We gone around about this before. I know it seems like what you're saying is true but the reality is that regardless of which number the die explodes on you're going reach the same result over the course of an evening or a career. Exploding on a one doesn't get you to a total of five any more often than exploding on a six does.
Take a look at that statement again.
Target: 5 rolling a d6 without explosions. Chance of success 33% (2 outcomes in 6).
Target: 5 rolling a d6 with unlimited explosions on 6. Chance of success 33% (2 outcomes in 6).
Notice that while the average jumped considerably, the chance of success didn't move at all.
Target: 5 rolling a d6 with a single explsion on 1. Chance of success ~41.6% (15 outcomes in 36).
Target: 5 rolling a d6 with up to two explsions on 1s. Chance of success ~43.5% (94 outcomes in 216).
Target: 5 rolling a d6 with up to three explsions on 1s. Chance of success ~43.9% (569 outcomes in 1296).
Target: 5 rolling a d6 with 4 or more explsions on 1s. Chance of success ~43.98% (3420 outcomes in 7776).
I worked through the math on the sort of case you're looking at here. Yes, in this case you get a higher chance of success
if the target is smaller than the die size. The trade off is that you lose any chance to succeed if you need a total of 10. Is that better? What if the target number is 8? Exploding on a 1 gives you about a 1 in 1.67 million chance of success. Is that better than exploding on a six? So I guess the question becomes is it more important to be able to throw an action die when you need 5 more than when you need 8 more.
Since the choice on when to spend an action die rests with the player, they're generally going to spend them when they increase the chance of success. I bet not too many of your players throw a d4 when they fail by 14. But by 3? Sure. 7 eh, not so much but maybe. That's all the meatbag statistician at work. Even if they never divide by 2 they're using knowledge of what that die is likely to throw.
The reality is averages don't reflect thresholds - because the results are not being summed. They are being converted in a binary operation to 0s (failures) and 1s (successes). In a more extreme case a series of ten results of 1, 1, 1, 1, 1, 1, 1, 1, 1, 11 yeilds an average of 2. Since the average is 2 and the threshold is 2, I succeeded half the time, right? Nope.
There's more than one type of average you know. The median of your data set is 1 while the mode is just a bit higher, both characterizing the dataset as full of fail. Traditional averages are best used with datasets that are normally distributed or flat distributions. Die rolls fall into these categories.
Similar argument as you mentioned about crits, its not the average number of crits in a sample of 400 rolls that maters, its how many checks are required to give me a 50% chance that one has occured. When all results above X are equivalent to X, a result of 100 is no better than a result of X, and while a result of 100 pulls the average up, it does not intrinsically shift the likelyhood of success. Explosions are result replacements (instead of a six, I now had 1/6ths chances of a 7, 8, 9, 10, 11, or 12 replacing that result), and if they take place on results at or beyond the threshold they do not shift the likelyhood of achiving that threshold. If they takeplace on results below the threshold, they do.
What you're not taking into account is that there isn't just a maximum result, there's also a minimum result. Reaching X+20 may not be any better than reaching X EXCEPT that my chance of success is now independent of my d20 roll! Think about that. If I have a +20 skill bonus, I can not fail on a DC20 task. Even a 1 roll a 1 I still succeed. If I get that certainty by spending an action die, I've effectively purchased a better than
flawless ability for the low price of a single action die. I really don't care if I end up beating the DC by 10 or 20 or 30 (except for bragging rights
) but likewise I don't care if I fail by one or 10. The tools I use to determine whether I want to spend that die are its range and its average. Where the die explodes changes the range but it doesn't change the average boost that I'm going to get from spending dice over time.
I guess you're including rolls like autofire and the knife mastery trick in damage rolls.
Actually I mean straight linear conversions. Sword Supremacy may be the only one that survived into Fantasycraft.
I have a build that really wants to succeed by 9 or by 14 due to using Blade Fury and All-Out Attack. With this sort of multiple threshold situation, I don't care about succeeding by 12, but I do care about 14. Since I know what value to expect from an action die and I can decide if I want to use one after seeing the initial result, I know that if my action dice are d8 or larger I have a very good chance of bumping up the result to the next threshold. Doing my knife damage again plus the eight from All-Out is a much sweeter deal than just rolling that die on damage.
Also damage and refresh rolls, opposed rolls, anything that counts effect. In short, a lot of rolls depend on being able to get a large result.
How about this as campaign quality
Glass Half FullOr empty if you prefer. Players may select whether their action dice explode on the highest or lowest number the first time they roll one. Once this choice is made, it may not be changed for a given player.
It's another thing to keep track of but it allows a choice between "anything goes" and "this won't suck."
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