A Touch Of Elders

I was thinking about the board game "A Touch Of Evil" the other day, and trying to figure out the math of the big showdown at the end of the game. In particular, I wanted to know how many dice should really be applied to any given Evil Elder, so I started looking at the math behind it all.

The conclusion I've drawn from this is that what the game presents as a strategic decision is actually more of a sucker's bet. It gives you the option of rolling very large numbers of dice against the Elders, but doing so is very likely to do exactly the opposite of what you expect it to. The whole point of targeting Elders is to reduce the damage you're taking, but if you put more than a die or two against them, you'll run a good chance of doing exactly the opposite.

Those pie charts show the results and percentages of rolling various numbers of dice against a single Evil Elder.

• The green section represents the odds of rolling a single success - exactly the amount you want to roll.
• The red section represents the chance of rolling two or more successes. You'd much rather roll 1 success than 2, since the extra successes are just wasted. That same die, if applied to the main Villain instead of his Evil Elder helpers, would have been 1 more step towards winning the game.
• The black section represents the chance of total failure - not killing the Elder.

So how many dice are the right number to roll? The answer is almost always 2, with only a few exceptions. If you're feeling cautious, dropping it down to 1 die is perfectly fine.

Silver Shot is one of the main exceptions. If you're using Silver Shot, you should only roll against the Villain, and never worry about the Evil Elders at all. Silver Shot doubles the damage of 6s rolled, making even a single die on an elder has nearly a 17% chance of wasting a hit, and you're as likely to waste a hit as make a normal one. Better to pour all your Silver Shot into the Big Bad, then to waste those juicy 6's blasting a single Elder into mincemeat.

Without Silver Shot, you can always afford to put one die against each Elder with no chance of it causing any side-effects or wasted resources. One die per Elder can only help your situation, or break even, it can never hurt you.

The winning strategy is to eliminate Elders quickly, but do so while minimizing the number of wasted extra hits. Every wasted success has the potential to make the fight last one extra round - and in that extra round the Villain will roll at least 5 dice, possibly 8 or more. On average, the Villain will do more damage in one round than any single Elder does in the whole battle. As helpful as it is to pick off Elders and reduce the damage you're taking, you should never lose sight of the fact that killing the Villain is the real goal. There's no better way to reduce the damage you're taking than to just win the game.

Wasting one or two hits total during the whole fight is probably not going to cost you an extra round of fighting, however, because you don't often win by rolling exactly the number of successes needed in the final round. This is especially true in the Cooperative game, where all the players get to roll in each round, and thus as a group average somewhat higher damage per round. If a group of heroes is averaging 4 or more damage per round (and they should be) then they can afford to waste one or two points without it usually dragging the fight out into extra rounds... most of the time.

Wasting three or more hits over the course of the battle, however, runs a big risk of extending the fight by a whole extra round. So, if you were facing just 1 Evil Elder then it might be worth rolling three dice (as a single roll of 3 dice can only ever waste 2 hits). But if there's 2 or more Evil Elders, it's very risky to apply more than two dice against each of them. Resist the temptation to pile dice up on an Elder "to make sure" you take them out. You can never completely eliminate the possibility of failing against an Elder in a given roll. Both 2-die and 3-die rolls have the exact same odds (44.44%) of scoring precisely 1 hit, the only boost that's gained by rolling the 3rd die all comes in the form of wasted successes, which you don't really want. With four dice, you're actually more likely to score 2 or more successes than to score only 1. Personally, I would never roll 4 or more dice against an Elder, as the risk-to-benefit ratio is too high. Those dice are just better if applied to the Villain.