You can always house rule your own games, it isn’t like you are in a tournament setting when playing.
Concerning Bios I decided to just brute force some probabilities, against a number of ‘target’ cards to see if its available at the beginning of the game, mulling if necessary to draw the card. I ran each sim 1,000,000 times for the probability.
Andy:
- 3 : 83.50%
- 5 : 95.22%
- 6 : 97.40%
- 9 : 99.69%
Bios:
- 3 : 84.16%
- 5 : 94.82%
- 6 : 96.98%
- 9 : 99.40%
45 card runner:
- 3 : 63.05%
- 5 : 81.24%
- 6 : 86.53%
- 9 : 95.13%
40 card runner:
- 3 : 67.86%
- 5 : 85.14%
- 6 : 89.94%
- 9 : 96.93%
Take all these numbers as you see fit.
edit: I ran the numbers on Bios looking for at least one of three cards multiple times and got [84.16, 84.08, 84.13, 84.00, 84.12], and for andy I got [83.50, 83.60, 83.85, 83.74, 83.66].
I have no idea why Bios wins over andy on the procon lotto.
edit2: This is all under the assumption that nvram does not get mulled, and is set before the drawing of the initial hand.
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Something seems wrong (or I am reading it wrong), but how can 9 target cards be easier to get than 3?
1 of the 9 I’d wager.
Ah, of course.
To be specific it is at least 1 of 9. All I did was emulate a draw, and a mull if necessary to see if at least 1 copy of a targeted card was in your hand. Basically what are the odds of a turn one opus, or some other card that your deck needs and needs real early.
I’m a bit too lazy to do the math right now, but the numbers seem intuitively off. Andy gets to see 9 and mulligan to 9, while BIOS gets to see 10 and mulligan 5…so BIOS’ numbers should be lower right? Maybe I’ll do the math after all.
Bios has a smaller deck size after mull, though. The only reason not to put the full 4 in NVRAM is if you get more than 2 that need to be tutorable. Late game and early game cards both have value in being put in NVRAM.
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Are you sure about your sim? For example, the probability of Andromeda seeing 0 copies of a 3x card pre-mulligan is governed by a hypergeometric distribution, i.e., PDF[HypergeometricDistribution[9,3,45],0] - Wolfram|Alpha
So, about 50%. Thus, the chance of not seeing a copy even post-mulligan is 0.5^2, which translates into a ~75% chance of getting it. Not ~83.5% as you cited.
I’m rusty with probabilities, though, so if someone sees the flaw here, please enlighten me.
1 - (0.5)^2, but your logic seems sound.
Edit: realized the terms being discussed got swapped. Nothing to see here. I agree the number seems inflated.
It’d be fine mechanically if the other NVRAM cards also put stuff in NVRAM.
For example:
Peddler Chip
When you install Peddler Chip, set the 3 three cards of your stack facedown as NVRAM.
[Trash]: Install a program from NVRAM
That’d work with anyone whilst being better with Ayla.
I don’t think FFG will have thought things through that way to support an ID though, most don’t get much aside from the designers pets (Geist and Smoke for recent examples).
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Does reasonably count? I had passed tests against checking the top x cards, making sure there are y positive values in z possibles. I’m shuffling an array of y values with a Fisher–Yates shuffle, Each array is shuffled against a freshly seeded golang rand.Rand instance.
Short answer I am comfortable with my sim, but it is not something that is fully tested nor for do I plan on spending the time to fully test this toy.
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Well, again, I’m not totally confident with my math, but I do know that Fisher-Yates is notoriously easy to mess up when implementing by hand…
I don’t mean to come off accusatory, of course: I just don’t want anyone to be misled as to the true probabilities here. My calculation for Bios trying to nail at least one of a 3x is:
i.e., 11 “chances” from a 45-card deck, followed by 5 from a 41-card deck. It comes out to ~72%, which would reverse the Andy/Bios advantage.
I am ready to strikethrough all of this if I’m wrong.
EDIT: Correction made thanks to @SavageOne.
Why are you using 10? I’m confused by that part and most of the math is over my head.
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Result is closer to expected (74.6% chance of getting at least 1 from 3 hits in a 45 card deck with 9 draws and a mull).
Pretty sure initial sim results are slightly off.
The way it’s worded makes me think the proper calculation is
6 from a 45 card deck
5 from a 41 card deck
5 from a 41 card deck
right? You look at 6 cards, pick 4 and then shuffle two back. Then you do the normal starting hand with possibility of mulligan.
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You’re right, should be 5 (opening hand) + 6 (initial NVRAM). Corrected in post.
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Not sure. If your procedure is the case, though, the probability shifts minimally to 71%
First I don’t think you are being anything other than honest and civil. To be honest it was a toy I did in an half and hour, mostly because I was interested and didn’t see any real numbers coming up in conversation.
Also as you implied there are a couple of places where errors may have crept in biasing my results. My guess would be an issue with my shuffle and the fact that I start with all of my true values at the beginning of my deck.
Even so I feel that at the least it shows that bios is very close to Andy for this type of consistency.
my simulation: def sim_bios(n, doubleNVRAM=False, D=45): deck = [1]*n + [0]*(D-n) #NV - Pastebin.com
results for at least one 3-of:
andy, no mulligan 0.4975 (agrees with NRDB, cool)
andy, with mulligan 0.7463
bios 0.7108
doubleBios 0.8310 (if the NVRAM stuff triggers on the original draw and the mulligan)
I tried putting together the closed form of this earlier today and got 71% for bios (but then saw the first sim results and thought “I guess I messed something up”).
So, the takeaways are qualitatively similar to @zagzagal’s simulation and @sappidus’s wolfram alpha magic: bios and andy are roughly similar in terms of early consistency. If Bios gets to do NVRAM baloney before drawing the mulligan hand, then she is significantly more consistent.
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