Tag Archives: fortune

Stacking the Odds Part II

The previous post on the probabilities for making lots of saves generated a bit of interest, and (as usual) some clever readers pointed out scenarios that should bear further analysis.  Altmann from the Penny Arcade forums asked:

“Can you work in the probability of making 4+ feel no pains as well? I know we’re getting into NASA shit but I’m curious”

Followed by Joe “Maynard” Cullen (of WarHeads fame) who pointed out that some wargear items also add complexities:

“The Wolf Tail Talisman gives a 5+ invulnerable save that happens before the armour save”

So in a similar fashion to my ultimate Ballistic Skill chart, I took it upon myself to rank the performance of a variety of armour types with rerolls, with Feel No Pain (FNP), and just plain regular saves.  This will give some insight into the relative merit of the saving throws we normally encounter in 40k.

As with Stacking the Odds Part I, the chart shows how likely each type of save is to take no casualties from an increasing number of saves.

So chart number one:

This charts the various types of save (and combinations) showing the odds of taking no casualties for up to 6 saves (I cut it off at 6 as about half of them approach zero at this point).  The legend on the right shows the ranking from best to worst with a 2+ rerollable save being the best, and a regular 6+ save being the worst.  The sharper eyed in the audience may notice that some of the save types listed in the legend don’t show up in the graph – namely “5+ FNP” and “3+ FNP”.  Rest assured this isn’t an error, it is simply that they are coincidentally covered by other save types that perform identically.  So a 5+ with Feel No Pain save works out the same as a regular 3+ save, and a 3+ with Feel No Pain save works out the same as a regular 2+ save.

Or do they?

The calculations are correct, but you need to interpret the data in the context if the game itself.  So saving on a 5+ followed by a 4+ for FNP is statistically the same as a 3+, until you get hit by an AP5 or AP4 weapon, at which point all you get is the FNP, which is just a 4+ save (as you can see from the chart is a lot worse than a 3+).  The FNP could also be blocked by a high strength AP- weapon, leaving you with just a 5+.

In a similar vein, the 3+ with FNP is the same as a 2+, but what if they got hit by a battle cannon? the 3+ is negated by AP3, and (assuming we’re talking about T4 units) the FNP is negated by the instant death rule.  So no saves of any kind!  But a squad of terminators would still get their 2+ and (assuming that 5 are wounded by the blast) they have a 40% chance of taking no casualties at all!

So what about those opening questions?  Well Altmann was interested in the effect of FNP on terminators, and to show the difference I’ve scaled the number of saves taken up to 30, and dropped the weaker save types.

The effect is actually pretty strong, if we take say 20 saves, a regular terminator squad has only a 3% chance of being unharmed while the FNP terminators have an 18% chance (again assuming that they aren’t hit by something that negates FNP!)

Joe’s suggestion of the Wolf Tail Talisman (WTT) is charted below. Assuming the squad has power armour, then it works out quite close to (but slightly better than) a 4+ reroll, and worse than a 2+ save.

This should let you compare the various save types available to you, but don’t forget the context of how saves and FNP get negated! If there are any other save types you want to see included, then please do leave a comment.

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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…


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