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On Discord we've just been discussing the table which shows the probability of getting a success which appears in the YZE games. It seems to be the same table in all the D6 pool based games.
The chance to get at least one success should be one minus (the chance to not get any successes).
The chance to get no successes is 5/6 raised to the power of the number of dice rolled [(5/6)^N, where N is the number of dice rolled]. One minus this matches the probabilities in the first, initial roll, column.
The chance to have no successes after the push is this probability squared, which should be the same as the probability for an initial roll with twixce as many dice. ((5/6)^N)^2 = (5/6)^2N
So the chance for at least one success after a push should be the same as the chance for a success on an initial oll with twice as many dice and I can't see why the "with push" probabilities are all slightly lower than this?
Anyone got any insight into how the book probabilities were calculated?

I don't have any insight into the creation of those probability tables, and would be interested in an official answer myself. But note that your math assumes that all dice (that did not show a success on the first try) can be rerolled. In some YZE games, including the original Mutant: Year Zero, you cannot push ability dice dice showing a "1" result, though. This could have led to the slightly lower probabilities you noticed, and maybe the original table has just been copied to other games even if they do not include such a reroll restriction. This is just a guess on my part, though.

I don't have any insight into the creation of those probability tables, and would be interested in an official answer myself. But note that your math assumes that all dice (that did not show a success on the first try) can be rerolled. In some YZE games, including the original Mutant: Year Zero, you cannot push ability dice dice showing a "1" result, though. This could have led to the slightly lower probabilities you noticed, and maybe the original table has just been copied to other games even if they do not include such a reroll restriction. This is just a guess on my part, though.

That's a point, it would lower the probability a bit. You couldn't do a general calculation for all systems because it would depend on the mix of dice - FBL skill dice for instance can be rerolled on a 1. Hmmm.

The MYZ point is a bit moot, as the probability table has identical probabilities in every dice pool YZE game, including games where the 1s don't mean anything (i.e. Coriolis and Tales From the Loop). It's meant to be a simple visual of the probability of rolling a single 6 without any other factors, and as such the maths should be pretty straightforward, as the OP says. Very curious to hear the official answer...

It's meant to be a simple visual of the probability of rolling a single 6 without any other factors, and as such the maths should be pretty straightforward, as the OP says.

I think this is just your assumption, as I don't remember this being stated explicitly anywhere. But I gladly admit I might remember it wrong; could you perhaps provide a quote?

As said above the FL games work a little different even if they share the YZ engine.
If you push the roll the you only get the same chance as the first if no dices has been locked. Like if you roll a 1 on attribute or gear dice in Mutant Year Zero. If that dice belonged to the skill then you could reroll it.

Tried to include a tablet but it might be the one you already talked about (got an error message).

Looks like this was addressed by Tomas - six years ago now! Here's the discussion: viewtopic.php?t=3139#p28110

Looks like this was addressed by Tomas - six years ago now! Here's the discussion: viewtopic.php?t=3139#p28110

Good catch, thanks for the reference! Looks like my point wasn't so "moot" after all. I'd still like to know how they arrived at the probabilities in the table(s), though - in M:YZ, you actually get different probabilites depending on the type of dice used (as has been stated above), and I would like to know how FL have aggregated them into the singular value listed.

Looks like this was addressed by Tomas - six years ago now! Here's the discussion: viewtopic.php?t=3139#p28110

Good catch, thanks for the reference! Looks like my point wasn't so "moot" after all. I'd still like to know how they arrived at the probabilities in the table(s), though - in M:YZ, you actually get different probabilites depending on the type of dice used (as has been stated above), and I would like to know how FL have aggregated them into the singular value listed.

Might be worth posting in / bumping that other thread...?

I think this topic is fine, as it's not specifically about Coriolis like the linked thread, but I have a hunch we won't get an official answer anyway... Might be worth shooting FL an email. I am not sure I care enough to do it myself, though.