GenCon saw the full spoiling of Doctor Strange, with an amazing spender attack: the Crimson Bands of Cyttorak. It has the ability to give an enemy character an Activated token. But what are the chances of this happening?
It requires rolling a critical, wild and hit result in the same roll, with a base of six dice.
It doesn’t matter if you get extra criticals, wilds and hits so long as you get at least one of each. Running their maths on this, the base chance of getting that mystic binding effect is 27% – about one in four. On the face of it, that’s not dissimilar to Loki’s Mesmerise effect on his Illusions attack (21%), but Doctor Strange has access to an item Loki would dearly love to have:
It’s important to note that this effect says reroll “all” not reroll “any”. You must pick up and reroll all off the dice. You can’t just fish for the faces you missed in your initial roll.
To give an figure to the chance when factoring in the Eye of Agamoto, we have to make some assumptions. For this, I’m assuming we will reroll any result that doesn’t trigger Mystic Binding, even if that result has a load of crits and wilds, so long as it lacks the full set. Any full set, we don’t reroll.
The maths gets complicated a little by the fact that you may be rerolling more than 6 dice, as you may have generated them from crits in the initial roll. Factoring that in, the overall chance of this getting what you need goes up to 49.5% – pretty much a coin flip.
Heading in to the Jank Tank
There are, of course, ways of increasing that.
Rerolling one dice is surprisingly useful. Another 48% of the time on the six dice roll you will have two of the faces you need, meaning a single reroll is very useful, though you only have a 1/8 or 2/8 chance of getting the face you need – depending on which it is. Most of the time you’ll be looking for a crit result, Overall, though, this increases you chance on the base roll from 27% to 34%.
You still get the Eye of Agamoto reroll all. Again, we need to make some assumptions. You have two rerolls to use and the order matters. If you get two of the three faces you need in your first roll, I’m assuming you use the reroll one first, trying to hit that last face, and then fall back on a full reroll if you don’t get it. If you only get one or zero of the faces you need, you use the reroll all first, then apply the reroll one. Under those assumptions, your odds of getting the full set goes up to 63%.
Increasing your dice pool is another way to skew the odds. There are lots of ways of adding two dice: a range of tactics cards will do it, as will Thanos’s Death’s Decree. Rolling 8 dice increases your base odd to 42%, and with the Eye of Agamoto, you go up to 69%
A final way could be using Recalibration Matrix to get another Eye of Agamoto effect. That by itself brings the total odds up to 65%
Combing these effects will of course increase the odds, but you will get diminishing returns on each one you employ.
In terms of team building, including a way of getting a single reroll (Wakandan affiliation, Baron Zemo or Shuri all spring to mind) seems the least restrictive. The ones involving tactics cards require more power and often positioning requirements, as well as using up your valuable tactics card slot. The cards that you spend before creating a dice pool (like One Two Punch) seems especially poor choices: Recalibration Matrix you can at least save if it turns out you don’t need it on that key Crimson Bands attack.
Having Dr. Strange to the Guardians’ Winging Tokens would also give you access to rerolls to pull off Cyttorak in a pinch, and give Dr. Strange access to other rerolls for added defense over and above his already nice defensive set.
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What is the math done to find the chances of rolling 1 of each of the Mystic binding requirements using X number of dice? I understand it may be complex.
There are two ways you can approach it. One is to write code which simulates a large number of rolls (10,000+) and look at the “empirical” data you get. The other is to have all the possible combinations of faces and calculate the probability of each combination. That expands exponentially with more dice, but that later way is how I generate my numbers. Some calculations have 10,000+ possible combinations when you get large dice pools. It takes a while to do, but once it’s done I can interrogate it quickly for any new abilities that might come out.