1. INTRODUCTION:

Written By GAMESLAYER989

2. EXPLODING DICE:

average value of an exploding die simplifies to:

and

3. ANYDICE:

4. THE CASE OF BLACK ONE:

(3+2+2+1+1+0)/6 =

1.5

(3+2+1+1+1+0)/6 =

1.333

1.5 / (1 - 1/6) =

1.8

5. MR. POSTER BOY:

converting focus into damage at a 1:1 ratio

6. THE MISSING LINK: REROLLS

7. ADDING FOCUS SIDES:

8. ONLY SLIGHTLY WRONG:

9. REY?

10. DECK LIST:

8. FINAL THOUGHTS:

akaand welcome to my first everOne thing that’s near and dear to my heart in this game is the, the Legacies version, the guy who cost me at leastand that's totally not the reason why I love him so much. I don’t love people for the money, let’s make that clear! Even though he is absolutely fantastic at bringing home the big bucks withg and all, but you know what? This article isn’t even about him! It’s instead about another great thing thatuses:. Not just any dice though, oh no, I want to discuss theare dice where IF you roll their, you get toand add up the results. If that next roll also rolls its, you get, and this keeps going on. What does this have to do with? Well, we kinda have a similar thing with a couple of dice in the game, and two prominent characters withhave started to regularly feature at top tables across the globe.I am of course, talking about. These two characters both havewhich allow you toof removing from the pool. Yes they’re conditional, but these can technically go- especially if pitted against each other!... LONGEST. FIGHT. EVER!So this begs the question, what’s the average value of their dice? Obviously, but for thein our maths we shall assume that. This means thatandeach have ato roll afor a, andfor a, which isand a. Without thethis would give us an average value of, aboutHowever, thatis obviously. It’s worth, which has aof hitting another, which is, and, and; you see the problem here. Theis more tricky to evaluate since it includes itself in its own definition, and we know that this can beWith that in mind, how can we get anwhen? Well, the chance you rollin a row is highly unlikely. At some point the probabilities are so insignificant as to be inconsequential, they won’t affect the final result in any meaningful way. To solve this we can use a, but that involves maths that I once understood but now can no longer remember. Never fear though, the internet is here! Apparently, theTo put that into perspective, it then averages, such as, who has anof, but less than a character with aand, likeEvidently,really adds a good amount of, in this case adding effectivelywhich… hey hang on, thatis on the! The logic checks out, thehas a value of. We can also understand it in this was:you are functionally getting another, which has an average ofOf course, you can’t trust everything you read on the internet. Especially when it involves maths that gets complicated enough that someone, like me, can easily make an error. The thing aboutand probability though, is that it’s very easy to simulate. I used a handy program on the internet called ANYDICE.com that allows you to. You can check the code here , make sure to select thewhen you output, as those are the values we care about. Yes, I know I could have written my die a lot simpler, but this is to illustrate the point!. Perfect! Ourand ourline-up!Now, you might be worried that this is already getting a little too divorced from reality, because after all:. Alright, I’ll bring it down a little and talk a little bit about a card I really liked and used back before it got rotated out, a card I swore was effective, and yet no one else seemed to play. The original,is a vehicle thatand ONLY has aand a. Naturally, you want yourto be cost effective, and oncedroppedwas competing in a world withand! Thein particular was a stern competition havingand, but costing just 3 resources. All the competing vehicles each have; in an ideal world theisforisforand so on. Also, the more yourare spent on a, the weaker you are to removal; that card that removed yourstopped you usingfor this round! There was however one thingdid that all other vehicles didn’t: It exploded!, not the vehicle.has athat doesthethe average value ofwould be:Meanwhile theis:The difference in value between the 2 dice is 1/6, for a full resource. Just not worth it! Counting in thehowever,becomes:That’s almostThehas a value of, meaning it has a, aand a. Does that make it worth the? Well I don’t think we quite have enough information to decide that.The thing is, this game also includesand. Theis actually, but it’s ability to have a(1 damage for each resource spent) can really helpof. Thetypically have a lot of, and aim to ignore this wholenonsense, instead forcing the, and therehasbeat, as they both have a maximum side