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Cardiology: Prized Vendetta

Decision: Should You Play Prized Vendetta?

TL;DR: 

Yeah, probably.  It's a solid accuracy booster against a single target.  Just don't drop Potion of Rage for it.

Factor: The Ideal

Let's start out by taking a very brief look at how good Prized Vendetta could be in a completely ideal situation: i.e. one in which you know ahead of time whether the roll you make is going to fail or not, and only reroll if you need it.  In that very idealized hypothetical, Prized Vendetta would increase your chance of hitting by the amounts given below:


1d2d3d1b2b1g
1s19%15%13%17%13%15%
2s25%23%20%24%21%23%
3s24%25%24%25%25%25%
4s21%24%25%22%25%24%
1h23%19%16%21%16%19%
2h24%25%23%25%24%25%
3h19%24%25%21%25%23%

Those are really good numbers. However, we have to remember that this is the best that Prized Vendetta can possibly be, and depends on you possessing a Cassandra-level ability to predict the future. 

Factor: Choices

When Mike Carlin of Steel City Underworlds asked us to look at Prized Vendetta, our initial reply was "Rerolls make for hard math" or something equally whiny.  It's true though.  Rerolls do complicate the mathematical analysis of cards because they create branching paths of probability, but that's actually the smaller of the two problems with analyzing rerolls in this format.  The real issue is that rerolls create choices - which are hard to integrate into "objective" evaluations.  

Additionally complicating this issue is the fact that attacking players don't know the defense results before they have to decide to reroll dice.  While this is easy enough with "single" and "any" dice rerolls - 99% of the time you just reroll anything that's not a success - Prized Vendetta only allows you to reroll all of the dice, or none of them.  (Yes, we are aware there is some doubt as to whether this is correct, but we strongly believe the FAQ on K'Charik and Awakened Weapon pretty much makes it clear how "all" dice rerolls work).   Due to this restriction, the player will be occasionally forced to reroll successful dice in the hopes of getting a better result overall.  And that makes for really complicated math.  However, after spending a few hours posed like a Rodin life model, we think we've come up with a few ways to suss out just how useful Prized Vendetta is.

Factor: No Success

There is one time when it's quite easy to decide to reroll: when you've got no successes!  The chart below details the percentage of rolls that will come up with no successes:

No Successes
1s66.67%
2s44.44%
3s29.63%
4s19.75%
1h50.00%
2h25.00%
3h12.50%

When you do run into this disheartening situation, you can reroll all the dice with no hesitation.  If we take the improvement chart from the section above, and factor in how good Prized Vendetta is when you only  reroll based on having no successes, we'll get the following improvements to accuracy:


1d2d3d1b2b1g
1s17%13%10%15%11%13%
2s20%16%12%18%13%16%
3s17%14%12%16%13%15%
4s14%12%10%13%11%12%
1h18%13%10%16%10%13%
2h15%12%9%14%10%12%
3h9%8%6%9%7%8%

Definitely less impressive, but the numbers still aren't bad.  It looks like Prized Vendetta is shaping up to be a pretty solid choice.

Factor: Some Success

In order to feel like you are fully taking advantage of Prized Vendetta, you're probably going to want to reroll at least some rolls that do have at least one success.  This is where the math could get really long and complicated: factoring in every possible roll on every possible combination of dice is not something our night-shift-working, don't-get-paid-to-blog-brains are willing to go through at this point.  However, we can pretty easily determine the chances that a reroll will end up better than the original.  Because that's what we're hoping for when we reroll, right?  

(To keep the chart from getting unwieldy, we will be looking at sword and hammer attacks separately, and we've omitted 4-sword attacks on this one).
 
OriginalChance of Better Roll
1s/ 0 success33.33%
1s/ 1 success16.67%
2s/ 0 success55.56%
2s/ 1 success33.34%
2s/ 2 success30.56%
2s/ 1 crit7.41%
2s/ 1 crit+12.78%
3s/ 0 successes70.37%
3s/ 1 success49.53%
3s/ 2 success42.59%
3s/ 3 success42.13%
3s/ 1 crit7.41%
3s/ 1 crit +122.04%
3s/ 1 crit +29.98%
3s/ 2 crit1.62%
3s/ 2 crit +10.46%

If you don't feel like parsing that out yourself, we can give you a brief summary.  If you are making a sword-based attack of 3 or fewer dice, don't reroll if you got any successes.  If you do, most of the time you'll end up with the same result, or a worse one.  For those of you wondering about 4-sword attacks, the same logic holds, except you do have a slightly better than average chance of improving a 1-success roll, so you might reroll those too.  Let's look now at how hammer-based attacks shape up with Prized Vendetta.  Your chances of getting a better roll on your reroll look something like this:


OriginalChance of Better Roll
1h/ 0 success50.00%
1h/ 1 success16.67%
2h/ 0 success75.00%
2h/ 1 success41.67%
2h/ 2 success30.56%
2h/ 1 crit11.95%
2h/ 1 crit+12.78%
3h/ 0 successes87.50%
3h/ 1 success68.06%
3h/ 2 success45.83%
3h/ 3 success42.13%
3h/ 1 crit37.06%
3h/ 1 crit +118.33%
3h/ 1 crit +27.41%
3h/ 2 crit2.91%
3h/ 2 crit +10.46%


Once again, the picture is pretty grim.  The only times you would want to reroll a basic hammer-based attack are on unsuccessful rolls or on a 3-hammer attack that rolled a single success.  In every other situation, the reroll is more likely to turn out worse than the original.

Factor: Other Options

 

Probably the most widely used option for increasing attack accuracy at this point in the game is Potion of Rage.  It balances giving a hefty two dice increase by being strictly single use.  Prized Vendetta doesn't sacrifice itself to give you the bonus, but in a way it's also at least kind-of single use.  Since Prized only works agianst one target in the game, you really should put it on someone who is likely to attack that target.  Additionally, since you're using an upgrade to boost the accuracy of your someone's attacks, you should probably put it on someone with a good attack - one that's worth spending glory to improve.  And in that case, unless your vendetta is against Mollog, it's likely that you won't be making use of Prized Vendetta (successfully, at least) more than once or twice.  

In that case, Prized Vendetta probably falls somewhere between really permanent bonuses to hit (like the ridiculously overpowered Hand of Sigmar) and single use bonuses like Potion of Rage.  Since it costs a glory point to play Prized, it really needs to perform well in order to be worth playing, given the restricted nature of it's bonus.  

All in all, even at its best, Prized Vendetta is outperformed on most attacks by Potion of Rage.  But since it's slightly more permanent, that's to be expected. 

Summary:

If you're already playing Potion of Rage, and you've got upgrade slots to burn increasing attack accuracy, Prized Vendetta probably has a place in your deck.  Just be aware of when to reroll and when to keep your original roll.

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