During our Winter Vacation, we re-posted old articles of ours that we felt were very helpful. Maybe you’ve read them before and you decided to skip them, but if you are newer to the game (or just had never seen them) then, go back and read them. At bare minimum there should be something useful to you there, but they could also open your eyes to the reality of our beautiful tiny game and start you on the path to internet glory. This is the old probability one.

For the sake of not making you click the link, we’ll quickly go over the more complex math algorithm which doesn’t really start off complex until we add multiple dice into the equation. For this quickie, we’ll only use TWO dice, 1 of Mother Talzin and 1 of FOST (picture below if you wish to see their die sides), so don’t be confused about why there are 3 dice in the picture below it.

Px = 1 – p(fail to hit ranged base)

= 1 – (4/6)(3/6)

= 1 – .333

= .667 OR 66.7% to hit at least 1 base damage on one reroll

Problem 1

So let’s change the spectrum a bit. Your opponent has claimed so you now have free reign to do what you want. Their Poe2 has 2 health left and you have a resource and 1 Talzin die and 1 FOST die in the pool on blanks. You have two cards in hand and are wondering the odds of being able to knock out the Poe2, but you’d like to avoid giving up 1 of those cards if possible, but if you can just about guarantee the kill, then you don’t mind giving up both.

Slow Old Math:

Py = 1 – (4/6)(4/6) – The math here dictates that on the Talzin die we can accept Focus or the 2 and then on FOST either 2, so both are 4/6 to whiff.

= 1 – .44

= .56 or 56% To hit on one roll

If including both rolls then

1 – (.44)(.44)

= 1 – .20 = .80 or 80%

Knowing that you’ll be able to defeat Poe 4 out of 5 times here makes it a worth while gamble, but can we realistically do this math in the middle of a game, especially if we aren’t the best at math??? Probably not…. but here is the shortcut that I’ve been using for a long time now. Many people have played against me and hear me whisper / say the math out loud post claims when taking lethal shots. Some people think I’m just a mad man with my Nightsister-ing ways, but in almost every case, the math dictates that I should do it or I feel that I need to gamble there to win. Here is a mini cheat sheet so you don’t have to go look up the percentages, but the numbers are approximate, so keep that in mind if the actual math is off by a percent.

1 side on a die = 1/6 = 16%

2 sides on a die = 1/3 = 33%

3 sides on a die = 1/2 = 50%

4 sides on a die = 2/3 = 66% (i know it rounds to 67% but its for the ease of division)

5 sides on a die = 5/6 = 84% (i know it rounds to 83% but its for the ease of division)

So let’s look at Problem 1 again, but use the “fast” math that I want to teach you. We need 1/3 of either Talzin or FOST and we know that it is 33%. Explaining this is not the easiest, but I’ll do my best

So math has a bunch of properties involving working with inverses and leftovers. I have no idea what the name of this actually is, but it involves taking the first percentage (33%), putting it to the side and then using the second percentage(33% again) on the remainder from the first (66%).

Talzin 33%, so the remainder is 67% but we’ll call it 66%.

Now we take the FOST 33% or 1/3 (i prefer fractions due to the ease of math) and multiplying it by the remainder.

66 / 3 = 22%

So now we just add the 33% from Talzin originally with the 22% which is the adjusted FOST percentage and we end up with 55%

33% + 22% = 55% and this is to hit on one roll

We can do that again for additional rolls.

55% means that the remainder is 45%. So we have 55% to the side

45% * 55% or 11/20, but thats hard to do so let’s just do 1/2 to be close, but know that you can take 10% of the end result and it’ll have brought you back to 55% (i’ll lose some of you here)

45% /2 = 22.5% then we add 1/10th of that which is 2.25 and we have 24.75% + 55% which makes it 80%.

55% + 22.5% = 77.5%

I left the more simple math in bold, but there are a bunch of shortcuts involved when you just need it on the fly. I would’ve gotten to 80% but even knowing you’re a bit better than 3/4 shot to hit the dice and put you in premium position is a worthwhile gamble. We could also hit 1 damage and 1 damage, but that is about 2-3% chance of likelihood so I didn’t bother with that.

I may have picked a pretty rough set of options, so let’s look at another problem that but this one doesn’t really have a correct answer.

Problem 2

Most of you know that I absolutely adore running both Bala-Tik and Nightsister. Knowing the math is the big reason that I find it very hard to leave home without her.

