Quick die math question

[Grod_The_Giant]

So I'm in a Fate game where the GM is having us roll d6-d6 instead of the usual 4dF, and I'm wondering-- when is it best, mathematically, to take the +2 and when is it best to reroll? What results are far enough below the normal swing that rerolling will likely lead to improvement?

[Tanarii]

Here's the anydice for the three options. You'll have to stare at the numbers yourself to figure out the answer yourself tho ... its just the raw chances of rolling.

http://anydice.com/program/ab09

The first is d6-d6
Second is (d6-d6)+2
Third is highest result of 2d(d6-d6)

Edit: also here's your chance of rolling a number of higher on d6-d6. That's what you really need, because you already know the result of your first roll +2. So you just need the chance to beat that roll.
http://anydice.com/program/11f5

(You'll have to click the at-least button, it didn't save that I had that option chosen.)

[daniel_ream]

How is this a math question?

FATE dice produce a bell curve centered on zero. There's a slightly greater chance of rolling 0 or above than -1 or less. So the only time you should reroll is if you got a -3 or worse on your first roll. For any higher roll, a linear bonus will always give you a higher expected value than a reroll.

[Grod_The_Giant]

How is this a math question?

FATE dice produce a bell curve centered on zero. There's a slightly greater chance of rolling 0 or above than -1 or less. So the only time you should reroll is if you got a -3 or worse on your first roll. For any higher roll, a linear bonus will always give you a higher expected value than a reroll.
I know that's true for the standard 4df, I'm wondering if it still holds true for the swingier d6-d6.

[Coventry]

I know that's true for the standard 4df, I'm wondering if it still holds true for the swingier d6-d6.

The same logic applies to d6-d6. Out of 36 roll combinations:

... 15 combinations that are -1 or below
... 6 combinations that are 0
... 15 combinations that are +1 or above.

So, "a slightly greater chance of rolling 0 or above than -1 or less". Reroll on a -3 or worse.

[daniel_ream]

The same logic applies to d6-d6.

...because it's still a bell curve.

[Grod_The_Giant]

Okay, good to know.

[Tanarii]

How is this a math question?

FATE dice produce a bell curve centered on zero. There's a slightly greater chance of rolling 0 or above than -1 or less. So the only time you should reroll is if you got a -3 or worse on your first roll. For any higher roll, a linear bonus will always give you a higher expected value than a reroll.
Is is a bad answer in terms of raw numbers. I don't know FATE so I don't know what the results mean, which would affect if it's worth taking a long shot, but ...

A reroll has a 41.67% or rolling a 1 or higher. That's 40% chance to beat taking -2 (original roll) +2 = 0.

It's a 27.78% chance to get a 2 or higher, beating -1 + 2 = 0.

It's a 16.67% chance of 3+, beating 0+2 = 2.

And the odds are even higher that you'll equal. If +1 is acceptable, even higher. See my original edit above for odds.

Edit: ah I see my error. I was assuming it was "reroll and keep the best of both rolls". Not reroll and discard the old roll.

[Cluedrew]

Here is my work:

ResultExactOr Better
+52.8%2.8%
+45.6%8.3%
+38.3%16.7%
+211.1%27.8%
+113.9%41.7%
=016.7%58.3%
-113.9%72.2%
-211.1%83.3%
-38.3%91.6%
-45.6%97.2%
-52.8%100%
To get the chance of a reroll being at least as good as a +2, check the Or Better chance of (Your current result +2). To get the change of a reroll being better than a +2, same for (Your current result +3).Short answer: On -2 or lower reroll otherwise add +2.

That doesn't take into account how much you are short from where you want to be, but then that starts depending on things like if you can accept a tie or not, if you feel like you need a certain number of shifts and so on.

[Tanarii]

Here is my work:

ResultExactOr Better
+52.8%2.8%
+45.6%8.3%
+38.3%16.7%
+211.1%27.8%
+113.9%41.7%
=016.7%58.3%
-113.9%72.2%
-211.1%83.3%
-38.3%91.6%
-45.6%97.2%
-52.8%100%
To get the chance of a reroll being at least as good as a +2, check the Or Better chance of (Your current result +2). To get the change of a reroll being better than a +2, same for (Your current result +3).Short answer: On -2 or lower reroll otherwise add +2.

That doesn't take into account how much you are short from where you want to be, but then that starts depending on things like if you can accept a tie or not, if you feel like you need a certain number of shifts and so on.
It's possible you're missing the same thing I did. There a chance you'll roll worse that your original roll when you reroll. Let alone worse than the roll+2.

