# Quick question for the maths gurus

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Quick request for anyone who is good with this stuff, since I’m rubbish!

what are the odds of a single blue dice rolling a crit and then drawing structural damage for the face up card?

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You got a 2/8 chance of the blue rolling the crit for a start, followed by an 8/52 of structural.  So it's 2/8*8/52, which reduces to 2/52.  1 in 26 roughly, if i'm doing the math right? 3.84%

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Correct. Assuming no cards have been delt yet and Dodonna isn't personally directing the shots.

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Question for my own curiosity, whats the odds when dodonna is involved?

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With Dodonna you still have a 1/4 chance to roll a crit. But then you will draw 4 cards. Your chance to draw a "Structural" (if no card has been dealt before) should be 8/52+8/51+8/50+8/49 = 63,4%. Your chance with Dodonna goes up to 15,8% to roll the crit and draw the card.

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4 hours ago, geek19 said:

You got a 2/8 chance of the blue rolling the crit for a start, followed by an 8/52 of structural.  So it's 2/8*8/52, which reduces to 2/52.  1 in 26 roughly, if i'm doing the math right? 3.84%

That shot cost me an ISD... Just had to know so thanks for that!

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11 hours ago, Triangular said:

With Dodonna you still have a 1/4 chance to roll a crit. But then you will draw 4 cards. Your chance to draw a "Structural" (if no card has been dealt before) should be 8/52+8/51+8/50+8/49 = 63,4%. Your chance with Dodonna goes up to 15,8% to roll the crit and draw the card.

Sorry, that is incorrect. Where you went wrong is not accounting for the possibility of drawing multiple Structural Damage cards on the same 4-card Dodonna draw.

I will show how to compute this explicitly, and I will try to explain every step, not because I assume you don’t know how to do this, but instead for the benefit of others following along who may not have seen these kinds of computations before.

(The following assumes zero cards have been drawn so far in the game. Actually everything that follows still holds true so long as any cards that have been dealt in the game have been face down. Only face up cards change these calculations.)

Let’s use P to denote the probability that we draw at least one Structural Damage card with Dodonna. Then !(read “not P”) is the probability that we draw zero SD cards.* Those two probabilities are related by

P = 1 – !P.

This is convenient because !P is relatively easy to compute.

In order to draw zero SD cards, we need the first card to be something else, AND the second card to be something else, AND the third card to be something else, AND the fourth card to be something else.

For the first card, we have 44 “something else” cards in the deck out of 52 total cards. So this probability is 44/52.

For the second card, assuming the first card was not SD, there are now only 43 “something else” cards out of 51 remaining cards. Therefore this probability is 43/51.

For the third card, assuming that neither of the first two are SD, there are now 42 choices out of 50, or a probability of 42/50.

And the fourth card similarly has probability 41/49.

Now we need all of these probabilities to hold in order to not draw any SD cards. In Probability Theory “AND” becomes multiplication. Therefore,

!P = (44/52)(43/51)(42/50)(41/49)

= 0.5014

Thus, the probability that at least one Structural Damage card is drawn is

P = 0.4986.

Almost 1 in 2 to draw the SD card.

So the probability of rolling a blue crit and Dodonna drawing a SD is about 1 in 8.

Hope that was clear.

* Usually “~” is used instead of “!”  for “not,” but in this forum it looks too similar to “minus.”

Edited by stonestokes

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Just noting that what is posted above works only for drawing a structural damage card rolling a blue crit with 1 blue die.

If you look for the chances of DEALING that damage card we will need literacy level.

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2 minutes ago, ovinomanc3r said:

Just noting that what is posted above works only for drawing a structural damage card rolling a blue crit with 1 blue die.

If you look for the chances of DEALING that damage card we will need literacy level.

I don’t understand

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25 minutes ago, ovinomanc3r said:

Just noting that what is posted above works only for drawing a structural damage card rolling a blue crit with 1 blue die.

If you look for the chances of DEALING that damage card we will need literacy level.

That's when Dodonna's Pride walks in

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1 hour ago, stonestokes said:

I don’t understand

1 hour ago, Visovics said:

That's when Dodonna's Pride walks in

No if you don't know to read.

What would add the literary percentage of the country to the equation.

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1 minute ago, ovinomanc3r said:

No if you don't know to read.

What would add the literary percentage of the c﻿ountry to the e﻿qu﻿ation.

ahh now I get it, for some reason I thought you meant about dealing actually enough damage to draw the card, oops