So, I was working an overnight shift and we were down, so I decided to crunch some numbers regarding spending fate points to get a +10 bonus versus rerolling.

Part of the reason I wanted to run these numbers is that, generally speaking, you have better odds of getting a success on most dice if you can roll the dice more than once rather than a flat increase to your chance of success. This is, of course, dependent on your probability of success to begin with, and the size of the bonus.

I've uploaded an excel file (link to RPG Geek file upload) you can use to check out the probabilities, I'll summarize below, note that there are some nuances to these comparisons:

Comparison 1 - Pre-First Roll Pass Percentage
The first comparison I make is a comparison of the raw probability you'll pass the test if you take the +10 bonus versus using a reroll. For the +10 bonus, it's simply your new target (IE. if your base target is 10, your probability of passing with the +10 is 20%).

For the reroll, the calculation is 1 minus the probability that you fail the test on your first roll, reroll, and fail the test again (note, this is an important concept to understand, I'll explain in a moment). Based on this concept, the only time the +10 flat bonus is better than the reroll (in terms of your chance to pass prior to making the first roll) is when your base target value is 10% or less, or 90% or higher (actually, the cut off point is some where between 10 and 15%, and 85 and 90%).

There is an important caveat to all this. Your chance to pass with the reroll is PRIOR to the first roll. If you don't take the +10 bonus to start with and fail on your first die roll, your probability of passing with a reroll is now exactly equal to your target value (and thus lower than the probability if you had the +10 bonus). That is, the reroll itself is just as likely to fail as your first failed roll. If this confuses you, look up the "Gambler's Fallacy."

Said another way, if you've saved your fate point for the reroll, fail the test, and need the reroll, you've already lost the probability benefit over the +10 bonus that the reroll provided you.

Comparison 2 - How Often the Fate Point is Useful for Passing
This is an interesting comparison. Basically, it asks the question "was spending the fate point the only reason I passed the test?"

For the +10 bonus, the answer is always 10%. 10% of the time, you will make a die roll that is above your initial target value, but within the extra 10 values the bonus provides you. Thus, only 10% of the time was the fate point spent usefully to pass the test.

For the reroll, we're asking a more specific question. That question is "how often will I need to spend a fate point to reroll and the reroll will help me?"

This answer ranges depending on the initial target value. If your initial target value is 10 or 90, the probability that you FAIL the first test, and PASS the reroll thanks to the fate point is just under 10%. For values of 20-80, your probability of FAILING the first test, and passing due to the reroll ranges between 16% and 25%.

Note that the way I've presented the data means that the +10 data and reroll data aren't necessarily comparable because they ask slightly different questions. Specifically, the reroll data doesn't account for the chance that you pass the first roll. That's because, if you pass on the first roll, you don't have to spend a fate point, so there's no way to calculate whether or not the fate point is useful.

Comparison 3 - How Often is the Fate Point Useful for Adding 1 or More DoS
Firstly, let me preface this as saying that although I did the math on this, it's probably not a good idea to add a +10 bonus to get an extra DoS. You could wait until you make the check to simply spend 1 fate point to add 1 DoS if you pass, and if you fail you could use the fate point to reroll (and potentially get a >1 net increase in DoS!).

Anyway, the question asks "how often does spending the fate point result in me either moving from any DoF to 1 DoS, or increase my DoS if I already had at least 1?"

For the +10 bonus, this is pretty straight forward. Your probability of going from any DoF to 1 DoS (because you pass instead of fail) is 10%. In addition, your target value is now 10 higher, so if you passed without the need of the +10 bonus, then your DoS is automatically increased by 1 from whatever it would have been.

Thus, the total probability that a +10 bonus increases your DoS is the probability you pass the check in the first place, +10%. So if you have a 40% initial target value, there's a 50% chance that the +10 bonus will increase your DoS by 1.

Calculating the DoS for the reroll is a bit more complicated. I'm not going to go through the exact formula, but I will say this: Dark Heresy 2 calculates your DoS as the difference between the tens place of whatever you roll, and the tens place of you target value, +1 for passing. Because of this, if your target value ends in a 0, you actually only have a 1% chance of getting exactly 1 DoS. Since all my math was based on tens, this makes for some interesting (and complicated) formulas.

