Probability and you: How to build the best deck

[agentflare]

the draws are 2 independent events, so the theoretical probability is the same.
first draw - 30 card deck, 7 cards drawn.
second draw - 30 card deck, 7 cards drawn.
no difference at all.

No the second hand is only drawn if no pillars were in the first hand

Probability of no pillars is = Probability no pillars draw 1 * Probability no pillars draw 2
Probability of pillars is = Probability of Pillars draw 1 + Probability of no pillars draw 1 * Probability of pillars draw 2

N = n1 * n2
Y = y1 + n1 * y2
Y+N = y1 + n1 * y2 + n1 * n2 = y1 + n1 * (y2 + n2) = y1 + n1 = 1

Admittedly, The chance of having no pillars is lowered, the chance was pretty low to begin with so the average isn't affected much. The chance is barely changed by the automulligan, maybe raised a bit. But anyways, since the difference is very small, i don't wanna calculate it.

[jumpoffduck]

Admittedly, The chance of having no pillars is lowered, the chance was pretty low to begin with so the average isn't affected much. The chance is barely changed by the automulligan, maybe raised a bit. But anyways, since the difference is very small, i don't wanna calculate it.

Good thing I already calculated it for you, right?

[agentflare]

Alright so updated with a method for rainbows. Anyone up for building an app for this? I would, but I'm kinda busy for the next 2 weeks.

[QuantumT]

In addition to not taking the mulligan into account, your method of calculating the cards is incorrect because it assumes that each individual draw is an independent event. According to your formula, a 7 pillar hand is just as likely as a 3 pillar one, which is incredibly wrong. A 3 pillar hand is ~5000 times more likely to occur than a 7 pillar hand.

In order to do this properly, you have to weight the probability of each number of cards and do a weighted average. This comes out to 2.34 without the mulligan, and 2.42 with it.

The differences might not sound like much, but the biggest difference is in the shape of the graph, which in reality is highly biased towards the 1-4 range.

If you'd like to see something on probability, I already did a thread on how it all works, which can be found here (http://elementscommunity.org/forum/index.php/topic,16010.msg218760.html).

[agentflare]

In addition to not taking the mulligan into account, your method of calculating the cards is incorrect because it assumes that each individual draw is an independent event. According to your formula, a 7 pillar hand is just as likely as a 3 pillar one, which is incredibly wrong. A 3 pillar hand is ~5000 times more likely to occur than a 7 pillar hand.

In order to do this properly, you have to weight the probability of each number of cards and do a weighted average. This comes out to 2.38 without the mulligan, and 2.48 with it.

If you'd like to see something on probability, I already did a thread on how it all works, which can be found here (http://elementscommunity.org/forum/index.php/topic,16010.msg218760.html).

I know it's not the most accurate way. It's just simpler to calculate it this way. It's reasonably accurate, and much faster. If I have time, i'll rewrite this. Just 1 question about using nCr, shouldn't it be nPr?

[agentflare]

Updated with nCr. You happy QuantumT?

[jumpoffduck]

Updated with nCr. You happy QuantumT?

Hm, what's your reasoning behind requiring exactly 3 pillars in the starting hand? I'd think that having more would be better. (True, drawing all pillars might be bad, but if that happens, chances are the next card'll be something else, which you can play).

Also, remember to account for automulligan + the fact that you have 12, not 10, quanta producing cards in your deck.

Edit: there's a .44515 chance of drawing 3+ pillars in the opening hand, by the way

[agentflare]

Updated with nCr. You happy QuantumT?

Hm, what's your reasoning behind requiring exactly 3 pillars in the starting hand? I'd think that having more would be better. (True, drawing all pillars might be bad, but if that happens, chances are the next card'll be something else, which you can play).

Also, remember to account for automulligan + the fact that you have 12, not 10, quanta producing cards in your deck.

Edit: there's a .44515 chance of drawing 3+ pillars in the opening hand, by the way

Remember parity? Play cards as soon as you get them?

[QuantumT]

Updated with nCr. You happy QuantumT?

People already have enough incorrect conceptions on probability. No need to give them more.