I tried this out last night, and players seemed to like it a lot:

On a natural 20 a player must make a quick decision before rolling damage:

1. Double the result of the roll, or

2. Roll double damage dice

The player is choosing between a flat distribution and a bell curve. This has very real strategic implications, and there are definitely situations where one would be preferred over the other. This is a nice little way to introduce some abstract strategy without bogging things down.

Sounds interesting, I'll have to try it for an upcoming game night!

ReplyDeleteWe do something similar: on a nat 20 the player must choose between full damage or double the rolled damage. For most, that means either 6 dmg or d6x2 damage.

ReplyDeleteInteresting. Out of curiosity, do you players tend to go one way or the other more often?

DeleteIf they are fighting monsters >1 HD, they should almost always prefer d6x2, because they'll only have a .33 chance of getting <6.

My friends and I also used "double or full" back in the 90s, and I still have fond memories of this approach. The choice becomes consistent, guaranteed damage versus a gambler's double or nothing.

DeleteI must be a probabilities idiot, but wouldn't it be best to always pick 'roll twice'? I mean, my inclination is to say that I always would want to score as much damage as possible as many times as possible... and if I were just rolling 1 dice and doubling it on a d6, if I rolled a 1 or a 2 on the dice, I would end up with a measly 2-4 points of damage, whereas if I am rolling 2d6, even if one of the dice scores low, the other dice might still score high, making up for my poor result and getting my opponents dead much quicker. What obvious principle of math that I should have learned in grade school am I missing here?

ReplyDeleteIf you simply want the highest probability of doing maximum damage you should actually double your roll. This would give you equal probabilities of rolling 2, 4, 6, 8, 10, or 12. There's a 16.66% chance for each outcome.

DeleteRolling two dice, as you propose, produces a bell curve probability. This would make the chance of rolling maximum damage a measly 2.77%.

So, I hate to say it, but if your simple goal is to maximize damage your intuition is misleading you. You would actually want to double your 1d6 roll.

So why would anyone want a bell curve if the probability of maximum damage is so low? Well, because the probability of minimum damage is also (equally) low. 2d6 rolls will tend to be around the mean of 7. If you're feeling conservative, or think your opponent might have ≤7 HP and you want to be as sure as possible of a kill, you should choose to roll two dice.

I hope this makes sense...?