Forum adverts like this one are shown to any user who is not logged in. Join us by filling out a tiny 3 field form and you will get your own, free, dakka user account which gives a good range of benefits to you: No adverts like this in the forums anymore. Times and dates in your local timezone. Full tracking of what you have read so you can skip to your first unread post, easily see what has changed since you last logged in, and easily see what is new at a glance. Email notifications for threads you want to watch closely. Being a part of the oldest wargaming community on the net. If you are already a member then feel free to login now.

I've seen a number of posts detailing the math of casting psychic powers (% chance of success, perils risk) here and elsewhere, but I haven't seen anything talking about how the math is changed when you can re-roll a psychic test. Whether once (Eldar runes) or every time (Chaos sorcerers with a familiar), I'm wondering if/how much the "safe" dice range changes when you have that option.

Can anyone provide a quick summary of the math? Thanks!

To calculate fail rate, multiply the fail rate fraction by itself e.g. A 1/2 chance with a reroll becomes 1/4 chance of fail (75% chance of success).

a 1/6 fail chance becomes 1/36

the chance of perils is basically the same

Very easy, take the original math as it gets quite complicate. For calculating it with a reroll simply square the chance of failure and subtract it from 1. For instance casting a WC3 power on five dice. 50% chance of success. 75% with reroll. 1-(1/2)^2. Rinse, wash, repeat for all other relevant data.

wtnind wrote:
To calculate fail rate, multiply the fail rate fraction by itself e.g. A 1/2 chance with a reroll becomes 1/4 chance of fail (75% chance of success).

a 1/6 fail chance becomes 1/36

the chance of perils is basically the same

Great, thanks. Your perils chance would be decreased slightly since you're able to roll fewer dice than you otherwise would without the re-roll, but I know what you meant.

So, if I'm understanding it right, WITH A REROLL, the success chances are:

Dice rolled for WC1 / Success % (Normal: 75% @ 2 dice)
1 - 75%
2 - 93.7%
3 - 98.5%

Dice rolled for WC2 / Success % (Normal: 80% @ 5 dice)
1 - n/a
2 - 43.7%
3 - 75%
4 - 90.2%
5 - 96.5%

Dice rolled for WC3 / Success % (Normal: 75% @ 7 dice)
1 - n/a
2 - n/a
3 - 23.5%
4 - 53.8%
5 - 75%
6 - 89.1%
7 - 94.9%

In short, if you have a re-roll, it definitely increases the potential efficiency of your psychic phase. This is an obvious statement, but this helps quantify it to know exactly how much. Thanks for the math help!