[ZeroSum]

Hoi, chummers!

I'm trying to weigh two 4-Edge Boosts against each other, and I am having a heck of a time with the maths behind it (statistics was a loong time ago).

Specifically, I'm looking into the following two options:
1. Add Edge to your dice pool
2. Reroll all failed dice

I can account for the math of re-rolling failures through relative dice probability (i.e. 1-in-3 chance of rolling a 5 or 6, with a further 1-in-3 chance on a re-roll), and this is also true for the exploding dice (1-6 chance of exploding dice, repeated, 1-in-5 chance of hit on non-6s), but I'm having trouble accounting for the variable Edge dice pool.

This is understandable, given that the actual mathematical value of either action will depend on two factors:
1. The size of the initial dice pool, and
2. The Edge attribute itself

So my question to you all is, how do you weigh the overall benefit of these two options, mathematically speaking. For those of you familiar with wargames, consider this a mathhammer exercise.

[Michael Chandra]

The balance between the two iirc is about 2.5 roughly. So if your dicepool is more than 2.5x as high as your Edge, rerolling is better, is my old rule of thumb. After all, we know that since exploding gives less hits than rerolling, an extra die on both sides makes rerolling better. Finding the balancepoints means everything above the balance is better rerolling-wise.

Mathwise, you want to find the break-even point where rerolls average equal the average of exploding dice.

First, let's calculate the average of a rerolled die:
R = 1/3 + (2/3*1/3) = 3/9+2/9 = 5/9.

Next, an exploding die:
E = 1/3 + 1/6*E => 6E = 2 + E => 5E = 2 => E = 2/5.

Now, with X dice and Y Edge, we want to find the point where X*5/9 = X*2/5 + Y*2/5. We should unify: 5/9 = 25/45, 2/5 = 18/45.
25/45 * X = 18/45 * X + 18/45 * Y
=>
7/45 * X = 18/45 * Y
=>
7X = 18Y
X = 18/7Y = (2 4/7) Y.
Insert an Edge attribute of 4 into that as Y, and we get 10 2/7 for X, so at 11 dice and 4 Edge rerolling is better.

Since 18/7 is only 1/14 higher than 2.5, you can just go 'Pool > 2.5*Edge' as rule of thumb, which is true below 7 Edge and at 7 Edge it just means you're treating the equal pool (18 dice) as superior rerolling. (Which it is: It's a more stable result.)

[ZeroSum]

Thank you! That makes a lot of sense, and I appreciate you dumbing it down for me. I was actually able to follow the math, so again, I appreciate it.

[Tecumseh]

Ah, a question I know the answer to and Chandra beats me to it!

I actually use the 18/7 myself because it creates an irregular result. I like the messiness since it doesn't result in whole numbers; you're always midway between two whole values.

But good write-up by Chandra.

[ZeroSum]

The reason I asked is because I eventually want to houserule Edge Boosts to have more impact.

I've mentioned in other threads that a) I don't like the minimal impact from rerolling a single die can have (especially since it forces players to make a choice that will not matter change the outcome 1/3 or 2/3 of the time, depending on whose die roll you choose to affect) and b) I do not care for the ability to affect your opponents dice rolls, from both sides of the table.

So, with that in mind my initial thought was simple. Remove the following Edge boosts:
Reroll one die (1), Negate 1 Edge of a foe (2), Count 2s as glitches for the target (5)

And then reduce the cost of the following by 1 (new values in parenthesis):
+1 to a single die roll (1), Buy one automatic hit (2)

The reason for this question was to try and weigh which of "Add Edge to your dice pool" or "Reroll all failed dice" I should reduce the cost of, so that it would cost 3 instead of 4. I think, based on the above, that I would choose "Add Edge to your dice pool" as costing 3 and leave "reroll all failed dice" at 4.

Just my personal opinion, of course, but I think this makes Edge boosts much more interesting.

[Stainless Steel Devil Rat]

Heh.  Spending 5 edge to make 2s count for glitches really is apparently priced with the assumption that you can see the roll then decide.  If it's before the roll, or on a roll behind a GM screen, I can't see spending 5 edge on a "maybe".