The end result is that your probability of increasing your DoS by 1 (or more) by rerolling is significantly less than the flat +10 bonus (it's worth reminding you though, if you already have at least 1 DoS, you could have just spent the fate point to add 1 more). The probabilities range from 9% for a base target of 10, to 50% for a base target of 90.

Comparison 4 - How Often is the Fate Point Useful for Adding 2 or More DoS
This question is like the last one, but basically says "how often does spending a fate point result in me adding at least 2 DoS, or going from any DoF to at least 2 DoS?"

For the +10 bonus, this is never. The +10 bonus can only add up to 1 DoS, no matter what your target value, and no matter what you roll.

For the reroll, the answer is "it's never better than a long shot." For a base target of 10 the reroll has an 8.1% chance of adding 2 DoS - that is, there's an 8.1% chance you'll fail the test, and then roll a 1-9 on the reroll.

For a base target of 90, the reroll only gives you a 37% chance to increase your DoS by 2 or more, or go from a failure to 2+ DoS.

Comparison 5 - How Often did Spending the Fate Point not Help Pass
This comparison is far more interesting. For the +10 bonus, the answer is "90% of the time you'll spend the fate point and it won't actually help you pass the test." That's... pretty bad, if you ask me.

For the reroll, the answer is a lot different - and this comes from the fact that you get to choose whether or not to spend the fate point AFTER you know whether or not it might be useful.

At worst, on the base target of 10, you have an 81% chance of rolling, failing, spending a fate point, and failing again. Already better off than the flat +10 bonus.

By base target of 50, you're down to a 30.6% chance of failing the first roll, spending a fate point, and failing the reroll. Compare that to the 90% chance you wasted the fate point for the +10 bonus and the bonus is looking pretty awful.

By base target of 90, you're down to a 1% chance that you'll fail the first test, spend the fate, and fail the reroll.

Comparison 6 and 7 - When is a Fate Point Wasted Getting Extra DoS
While I calculated all of these, I'm not sure they're worth going over (have I pointed out that you can just add 1 DoS using a fate point after the roll?).

If you really needed to get 2+ DoS added to your result, then rerolling is your only option. The probabilities presented in the excel represent your first roll being in a range in which getting 2 DoS extra is even possible (you're not at the maximum DoS possible, or 1 less than the maximum), and then you reroll and don't get 2 extra DoS. The percentages that you spend the fate point and don't get 2+ extra DoS range from 83% for a base target of 10, to 44% for a base target of 90.

Comparison 8 and 9 - Did I Choose Poorly? Would the Other Option have Worked?
These comparisons basically ask the question, "how often will the choice I make result in failure, but if I had made the other choice, I would have succeeded?"

The columns at the top in the excel represent the choice you DID make, and that the correct choice was the other column.

When it comes to just passing the test, for the +10 bonus, the probability is basically the probability that you fail your test roll with the +10 bonus, but if you had a reroll, you would pass. The probability ranges from 0% (for a base target of 90), to 8% (for a base target of 10 or 80), all the way up to 20% (for a base target of 40 or 50).

For passing when you chose to reroll, the probability is the chance that your first roll fails, and your second roll fails, but your first roll would have passed if you had taken the +10 bonus. Worst case for those choosing the reroll is the base target of 10 where 9% of the time you'll wish you'd taken the +10 bonus. That works it's way down linearly to the base target of 90 where there's only a 1% chance that the +10 bonus was the right choice over the reroll.

Conclusion
It appears to me that the flat +10 bonus is woefully inadequate compared to your other options for spending the fate point - namely, rerolling or adding 1 DoS.

I definitely think this is house rule worthy, although I'm not sure if the better house rule would be to increase the bonus (say, to +20 or +25), or to let you take the bonus after the roll, but decrease what the bonus is worth (say, to +5).

Namely, the most dramatic problem with the flat +10 bonus is the incredibly high chance that you spend it, but you didn't need to because it makes no difference. 90% of the time the fate point was wasted, compared to 81% at worst for the reroll (and that drops off quickly, all the way down to 1%).

This latter fact makes me think the solution is to let you make the choice after the roll, but I'm concerned that the spirit of spending the fate point is not to allow you to guarantee a pass anytime you roll within 10, but instead to give you a "second chance" or to slightly improve something that is already a success.