At least ... if that's how the reroll works. If you get to keep your old result if you reroll it might be worth it for as little as a 16% chance to beat out a original roll of 1 + 2, depending on the target number you need.

[Cluedrew]

I may have but I did the math given your current roll, which means the second roll is an independent result with the same distribution. And I'm pretty sure it is just reroll, not best of 2. I got the rule-book open right now and it doesn't say either way. In my experience that usually means reroll and use new result.

By chance, I only got the rules on Friday, less then 48 hours ago. Still haven't gotten to play it.

[daniel_ream]

FATE Core is annoyingly silent on this, but it's always been "reroll and take the new result".

Oh yes, and p. 68:


Rerolling the dice is a little riskier than just getting the +2 bonus, but has the potential for greater benefit. We recommend you reserve this option for when you’ve rolled a –3 or a –4 on the dice, to maximize the chance that you’ll get a beneficial result from rerolling. The odds are better that way.

[Tanarii]

Not having played fate, how do the core rules 4dF generate a range of -5 to +5?

[Martin Greywolf]

Not having played fate, how do the core rules 4dF generate a range of -5 to +5?

They don't, 4dF is +/- 4, but OP specified 1d6 - 1d6 instead, used as a means of not having to buy new dice.

In real play, using FP to reroll is rarely a thing that happens. There are two general tactics to fighting, Death of a Thousand Cuts and Omega Strike.

Death of a Thousand cuts relies on chipping away at opponent's stress track bit by bit until it's gone. You need to barely beat the opposing roll to do that, but to really do it as players, you'd need a lot more FP than you really have, so it's mostly used against NPCs that are weaker than you are. NPC mooks do use this one a lot more.

Omega strike involves stacking as many free invokes on target as possible ta make an attack that can't be eaten up by stress/consequence at all. In this case, you defend from enemy attacks and stack up aspects on a guy. If both sides do this, you get a rather interesting cat-and-mouse game where everyone is trying to get rid of aspects on him, slap aspects on the opposition and carefully maneuver with descriptions to make a few aspects moot by what's going on in the game world.

Now, since players usually go for Omega strike when FP are spent, you'll not be deciding on when to spend FP based on whether you have enough free invokes in play to reliably off a guy. In a case like this, it's almost never a good idea to re-roll, simply because even if you re-roll a really bad number, there's no guarantee of getting a better result. Either you have enough on your dice to go ham (and re-rolling would only serve to make a sure thing not so sure), or you don't and need to wait for another opportunity.

There is one exception to this, and that is if you are under time constrains. In that situation, you can be driven into a corner where you either go for it now and maybe win, or wait and never win.

That, of course, only applies to conflict, for overcome rolls, it's re-roll at -2 (-3 for 4dF) if and only if a +2 won't help - again, no reason to make a sure thing not sure.

Contests are the most complicated case, since a lot depends on whether or not you succeed with style, what are the skill dots you and your opponent bring to the table, if you're trying to create aspects, how far away from success your opponent is (sometimes, you need that FP just to make them not succeed with style) etc etc.

For the more math-based among you, in FATE, basic dice assumptions are a bit turned around, you're not in economy where you try to roll as much as you can, you always know what number you want to beat by the time spending FP comes into play. To get a full picture of when to do what, you'd have to also take into account how high you want to roll and what your and enemy reserves of FPs are (sometimes, spending a single FP to make the enemy spend his FP too and be dry for the rest of the match is well worth it). By this point, we're pretty much dealing with a economy model of spending FPs for won rolls, not just simple probabilities.

[Tanarii]

They don't, 4dF is +/- 4, but OP specified 1d6 - 1d6 instead, used as a means of not having to buy new dice.Okay. In that case, how does 4dF generate a range of -4 to +4. Is it 4 dice of -1, 0, or +1?

[Cluedrew]

Yes, A Fudge die (dF) has three results, written as a plus, minus and blank (two sides each), that give values +1, -1 and 0.

I don't know about combat strategies, the basic math should hold for a single check, a challenge, contest or conflict.

[Max_Killjoy]

They don't, 4dF is +/- 4, but OP specified 1d6 - 1d6 instead, used as a means of not having to buy new dice.

In real play, using FP to reroll is rarely a thing that happens. There are two general tactics to fighting, Death of a Thousand Cuts and Omega Strike.

Death of a Thousand cuts relies on chipping away at opponent's stress track bit by bit until it's gone. You need to barely beat the opposing roll to do that, but to really do it as players, you'd need a lot more FP than you really have, so it's mostly used against NPCs that are weaker than you are. NPC mooks do use this one a lot more.