[ZeroSum]

Heh.  Spending 5 edge to make 2s count for glitches really is apparently priced with the assumption that you can see the roll then decide.  If it's before the roll, or on a roll behind a GM screen, I can't see spending 5 edge on a "maybe".

Yeah, as I mentioned in another thread, I think the writers forgot to include a provision that dice should now be rolled in the open. If both sides (player and GMs) can influence the other's dice rolls, I fail to see how you could roll anything in secret.

[penllawen]

Heh.  Spending 5 edge to make 2s count for glitches really is apparently priced with the assumption that you can see the roll then decide.  If it's before the roll, or on a roll behind a GM screen, I can't see spending 5 edge on a "maybe".

Huh. This somehow didn't occur to me. As GM, I routinely make all my rolls in secret.

[ZeroSum]

As GM, I routinely make all my rolls in secret.

Unless I'm running learning games, I do too. With stock 6th Edition rules, I don't think I can do that any more.

[Michael Chandra]

Heh.  Spending 5 edge to make 2s count for glitches really is apparently priced with the assumption that you can see the roll then decide.  If it's before the roll, or on a roll behind a GM screen, I can't see spending 5 edge on a "maybe".

In the QSR, it's explicitly noted as a 'before roll' boost, which makes it really strange.

[skalchemist]

Heh.  Spending 5 edge to make 2s count for glitches really is apparently priced with the assumption that you can see the roll then decide.  If it's before the roll, or on a roll behind a GM screen, I can't see spending 5 edge on a "maybe".

Huh. This somehow didn't occur to me. As GM, I routinely make all my rolls in secret.

Heh, I haven't rolled anything in secret as a GM since...wow, I can't even remember.   I've run too many games where either a) the dice need to be in the open due to mechanics and/or b) there was simply no point to keeping anything secret.  It never would have occurred to me to roll anything in secret in Shadowrun 6.  The GM advice section doesn't mention it either way.

Did past versions specify in GM rolls in secret in the rulebook?  Is this a very common Shadowrun GM thing to roll in secret?

[ZeroSum]

Did past versions specify in GM rolls in secret in the rulebook?  Is this a very common Shadowrun GM thing to roll in secret?

I remember having plenty of discussions with various groups on this, and it usually comes down to playstyle.

Honestly, I prefer rolling GM rolls in secret so that worst case, I can fudge some rolls that might otherwise have catastrophic effect on the party. I haven't done it often, but sometimes it can be useful.

More importantly, I like the tension it can build. Call for perception tests, roll some dice behind the screen, nod and go "hmm. yeah, you don't notice anything" is a pretty basic GM tool to build suspense. With open dice rolling, that gets harder. Again, just different approaches is all.

[skalchemist]

BTW, Michael, that's some good math you did up there.  I never would have had the insight to see that because the exploding die sequence is essentially a nested infinity the formula really boils down to E = 1/3 + E/6.  It took me a few minutes to realize what you had done there.  I mean, the answer (2/5) can be seen by just graphing each value (e.g. 1 roll, 2 rolls, 3 rolls, etc.), but WHY that is the answer, I'm not sure I would have hit on that no matter how much I thought about it.

[ZeroSum]

BTW, Michael, that's some good math you did up there.  I never would have had the insight to see that because the exploding die sequence is essentially a nested infinity the formula really boils down to E = 1/3 + E/6.  It took me a few minutes to realize what you had done there.  I mean, the answer (2/5) can be seen by just graphing each value (e.g. 1 roll, 2 rolls, 3 rolls, etc.), but WHY that is the answer, I'm not sure I would have hit on that no matter how much I thought about it.

Agreed; the what is sometimes easy. The HOW and WHY is much harder. Much appreciated, for sure.

[Michael Chandra]

Thank god at least something from my math classes at uni stuck. (I am not kidding there: I've had to math with infinite sums at uni and this trick and the sum of 1/x^n being 1/(1-x) are the primary tricks that I remember from the top of my head.)