Magic Missile
I'm taking this version of the iconic spell for a spin:
Once memorised, the magic-user can deploy the spell in one of two ways:
1. Spell hits automatically for 2 - 7 points of damage.
2. Spell requires a throw "to hit" its target but if successful scores 1 - 12 damage.
So far, our mage is opting for #2 but sadly he's wishing he didn't half the time but when it works... big smiles.
I initially started with the d10 for option #2 but the payoff didn't match the risk, sure you can still throw a one on a d12 but the chance to score up to five extra damage over option #1 is tempting.
How are you rolling the 2-7 range? 1d6+1?
ReplyDeleteWhat is the chance of missing the "to hit" roll?
Yep, d6+1. In Basic D&D (Holmes) the magic-user must throw to hit the target with his magic missile - only then does he do damage. It's a standard d20 throw versus AC and treated as a long bow attack for range adjustment.
ReplyDeleteSo the "right" choice (purely on average damage dealt) would depend on the attack bonus vs AC.
ReplyDeleteAnd since many systems (including Holmes?) tend to have increasing attack bonus, but AC is relatively static, that implies that the "reliable" damage is statistically better for lower levels, and at higher levels you'd want to roll to hit & for extra damage.
And the only time you wouldn't want to go with the better average result would be when the opponent is near to death, where either the 1d6+1 will kill them, or where 1d6+1 can't kill them but 1d12 can. Because "overflow" hitpoints don't help, and denying them that final action might matter.
And, I do understand, looking at things from a purely statistically mechanical standpoint misses the point. It's fun to try for that big explosion! It's fun to reliably land a hit right through the well defended arrow slit when nobody else can touch that archer!
I think the d12 is to low, how about double damage ?( 4-14) Makes s taking a chance more tempting.
ReplyDeleteThe average damage from 1d6+1 is 4.5
ReplyDeleteThe average damage from 1d12 is 6.5
So that average of +2 points damage is about +45% damage.
Which means if you hit 2 out of 3 times, you'll come out with about the same total damage.
If you hit more regularly than that, it's absolutely tempting to take the chance.
If you hit less often than that - say, you hit about half the time - then I agree, you'd probably want to double the damage instead, to make it more worthwhile.
Individual players also tend to have personal preferences about reliability/swinging results. Some like to regularly do damage, others like the chance to do bigger damage and accept that means sometimes they'll do minimal damage. The d12 certainly leads to less reliable damage.
Hi Tony Demetriou the notion of an "average result" for a single die throw is hypothetical only. Each number has the same chance of occurring. Drop some extra dice into the mix and you get a bell curve that allows you to see some trending. The larger die type offers a greater pay-off balanced by the double risk of a) missing and b) rolling less than you could with a free shot. It's why some people put money on the roulette wheel instead of in the bank. Risk = exciting.
ReplyDeleteMike Hill Sorta. The notion of an "average result" for one particular dice throw is totally hypothetical.
ReplyDeleteThe notion of an "average result" when discussing a series of dice rolls is practical, because the more times you roll the dice, the closer your accumulated, total result will be to the average.
So if I roll a d6, my average result will be 3.5 But I'll (obviously) never roll a 3.5 result.
I'm just as likely to roll a 1 as a 6.
However, if I roll that d6 a thousand times, and add all the results, I'm likely to get a result close to 3500.
If I get the choice of rolling 1d6+1 or rolling 1d12, and over the course of my gaming career I roll that dice a thousand times, then if I chose 1d6 I'd have done about 4500 points of damage, and if I'd chosen the 1d12 (assuming no to-hit roll) I'd have done about 6500 points of damage.
That's not just theoretical. The practice result would be that one choice leads to more total damage dealt than the other choice.
In your actual example, the larger dice needs to roll to hit first. So yes, depending on how likely you are to hit, that changes the total average outcome. Since to-hit rolls and enemy AC vary based on the in-game situation, there's no clear way to calculate the exact probabilities (which is a good thing!)
And 1d12 is more variable. I agree. You might roll badly.
But variability is a separate axis to average results. And the variability is minimized if you're doing a series of rolls because when you're rolling multiple dice - as you point out - you get a bell curve. And a bell curve, which his biased towards the median result.
We can think of five damage rolls in a row as similar to one roll of five dice where we add the damage, in terms of calculating probability.
And yep, risk = exciting.
At the end of the day, the only question that matters is "are all the players having fun?" and it sounds like, in your game, they are.
Or, another way to phrase it:
ReplyDeleteRolling d6+1 versus d12 for damage means that your total damage dealt in a session might be 14d6+14 versus 14d12, which is a nice happy curve.
http://anydice.com/program/723a Hit "Graph," and also check out how significant it is even with session rolls as low as 4.
Risk vs. reward, in my case, I'd have to go with the reliable 2-7 damage option, since I'd always do at least 2 points of damage. If I chose the riskier "to hit" version, and only get to throw a d12 instead of 2d6, I'd more often do only 1 point of damage. Statistically speaking, I can throw natural 1's more than any other player at the table! The risk might be worth it if it was 2d6, rather than 1d12! ;)
ReplyDeleteHaha Robert Weber, our resident magic-user has your die roll curse too. He still struggles to resist the draw of the d12 though!
ReplyDelete