I like how thorough you were with this, but it seems like a lot of work when there's a much simpler way to come to the same conclusion.

You add +10 before rolling to add 10%

You choose to roll again AFTER rolling to add whatever your original chance of success was again.

Unless your original chance of success is 10% or less, a re-roll is always a better choice. Even making the +10 take place after the fact isn't really that much better.

Also, I see that you're doing the math of re-rolling meaning the chance of the first roll failing and the chance of the second roll succeeding. However, the chance of the first roll failing does not actually affect the choice to spend a point on the re-roll, because that information has already been set. The player already knows the outcome of the first roll when making his decision, so you don't need to account for it in the math of which is better.

Your actual comparison should be between the making a roll with a +10 OR making an unmodified second roll.

I allow the +10 to be added after the roll. Basically you may see your result, and then choose to spend a FP to either add 10 (which will grant the 1 DoS on a success) or re-roll

Also, I see that you're doing the math of re-rolling meaning the chance of the first roll failing and the chance of the second roll succeeding. However, the chance of the first roll failing does not actually affect the choice to spend a point on the re-roll, because that information has already been set. The player already knows the outcome of the first roll when making his decision, so you don't need to account for it in the math of which is better.

Your actual comparison should be between the making a roll with a +10 OR making an unmodified second roll.

You appear to be confused. You said "math of re-rolling meaning the chance of the first roll failing and the chance of the second roll succeeding."

The only time I perform the math of a reroll is in the initial raw pass percentage where what you describe is NOT what I do. The probabilities there are the chance you succeeding on the first OR second roll, and I'm very clear about that in the above post. There is no other place in the excel where your probability of passing is ever calculated again.

Making the comparison between the roll with a +10 and ONLY a second roll would be misleading, particularly because it does NOT represent your chance of passing if you don't take the +10. It represents your chance of passing IF YOU FAILED THE FIRST ROLL.

But, you could not fail the first roll without taking the +10. Ergo, I would say that my comparison is a better representation of the probabilities.

In addition, if you want just the probability of the second roll passing, it simply equals whatever your target value is, and the +10 is simply 10% better.

Ah, I was reading it on my phone so I didn't capture the full gist of what you were saying about it. My mistake on that.

I can see what you mean now about the decision being whether to save your fate points for a re-roll or to spend +10 on something. However, the reason why I'm differing with you on this is that you frame the decision as "Should I add +10 to THIS roll or should I hold off on it in order to reroll THIS roll if it fails." However, I'm looking at the decision as one of "given the math in this game, somewhere between 1/2 to 1/3 of my rolls are going to be failures, so should I add +10 to a single roll, or reserve my fate points for a future roll which I might fail." Basically, you are forced to gamble on whether you're going to have any failed rolls to re-roll with Fate Points, but adding the +10 forces you to put everything into a single roll that is not guaranteed to need help versus a future roll that will definitely need to be re-rolled. In one case you gamble on having an outcome you definitely want to change versus gambling on having an outcome that may or may not need any help (as DoS aren't always that important). You also have the case that re-rolling a failed roll can add many more DoS than simply adding +10 to a roll can. In the case of re-rolling a failed roll, your chances of benefits are almost always higher than they would be to just adding a +10.

That said, your math on whether it's worthwhile to spend a fate point to re-roll for better results on a successful roll is spot on.

You also have the case that re-rolling a failed roll can add many more DoS than simply adding +10 to a roll can. In the case of re-rolling a failed roll, your chances of benefits are almost always higher than they would be to just adding a +10.

Actually, my probabilities are that the fate point was useful for adding +1 (or more) or +2 (or more) DOS. That is, it's the probability that spending the fate point actually results in that happening. This is slightly different from the chances of you having 1 (or more) DOS.

Under this analysis, the +10 bonus is absolutely better at helping you get more DOS. This is true because the +10 bonus automatically adds 1 DOS to any roll that is already a success. In addition, it gives you a 10% chance to get 1+ DOS instead of a failure.

The reroll, on the other hand, has to compete with it both being possible for you to get extra DOS after your first roll (which isn't always the case), AND you have to actually get those extra DOS when you perform the reroll. That really hurts your chances when it comes to the reroll.

BUT, the reroll can give you more than 1 DOS extra. The +10 bonus can't. So, in that way, the reroll definitely has more utility.

