HeroScape Math for a custom power

[Tai-Pan]

Hello,
I have a custom based on the Warrior Queen of Jhansi, an Indian queen who led a rebellion against the British.


She has this power:
HOPE FOR THE WEAK AURA
When a figure you control within 4 clear sight spaces of Jhani Ki Rani rolls only one skull when attacking an adjacent figure, the defending figure may roll no more than 1 defense die.


I've tested her a couple times the last couple days and I'm stuck on the math. I asked a math teacher to check it, but her answer didn't make a lot of sense either.


Is this power more likely to activate for a figure with 1 attack or 2 attack?


My math said that it would activate 50% of the time with 1 attack and only 25% of the time with 2 attack, because I specifically need the results to be a skull and then a non-skull, meaning 1/2 x 1/2. The math teacher's result said the probability is the same, because of the possible results, 1 skull and 1 non-skull or 1 non-skull and 1 skull make up 50% of the possible rolls (the others being double skulls or double non-skulls). But for my logical feeling (a contradition in itself) neither answer feels right. When I roll 2 dice, the most likely number of skulls is 1. So it feels like two dice should be better for exactly 1 skull than 1 die, as opposed to being half as likely or exactly as likely.


Can someone help me (and the math teacher)?

[superfrog]

Math teacher is correct.

Think of attack rolls like coin flips: 50% chance each of heads(skulls) or tails(non-skulls).

So with one coin, you have two equally likely options: H or T. Half of those have exactly one head.

With two coins, you have four equally likely options: TT, TH, HT, or HH. Half of those have exactly one head.

Your playtesting experience of 1 skull being "most likely" is correct, but there's three options: 0, 1, or 2 skulls. Referring back to the earlier list of four options, 0 skulls happens 1/4 of the time, as does 2 skulls. 1 skull happens 2/4 (or 1/2) of the time making it the most likely option. But that doesn't mean it happens most of the time, it just happens more than any other single option.