You god roll that beauty in the picture. Don’t ask where your upgrades are or why they are untapped… sssshhhh. Anyways, your opponent mitigates the Nightsister die and you have to think long and hard what the plan is here. You do some quick math to figure out if you want to ditch a card from hand to reroll multiple cards or to YOLO with Nightsister Pings. So let’s take a look at the math and some of it is just to point out stuff.

Reroll 1 Ciena die: 1/6 = 16%

Reroll 2 Ciena dice: 1/6 and 1/6 = 16% + (1/6 of 84%[remainder]) = 16% +14% = 30%

Reroll 1 Bala die: 1/3 (base or focus) = 33%

Reroll 2 Bala dice: 1/3 and 1/3 = 33% + (1/3 of 66%[remainder]) = 33%+22% = 55%

We easily determine that rerolling Bala’s dice instead of Ciena’s is the best play. If we had a Bait and switch in hand, then we have to look at different math again. Even though Bala has the focus, we don’t want to lose the additional die to the focus if we don’t have to, so we use Ciena die as the main one here.

Reroll 1 Ciena die: 1/2 = 50%

Reroll 2 Ciena die: 1/2 and 1/2 = 50% + (1/2 of 50%[remainder]) = 50% + 25% = 75%

Realistically if we have a Bait and Switch in hand and want “max damage” we probably pitch to reroll 1 or use NS ability on Ciena die and then “conveniently” spike someone for 7 damage. Without a B and S, we know that rerolling Bala’s 2 dice is the most likely of events to get us to resolve the other modified damage. Other things go into the math, like Bala using the focus side means that we’d lose the other die anyways, so we might as well gamble and take the extra percentages.

Problem 3

This last problem we’ll talking about is drawing card percentages. Some of us like to rely on the “Heart of the Cards” but you can’t pray to Fortuna for an entire tournament. Whether it be finding an upgrade, a resource ramp card, or mitigation, we’re all often looking for something during our subsequent draws. Most people don’t think about ditching cards from their hand at the end of the round to improve their odds to finding what they need and that can often differentiate the X-0’s from the X-3’s who scrub out at an event.

Situation: We have 18 cards in the deck left and 2 cards in hand. We want to draw a piece of die mitigation and only have 6 of them left in the deck. At base value, you’d think that you are pretty guaranteed to draw one since 6/18 is 1/3rd and you have 3 draws, but if you follow that math, then you are as wrong as the people who say you have a 50/50 to win a match since you either win or you don’t.

First Draw: 6/18 = 1/3 = 33%

Second Draw 6/17 = 35% but we’ll use 33% or 1/3 again here because math is hard

Modified 2nd Draw: 33% + (1/3 of 66%[remainder]) = 33% + 22% = 55% so far

Third Draw 6/16 = 3/8 = 37.5%

55% + (3/8 of 45%[remainder]) = 55% + 17% = 72%

But lets just kept using 1/3rd because the math is hard, so if the 3rd draw used 1/3rd instead

Modified 3rd Draw: 55% + (1/3 of 45%) = 55% + 15%= 70%

So we’re looking around 70-73% likelihood of drawing the mitigation, which to me isn’t high enough. If I don’t need the other card or two I’d have to consider ditching them if i REALLY REALLY need the mitigation. I’ll continue with the 1/3rds even though the 4th draw is actually 2/5 and the 5th draw is 3/7 (40% and 42% respective which is much higher than the 33% we are using)

Modifed 4th Draw: 70% + (1/3 of 30%[remainder]) = 70% + 10% = 80% (12% if using the 2/5)

Modified 5th Draw: 80% + (1/3 of 20%[remainder]) = 80% + 7% = 87% (8% if using 3/7)

The real math is 90%, but being close enough is what counts when you have to decide on the fly and can’t sit there with a calculator. So do we go with the 7 out of 10 times, or do we go with the 8 out of 9 times when we feel that we really need w/e it is that we are looking for.

Conclusion

I’ve honestly no idea if what I just attempted to explain will be understood, but if read a few times, i think it might be able to be followed. This most likely won’t bring you riches and prosperity, but if it helps you to win even a single game in a tournament that was important to you, then I did my job. We are playing a dice based game so luck will always be involved, but when you can logically curb the out of favor chances, you’ll often be able to find more consistency and find higher overall winning percentages.

~HonestlySarcastc

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