Omega strike involves stacking as many free invokes on target as possible ta make an attack that can't be eaten up by stress/consequence at all. In this case, you defend from enemy attacks and stack up aspects on a guy. If both sides do this, you get a rather interesting cat-and-mouse game where everyone is trying to get rid of aspects on him, slap aspects on the opposition and carefully maneuver with descriptions to make a few aspects moot by what's going on in the game world.

Now, since players usually go for Omega strike when FP are spent, you'll not be deciding on when to spend FP based on whether you have enough free invokes in play to reliably off a guy. In a case like this, it's almost never a good idea to re-roll, simply because even if you re-roll a really bad number, there's no guarantee of getting a better result. Either you have enough on your dice to go ham (and re-rolling would only serve to make a sure thing not so sure), or you don't and need to wait for another opportunity.

There is one exception to this, and that is if you are under time constrains. In that situation, you can be driven into a corner where you either go for it now and maybe win, or wait and never win.

That, of course, only applies to conflict, for overcome rolls, it's re-roll at -2 (-3 for 4dF) if and only if a +2 won't help - again, no reason to make a sure thing not sure.

Contests are the most complicated case, since a lot depends on whether or not you succeed with style, what are the skill dots you and your opponent bring to the table, if you're trying to create aspects, how far away from success your opponent is (sometimes, you need that FP just to make them not succeed with style) etc etc.

For the more math-based among you, in FATE, basic dice assumptions are a bit turned around, you're not in economy where you try to roll as much as you can, you always know what number you want to beat by the time spending FP comes into play. To get a full picture of when to do what, you'd have to also take into account how high you want to roll and what your and enemy reserves of FPs are (sometimes, spending a single FP to make the enemy spend his FP too and be dry for the rest of the match is well worth it). By this point, we're pretty much dealing with a economy model of spending FPs for won rolls, not just simple probabilities.


And yet some people claim that "narrative" systems are more streamlined and less "in the way"... I'd say that those things are pretty tangential to the "focus" of the system. See also, FFG's Star Wars.

IMO, almost nothing slows a system down like discussions, debates, negotiations, "betting", etc.

[ImNotTrevor]

Let's not make a thread about math into an opportunity to air grievances about the existence of a style of game one happens to dislike.

[Max_Killjoy]

Let's not make a thread about math into an opportunity to air grievances about the existence of a style of game one happens to dislike.




Just an observation.

(If there's any grievance, it's not against the style or system, just the misrepresentation, and false contrasts.)

[ImNotTrevor]

Just an observation.

(If there's any grievance, it's not against the style or system, just the misrepresentation.)

The observation remains irrelevant to the topic of the thread, and is not really helpful.

Whatever perceived misrepresentation you want to talk about can be done in threads not about math. If you've got a bee in your bonnet about it, you can always start up a thread and have at it there. Let's not drag it into math threads, of all places.

[Max_Killjoy]

The observation remains irrelevant to the topic of the thread, and is not really helpful.

Whatever perceived misrepresentation you want to talk about can be done in threads not about math. If you've got a bee in your bonnet about it, you can always start up a thread and have at it there. Let's not drag it into math threads, of all places.




Consider that so far, the number of posts asking for it to not go that way, outnumbers the posts of anyone taking it that way.

[Grod_The_Giant]

I mean, I've got my answer, the original purpose of the thread is done, but still: can we maybe not wander into random threads and start airing old grievances, Max?

[Knaight]

And yet some people claim that "narrative" systems are more streamlined and less "in the way"... I'd say that those things are pretty tangential to the "focus" of the system. See also, FFG's Star Wars.

IMO, almost nothing slows a system down like discussions, debates, negotiations, "betting", etc.

Wow, about a whole paragraph of analysis for combat tactics. Clearly that makes this came comparable to the numerous traditional games that have entire forums putting out page after page (D&D is the obvious example here, but it's not like GURPS or Shadowrun analysis is hard to find in bulk).

[Max_Killjoy]

Wow, about a whole paragraph of analysis for combat tactics. Clearly that makes this came comparable to the numerous traditional games that have entire forums putting out page after page (D&D is the obvious example here, but it's not like GURPS or Shadowrun analysis is hard to find in bulk).

Not really what I was getting at, but I've been asked to let it be.

(Wasting more time on all the responses than the actual post possibly could have on its own...)

[Cluedrew]

To Max_Killjoy: Start a new thread. Then you can discuss it as much as you want and still be on topic. I for one am curious about whatever point you thought was so important.

... To say something on topic if you only need =0 and have a -1, it might also be worth going for the reroll, especially if succeeding with topic would be a big help. But it is still a risk.