of 3. Or does it?Hah, and you thought my earlier rambling had no point to it!is perhaps heroes' biggest poster-boy for, with hisallowing him toand so. The deck I have been alluding to many of you would know as, taken to last year'sbyfrom. This was my version of that deck:This deck, similar to, was designed to have aandin order toof our large number of dice. However, I would often have situations where I had a lot of, andhelped resolve that issue. Sincehas a(you always get to resolve it and reroll it), you can think ofto turn itsto aas if it is in fact. It’s not great, especially in a situation where you’re turningfrom aor ato itsjust to "benefit" from the. However, if we assume there will beorafterwards, then as thehas an average value of, that isn’t particularly good seeing that the alternative would be aThere’s beenI have set out earlier however, NAMELY,. This is obvious, when you look at it this way: If we reroll every time we hit athen obviously. This is where the maths gets really complicated, so instead I’m going to go the simulation route for this.Let’s assume that on athere arewe are willing to immediately resolve. For thethat would be itsand, forit's theand. Any other result we will, and then we take what we can get. Do you see that? Calculating withtheincreased by(fromto), whereas theincreased by(fromto). The more rerolls, the greater the average becomes with If we decide to take the 2 Ranged instead of rerolling, we actually go up to. Fancy that, I should not have been rerolling thosewhen I only had aandSpeaking of, let’s add them into our model. This program assumes we haveavailable to us: If we don’t hit anything with ourwe insteadinto the. If we do hit our maximum side though, then we’ll have athat can be used to gain a value of ... let’s say 1. For a Fang Fighter the average value becomes: 3.28 . A consistent value of 3, but sometimes we get to keep our Without rerolls, our average value becomes 3.17 , the reroll really doesn’t do much, as we are turning to theanyway, there’s justwe get higher than abecause we get to keep our For Black One the average value becomes: 3.72 . Why is this increase so significant? Well,, and theinherently rerolls. At this point we actually go down to 3.64 if we take thewhen it’s immediately offered, and withat all we go down to 3.40 . A stark contrast to, which benefits with a reroll by onlymore compared toWith aand a 4.28 vs 4.98 . For thethis makes logical sense, we cannot do anything more withthan we could with, so the total value only increases by, the value of the. Onhoweverhas aofby way of a. At this point it is correct to only ever take, otherwiseto theand resolve. I had a play around andwas the best I could get, which means an extremely likely chance to beand ainto aof a. It bears repeating however the assumption thatcan always go somewhere else for a value of 1, and only 1, not focusing ainto aor anything else., is ato play the? Well remember how earlier I mentioned the? Well now, we can see that in our scenario here of, thehas an average value of, costing, as opposed to, costing. By this measure,is still. I guess I might have been wrong after all. Still though, it’s better than people give it credit for! Under the right circumstances it is only slightly inefficient compared to theSo, back to. I mentionedfor a reason dammit, and that’s because hisis a perfect fit to provide Rey with the shield necessary to make her Special explode! When you turn one ofto aafter grabbing awith a, you are getting anfrom. This is because theis worthinstead of, massively increasing(in this instance) used on it.What about with theand aWell, fromthat getsand 6.60 ! Of course, we are having to spend part of athat could have been something else, like a; if we include that in the calculation then it drops to a ‘humble’ 5.59 . It’s unlikely we getthough, more likely we only get 1 and instead have anbecause of, bringing us to 4.49 or 3.59 if we include the(the fact that it could have been something else instead of a) of. Still though, whenhave a maximum ofor, thenis quite a cut above most of the other characters in the set, provided she can always meet her, such as by havingas her partner. Pity it’s all in...Since you got this far, it would be remiss to give you all this theoretical knowledge without a deck to apply it to, so here is athat I have been tinkering with lately, attempting to abuse thoseas much as possible. Remember, be greedy, and, I hope you all learnt something from this, because I certainly did.is an awesome program and I highly recommend you try it out for yourself. And thank you tofor hosting and editing this article, because oh boy you guys did not want to be stuck reading the first draft :P