Recently, Pat Dunford from Across the Bifrost asked me to dig in to the maths of Star-Lord’s ability Plucky Attitude for their Guardians of the Galaxy episode.
It’s an ability that gives you the options to reroll all your dice if you get no hit symbols on attack or block symbols on defense.
Working on the maths of this, you have to make some assumptions that might not be true. You will find yourself in situations where you don’t need to reroll dice as you already have enough blocks rolled, or you’ve already rolled enough damage to daze/KO the charcater, even though you’d get more results on average if you did reroll.
So to make the maths manageable, we assume you are trying to maximise hits/blocks and will always rerolls if it increases your average.
For example, on his Element Gun, you roll Crit, Wild, Block, Blank, Skull and explode in to another blank. You have two hits, but could reroll five dice. On five dice you would expect 2.5 hits, so we would reroll. If instead had three hits and six dice to reroll, we wouldn’t reroll, as it doesn’t improve our expected damage.
The exact situation will determine times when you want to reroll. Against M.O.D.O.K. for example, you will choose to use your possible reroll more often, but this is the assumption the following maths is predicated on.
Star-Lord has a 3 defense across the board, so that simplified the maths. He will not roll a block on 3 dice 63.47%. Of those times, you would benefit from using it on 42.38% of all rolls – so almost exactly 2/3 of the times you could use it (66.78%)
When you do is it, the number of expected blocks comes out like this:
It’s pretty close to 4 dice for 1 and 2 blocks – certainly a big improvement over 3 vanilla dice.
You trigger his ability a lot less often: you are rolling more dice, and more sides of the dice are hits (2 out of 8). It works out to being able to use it 19.18% of the time and you’d typically want to use it 12.49% of the time (so again around two thirds of opportunities). The impact it has is much smaller than on defense:
It’s a nice bump to have, but it isn’t really pushing his damage up too much.
With even more dice it triggers even less often. Only 9.91% of dice trigger the ability, and you would typically want to use it just 6.92% of the time – again around two thirds of the time (69%).
Again, in terms of damage bumps, it adds a little, but not a lot.
You might think you could use it to help fish for wilds, but as a crit is only a 1-in-8 chance, you’d need to be rolling either more than 8 dice or have no crits if you already rolled at least one crit and no hits. That only happens 2.41% of the time. It’s not going to be a great help there, but if you really need those two statuses, then you’re looking at around a 24% chance of getting two wilds on 7 dice – the most common number to be rerolling with Plucky Attitude. Maybe that’ll swing a game once in a while, but it isn’t something to build a plan around.