebirth ability, three Phoenixes have 60% chance to raise one unit, and 6 Phoenixes have 100% chance to raise one unit with a 20% chance of raising a second.

Thanks to Reddit users Karyoplasma and Mortarial  we have additional information about this ability:

Also, did you know, that “more Phoenixes die” is not equal to “more Phoenixes will Rebirth”. The formula is N/5 + X, where N is initial number of Phoenixes, X – remainder of division. Thus, from 10 dead Phoenixes will Rebirth always and only 2 Phoenixes, while from 9 there may Rebirth up to 5 Phoenixes.

This means that you can calculate the chances of the rest group being reborn individually by using binomial distribution. Given that n is the number of Phoenixes successfully reborn, k the number of Phoenixes to check and p for the chance of success, the formula is:

n!/(k!*(n-k)!) * p^k * (1-p)^(n-k)

p is 0.2 because of the 20% chance, n is N mod 5 with N being the initial stack size (4 in the case of 9 Phoenixes) and k is the number of phoenixes that get reborn from the remainder of the stack.

So you have the following chances:

  • 40.96% to get 1 Phoenix

  • 40.96% to get 2 Phoenixes

  • 15.36% to get 3 Phoenixes

  • 2.56% to get 4 Phoenixes

  • 0.16% to get 5 Phoenixes

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