Some of the options are better in general (e.g. re-roll), the others are much more situational, but in these situations they are better than a reroll (e.g. +1DoS when you just need it).

Some of the options are better in general (e.g. re-roll), the others are much more situational, but in these situations they are better than a reroll (e.g. +1DoS when you just need it).

"Sometimes the sun is up, but when it's not it can be dark."

Some of the options are better in general (e.g. re-roll), the others are much more situational, but in these situations they are better than a reroll (e.g. +1DoS when you just need it).

"Sometimes the sun is up, but when it's not it can be dark."

I am not really surprised that you don't know the difference between "general" and "situational".

He was making fun of you for writing a tautology like it was some intelligent point.

He was making fun of you for writing a tautology like it was some intelligent point.

Well...at least I need other people to make fun of me, whereas your words are sufficient to do so for yourself.

Using words like "tautology", does not show any superior intellect to me, it just shows a certain attitude that I don't like much.

He was making fun of you for writing a tautology like it was some intelligent point.

Well...at least I need other people to make fun of me, whereas your words are sufficient to do so for yourself.

Using words like "tautology", does not show any superior intellect to me, it just shows a certain attitude that I don't like much.

The best part is that what you said is not actually a tautology, nor is Nimsim's failed attempt at ridicule (which I think had little to do with tautologies, and stemmed more from his inability to see the difference between general and situational) necessarily one.

Or, you know, the opening post of this thread basically elaborates very heavily on gauntzeros point (that situational bonus is VERY situational and that general bonus is VERY general) to where it basically came off as him just parroting a point without having bothered to read what the op wrote.

Not to mention, there's a subtle implication there that the rules as-is are fine because sometimes someone will REALLY want that +10 bonus. Which is also a bad argument.

Thats not a bad argument at all.

Why should it be bad to have additional options if the situation calls for it ?

Is it better to stuck on 1 option ?

[...]

Not to mention, there's a subtle implication there that the rules as-is are fine because sometimes someone will REALLY want that +10 bonus. Which is also a bad argument.

Why would that be a bad argument? I think GauntZero summed it rather well; one is generally better, but the other is situationally better.

A playing having the option to individually gauge and decide which to choose is really the only argument necessary for keeping both functionalities.

Also, spending a +10 Fate Point before rolling comes with the possibility of spending another Fate Point to add another +1 DoS afterwards, unless that has changed in DH2. While consuming yet another Fate Point, that's something you can only do if you first have succeeded on a roll at all.

I love the calculations and I think that ialsoagree did a stellar job, but it only really confirmed what I think everyone already knew - that rerolls after a failed roll are generally better than +10's before a roll. It doesn't actually change anything, nor make a true argument as to why functionality should be changed.

They're options, and they are obviously not intended to be mathematically equal, but a decision for the player to make based on his situation.

There are a dearth of options in the game in which an extra degree of success or +10 to a roll is going to be of such vital importance that they're worth decreasing the overall chance of failure over. That +10 does a poor job of actually increasing success chances, as shown above. Literally its only purpose is adding a degree of success that's all that the game system supports as an effect: success or extra DoS.

So why is "well it's more options" a bad argument? Because giving options that are demonstrably bad to players is a recipe for having them waste points by accident or for wasting ink for people who know better to ignore that choice. The above analysis shows that the +10 is useless compared to a choice of adding a DoS or a reroll. The niche of a relatively much smaller increased chance of success and chance of an extra DoS (which, if it occurs, means you didn't need the extra chance of success) is not enough to be a worthwhile choice.

The +10 is a trap option and should be removed or made to be more on par with the other uses of a fate point. Only when the choices are actually of relative equality does it become a choice rather than "always use the obviously best option."

1.) +10 can be used in combination with a re-roll, if the test is really important. First +10, then re-roll if it didnt work.

It is also usefull for tests with very extreme values. Very low chances may benefit more from +10 than from a re-roll.

And if you have a very high chance (80%+), this can be a good boost to your DoS, better than a possible re-roll could be.

2.) An additional DoS can be taken AFTER you know your roll. That means, you can use it exactly when you need it to an effect that you exactly know. It is the missing DoS when you just need it. This can be extremely valuable when the situation calls for it, and in this instances, it can be much better than a re-roll.

They are only "trap options" when you use them in a stupid way.

