# Daily Archives: 30 March 2011

## Undo! Undo!

Sometimes things just don’t go your way.  We’ve all had that situation where you really wish you could do that roll again.  Thanks to wonders such as twin-linking, or lightning claws, sometimes we can.  Today we are talking about re-rolls, and (as is my habit) here’s a question:

A bolter shot hits and wounds a Warlock on a Jetbike, he needs to make a 3+ armour save to survive.  If the farseer had cast Fortune to give him a reroll on that save, how much more likely would he be to survive? and would he have been better off in Terminator armour instead?

Rerolls don’t change the range of possible results (i.e. 1-6) but they do change odds of a particular result.  I’m following the usual format for the percentage odds here so I won’t labour the discussion with what each row means.

 1 2 3 4 5 6 = 2.78% 8.33% 13.89% 19.44% 25.00% 30.56% < 0.00% 2.78% 11.11% 25.00% 44.44% 69.44% > 97.22% 88.89% 75.00% 55.56% 30.56% 0.00% <= 2.78% 11.11% 25.00% 44.44% 69.44% 100.00% >= 100.00% 97.22% 88.89% 75.00% 55.56% 30.56%

Well actually … it is a little different this time so perhaps I should give some explanation to the more interesting bits.

• The ‘equals’ row gives the odds of a particular result if you were to roll two dice and pick the highest.
• The ‘less than’ row shows the odds of failing a particular result, e.g. theres a 25% probability of failing a 4+ (rerollable).
• The ‘greater than or equal to’ row shows the odds of succeeding on a particular result, e.g. the odds of succeeding in a 5+ (rerollable) is 55.56%

“So what?” says you.  In isolation it’s not that insightful, but if we compare it to the odds of a ‘normal’ (i.e. not re-rollable) outcome it gets very interesting.  The odds for a normal roll are covered here, but I’ve graphed the odds of success for normal vs rerollable to really show the difference.

Ok so the odds of getting a 1 or better is 100% in both cases … duhBut what about that Warlock from the beginning?

The jetbike Warlock has a 33.33% chance of failing that save (with no reroll).  If the Farseer has done his job and put Fortune on that Warlock, then the reroll brings the probability of failure down to 11.11%.  The reroll makes him three times less likely to fail! and what about that terminator armour? it has a 16.67% chance of failing that save – that’s twice as good as the basic Warlock, but one and a half times worse than the Fortuned Warlock!

A fortuned jetbike Warlock has significantly better saving throws than a Terminator with a Stormshield – think about that before you try gunning down a Seer Council.

Take a moment to really look at the chart.  The rerollable 6+ is almost as good as a basic 5+, and is about twice as likely as a normal 6+.  The 5+ reroll is better than a basic 4+, and so on until they converge at 1.  Also notice those trendlines I’ve added, the basic rolls get linearly less likely, but the rerolls stay high and then gradually fall off as you hit 6.

Of course, not all re-rolls are there to mitigate failure – sometimes you can be forced to reroll a success, but that analysis will have to wait for next time…