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Apocrypha Adventure Card Game» Forums » General

Subject: The Math of Apocrypha rss

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Samwise Crider
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I'm used to the basic math of calculating dice probabilities for determining the likelihood of success in, say, PACG. But how does one work out something like rolling 6 dice, reroll 2 if needed, pick the best 3.

Is it better to roll 5 dice in Apocrypha to go for a 12, or 6 dice for a 14? That kind of thing.

I'd guess there's a formula to calculate such odds, but it's beyond my math skills to easily work it out.
 
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Craig Stockwell
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I'm on my cell phone (and distracted), but a straightforward way is:

1 - [(failing outcomes)/(total possible outcomes)]

That's inelegantly expressed, but works.

For example, if you roll 3d6 for 10, you fail in 81 different outcomes, of 216. Your fail probability is 37.5%, so your success probability is 62.5%.

Now at one through three dice, you could also just count success outcomes and divide by total outcomes. Once you cross the threshold to more than three dice (and you only get to keep three), then it's easier to count failing outcomes.

If someone doesn't post the formula in the next day or few, I'll sit down and figure it out.

Of course, reroll/upgrade/downgrade/flip/explode/trash complicate matters ... but you have to start somewhere!
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Mark Beazer
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I can help a little (there are likely some rounding errors in here, but so what?)

3 dice 4 dice 5 dice 6 dice 7 dice 8 dice
3 100 100 100 100 100 100
4 99.5 99.92 99.99 100 100 100
5 98.15 99.61 99.92 99.98 100 100
6 95.37 98.84 99.73 99.94 99.99 100
7 90.74 97.22 99.2 99.77 99.93 99.98
8 83.8 94.29 98.05 99.33 99.77 99.92
9 74 89.51 95.86 98.37 99.36 99.75
10 62.5 82.48 92.05 96.41 98.38 99.27
11 50 73.07 86.01 92.82 96.33 98.12
12 37.5 61.65 77.46 87.02 92.61 95.82
13 25.93 48.77 66.13 78.16 86.12 91.26
14 16.2 35.49 52.56 66.05 76.13 83.39
15 9.26 23.15 37.71 50.93 62.09 71.13
16 4.63 13.04 23.42 34.28 44.66 54.07
17 1.85 5.79 11.39 18.09 25.34 32.7
18 0.46 1.62 3.55 6.23 9.58 13.48

Darn, it looks so much neater in the editing window! But the data is there, format it to your tastes.

So, 5 dice to get a 12 will succeed about 77% of the time. 6 dice to get a 14 will succeed 66% of the time. The high end of the curve is pretty mean!
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Austin Fleming
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carrion wrote:
I can help a little (there are likely some rounding errors in here, but so what?)

3 dice 4 dice 5 dice 6 dice 7 dice 8 dice
3 100 100 100 100 100 100
4 99.5 99.92 99.99 100 100 100
5 98.15 99.61 99.92 99.98 100 100
6 95.37 98.84 99.73 99.94 99.99 100
7 90.74 97.22 99.2 99.77 99.93 99.98
8 83.8 94.29 98.05 99.33 99.77 99.92
9 74 89.51 95.86 98.37 99.36 99.75
10 62.5 82.48 92.05 96.41 98.38 99.27
11 50 73.07 86.01 92.82 96.33 98.12
12 37.5 61.65 77.46 87.02 92.61 95.82
13 25.93 48.77 66.13 78.16 86.12 91.26
14 16.2 35.49 52.56 66.05 76.13 83.39
15 9.26 23.15 37.71 50.93 62.09 71.13
16 4.63 13.04 23.42 34.28 44.66 54.07
17 1.85 5.79 11.39 18.09 25.34 32.7
18 0.46 1.62 3.55 6.23 9.58 13.48


Darn, it looks so much neater in the editing window! But the data is there, format it to your tastes.

So, 5 dice to get a 12 will succeed about 77% of the time. 6 dice to get a 14 will succeed 66% of the time. The high end of the curve is pretty mean!


If you add [ c ] before and [ /c ] after (without the spaces), it will keep the columns straight, as above.
 
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Justin Boehm
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anoirtrou wrote:
carrion wrote:
I can help a little (there are likely some rounding errors in here, but so what?)

3 dice 4 dice 5 dice 6 dice 7 dice 8 dice
3 100 100 100 100 100 100
4 99.5 99.92 99.99 100 100 100
5 98.15 99.61 99.92 99.98 100 100
6 95.37 98.84 99.73 99.94 99.99 100
7 90.74 97.22 99.2 99.77 99.93 99.98
8 83.8 94.29 98.05 99.33 99.77 99.92
9 74 89.51 95.86 98.37 99.36 99.75
10 62.5 82.48 92.05 96.41 98.38 99.27
11 50 73.07 86.01 92.82 96.33 98.12
12 37.5 61.65 77.46 87.02 92.61 95.82
13 25.93 48.77 66.13 78.16 86.12 91.26
14 16.2 35.49 52.56 66.05 76.13 83.39
15 9.26 23.15 37.71 50.93 62.09 71.13
16 4.63 13.04 23.42 34.28 44.66 54.07
17 1.85 5.79 11.39 18.09 25.34 32.7
18 0.46 1.62 3.55 6.23 9.58 13.48


Darn, it looks so much neater in the editing window! But the data is there, format it to your tastes.

So, 5 dice to get a 12 will succeed about 77% of the time. 6 dice to get a 14 will succeed 66% of the time. The high end of the curve is pretty mean!


If you add [ c ] before and [ /c ] after (without the spaces), it will keep the columns straight, as above.


Also if you hit reply instead of quick reply, there is a "c" button you can hit while your text is highlighted that will add that for you.
 
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C Sandifer
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This demonstrates nicely why Gabriella is stronger than she first appears. That extra +1 is a big help.

12 is much easier than 13, 15 is much easier than 16, etc.
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Mark Beazer
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Yes, when the target number gets high, a humble +1 makes a big difference.

And thanks for the input tips. Maybe next time I'll remember them
 
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Mark Beazer
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Let's see how I do, here is a table of chances, but discarding the single highest die...

4 dice 5 dice 6 dice 7 dice 8 dice
3 100 100 100 100 100
4 98.38 99.67 99.93 99.99 100
5 94.21 98.51 99.64 99.92 99.98
6 86.96 95.94 98.86 99.7 99.93
7 76.85 91.23 96.93 98.96 99.65
8 64.51 84.03 93.29 97.26 98.9
9 51.23 74.38 87.46 94.1 97.31
10 38.35 62.73 78.96 88.58 93.97
11 26.93 50 67.98 80.32 88.23
12 17.52 37.27 55.2 69.35 79.68
13 10.49 25.62 41.52 55.82 67.58
14 5.71 15.97 28.41 41.09 52.8
15 2.78 8.77 17.17 26.89 36.98
16 1.16 4.06 8.7 14.72 21.65
17 0.39 1.49 3.49 6.38 10.07
18 0.08 0.33 0.87 1.76 3.07


Ah, that worked nicely.
 
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Nathan Bredfeldt
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Thanks for the tables. This helps me better weigh the risk vs need as far as taking a mutation for an assist. I never know what to do in that situation.
 
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Mark Beazer
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DrNate wrote:
Thanks for the tables. This helps me better weigh the risk vs need as far as taking a mutation for an assist. I never know what to do in that situation.


Yep, the decision to assist or not is a tough one, or even whether to play that boost you'd rather save, so it is good to know just how bad you need help. Obviously these tables don't cover everything, but you an still use them to get a feel for the true odds.
 
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Samwise Crider
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Yes, thanks for the number crunching!
 
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