Add Omen debuff

[jmegner]

https://wahapedia.ru/kill-team2/kill-teams/hand-of-the-archon/#Ability

Each time attack or defence dice are rolled for that operative ... If it is an enemy operative, your opponent must re-roll dice results of 6.

I think it wouldn't be too hard as long as I don't allow mixing with balanced/command style rerolls.

Omen debuff changes your individual die outcomes in a very consistent way regardless of ceaseless/relentless/NoReroll. To add in Omen, you just add in some "stage 0" probabilities to your latest-stage probabilities. Explanation below.

Imagine there are stages. Stage 0 comes from BS and Lethal only. For BS=3+, the fail/norm/crit (f/n/c) Stage 0 probs are...

• pf0 = 2/6
• pn0 = 3/6
• pc0 = 1/6

Then Stage 1 handles ceaseless/relentless/NoReroll. Let's pretend ceaseless...

• pf1 = 7/6*pf0 - 1/6
• pn1 = 7/6*pn0
• pc1 = 7/6*pc0

Then Stage2 handles Omen debuff by adding { pf0/6, pn0/6, pc0/6 - 1/6 } ...

• pf2 = pf1 + 1/6*pf0
• pn2 = pn1 + 1/6*pn0
• pc2 = pc1 + 1/6*pc0 - 1/6

So, for BS=3+, Ceaseless, and Omen, we have final die outcome probabilities of...

• pFail: 28%
• pNorm: 67%
• pCrit: 6%

Interestingly, I used to think of ceaseless as multiplying the probability of norms and crits by 7/6, but a more robust way that mixes well with other rerolls like Omen debuff is adding some Stage 0 probabilities: { pf0/6 - 1/6, pn0/6, pc0/6 }.