Nobody protects you from stupid decision anyway though.

So your one time that the +10 option is useful is an additional spend after spending a FP on a much more valuable re-roll? Why bother letting players spend it on the first roll, then? The extreme values spend is you blatantly ignoring the above analysis. The only time a +10 is better for yor success is if your base chance is lower than 11%. It's already established as being better than a reroll for getting more DoS, but there's already a FP spend that lets you add a DoS and you don't have to gamble on spending it before the roll happens. So your two possibilities for the +10 (better success chance or extra DoS) are obviated by the other FP spends of a BETTER chance of success or just adding the DoS.

Also, no one was saying there's a big problem with adding 1 DoS. It could probably use a buff too given how often DoS aren't really that important, but the point of this thread has been about how bad the +10 is.

And it's funny how you think it's the players fault if there are bad mechanical options in a game for choosing them. This isn't a case of a player choosing to run up to a snipers nest down a narrow street to hit it with his sword, it's the player choosing from a set of options that are presented as being equivalent and require outside game knowledge to know otherwise.

[...]

And it's funny how you think it's the players fault if there are bad mechanical options in a game for choosing them. This isn't a case of a player choosing to run up to a snipers nest down a narrow street to hit it with his sword, it's the player choosing from a set of options that are presented as being equivalent and require outside game knowledge to know otherwise.

Throughout all the lines, I have never seen these things being presented as being equivalent. They blatantly obviously aren't. Saying that these are presented as being equivalent is like saying that healing 1d5 Wounds is presented as being equivalent to adding +1 DoS to your successful Test.

There is no relation. They apply in different circumstances, also known as situations. Hence, situational.

Like any other option, it is up to the player to gauge when to do what. This doesn't mean that it's a trap, it only means that a player is allowed to fail, he is not being coddled or led by the hand. Making poor decisions is just as important as making good ones, lest it devalues any semblance of freedom.

There are demonstrably situations where adding +10 is better than a reroll. Just because two options do not confer the same statistical likelihood of an equal benefit does not mean that it's a "trap", nor does this require "outside game knowledge to know otherwise", it just requires someone to not be a drooling idiot.

Was there really *anyone* that was thrown off by the results presented here? I'm admittedly terrible at math and I sometimes struggle with the simplest calculations, but even I would always have taken a reroll over a +10 before rolling in almost all cases - except those cases where I wouldn't, simply because I really felt I needed that +10 and then being able to add another +1 DoS.

It's easy enough to know that affecting a dice roll and instantly regaining health are separate things. However, the book presents all of the options to affect a roll together, with the implication that they will all provide equal benefit. The times that the +10 add a benefit are so rare as to be non-existent, making it a waste of space 99% of the time and making it too likely a player who chooses to use it will have wasted his fate point on it if he uses it during one of those 99% times.

Also, as I said, the two outcomes for the +10 are increasing chance of success OR giving you an extra DoS if your roll would succeed anyway. It doesn't provide both benefits because if one exists the other does not matter. It makes more sense to wait until the roll is made and then add the DoS, or reroll for a much better chance of success than the +10 would give.

What's being argued is to make the +10 a better option. Bump it to +20 and allow it to be spent after te roll is made. Get rid of the option to add a DoS. At that point you have a much more interesting choice to make between that and a reroll.

ialsoagree mind running the numbers on +20 before vs reroll? I'm curious how that looks.

Statistically speaking, any +% gained before the roll isn't going to be as useful as a re-roll unless your base % is lower than the bonus. I.E. that reroll with a score of 40% has a better chance of passing than adding an extra 10% before the first roll.

Personally, I'd say that being able to add 2d5 to the roll after you make the roll would be a better option. It still has an element of chance to it, but it's much more useful since you can strategically apply it.

EDIT: With the role-based Fate Point expenditures, an extra degree of success will generally be of limited use, but it can help when you just have to have that extra +10 after a successful roll.

Objulen, awesome idea. In fact, I'm going to use it or suggest it in any game I play in. I think your suggestion of using 2d5 is way better than the original option. Not just because you can use it after the roll, but because it lends a degree of chance that is already at the heart of fate point expenditures.

CPS, how about I do a second excel of various alternatives to the +10 including +20, adding 2d5 to the target after the initial roll. Any other suggestions I could run numbers on?