fuzzer | 2015-08-26 23:51:50 |
How many possible hands are there for a Spectromancer game? take a guess! I'm not a mathematician so it's possible my calculations are wrong but here is what I came up with (I didn't consider banned combos):
for each of your 4 elemental houses there are 495 combinations. for your special house there are 70 combinations. so: 495 * 495 * 495 * 495 * 70 = 4,202,607,543,750 combinations and this is just for your hand. if we wanted to calculate the possibility to have 2 exact game-draws we need to consider the opponent's draw, so: 4,202,607,543,750 * 70 * 70 * 70 * 70 * 70 = (opponent's possible draws are more limited and I calculated for a game between 2 different special houses) 7,063,322,498,780,625,000,000 combinations for a specific game card draw! if we want to calculate the Spectrmancer game number-of-different-possible-games we need to consider there are 16 different mancers, so: 1,696,811,873,421,357,000,000,000 possible different games!
what I'm saying is - if you draw a hand and think 'I had this hand before!' - you're most likely are wrong! ;)
CyberneticPony | 2015-08-27 00:27:54 |
what I'm saying is - if you draw a hand and think 'I had this hand before!' - you're most likely are wrong! ;) The 1% rule narrows down what combinations crop up the most often. So actually, you're wrong, having the exact same hand is more common, even though it's still not very common!
fuzzer | 2015-08-27 00:52:59 |
... The 1% rule narrows down what combinations crop up the most often. So actually, you're wrong, having the exact same hand is more common, even though it's still not very common!
even so, so far you have played 2107 games. I believe you hadn't drew the same hand twice! it's an assumption, but the statistical probability that you had is very close to zero.
Modified by fuzzer on 2015-08-27 00:54:33 Wavelength | 2015-08-27 05:57:29 |
I was shocked that your "495" and "70" numbers were correct as they seem like suspiciously "un-permutational", but yeah, all of the nice even numbers get divided out in 12!/(4!*8!) also known as "12 pick 4".
Anyhow, there are a ton of different draw rules in place to narrow down the rules. For example, you will never ever draw F6 and F9 together because of the "one and only one sweep" rule - and this by itself will knock off millions of combinations from "12 pick 4". The number of special card combinations is known to be 16 (2 to the 4th power), not 70, because of the "pairs rule". As Pony mentioned, the 1% draw rule also means that a rather small minority of combinations are much more likely (and I mean MUCH more likely - hundreds of billions of times more likely) to be drawn than the vast majority of "theoretically possible" draws that include three or more 1%ers.
Given that most schools in practice probably have a couple hundred common draws (I don't want to do the rigorous math right now), we can assume that a mono-player might have 500 * 200 * 200 * 200 * 16 possible draws (500 for Fire since it is only partially constrained by 1%ers), which as my rough guesstimate would be 64 BILLION reasonable combinations.
Although this player will have a lot of extremely similar draws over 3000 games (with maybe 18 out of 20 cards matching), it's cool to think that it's very unlikely to ever get the same draw twice over 10,000 games (the combined odds would be just under 0.1% if I've calculated correctly?) and that even if you do pull this extremely rare event, your opponent's draw will probably be different too!
fuzzer | 2015-08-27 08:02:12 |
yeah, the 1% rule will cut down billions. and I'm a bit ashamed I forgot the "pairing rule" for your special house that cuts down the combinations from 70 to 16 - which will cut down billions too. but even so, for 2 games to be exactly similar (same possible plays) - both your draw and your opponent's must be the same (X2 combinations because the beginner is random). if I had to guess - my guess would be that so far there wasn't ANY exactly similar 2 games! (possibilities-wise) I estimate Spectromancer had probably above 1 million games so far (sounds right?) - but, out of the billions of possible game draws, I believe no 2 games were similar! if I'm right in this non-intuitive guess - than this is a proper answer to people who say Spectromancer is limited in it's possibilities because of its limited number of cards! Modified by fuzzer on 2015-08-27 08:28:26 CyberneticPony | 2015-08-27 11:12:38 |
yeah, the 1% rule will cut down billions. and I'm a bit ashamed I forgot the "pairing rule" for your special house that cuts down the combinations from 70 to 16 - which will cut down billions too. but even so, for 2 games to be exactly similar (same possible plays) - both your draw and your opponent's must be the same (X2 combinations because the beginner is random). if I had to guess - my guess would be that so far there wasn't ANY exactly similar 2 games! (possibilities-wise) I estimate Spectromancer had probably above 1 million games so far (sounds right?) - but, out of the billions of possible game draws, I believe no 2 games were similar! if I'm right in this non-intuitive guess - than this is a proper answer to people who say Spectromancer is limited in it's possibilities because of its limited number of cards! Due to the player count, it's bound to have happened to someone, even though it's still super unlikely. But that's why we keep coming back for more; every game is different!
minhtuan | 2015-09-08 02:49:09 |
The mana distribution is randomized each time too, so the number of possible positions would be multiplied by a few millions more. Modified by minhtuan on 2015-09-08 04:31:36 fuzzer | 2015-09-08 04:07:33 |
The mana contribution is randomized each time too, so the number of possible positions would be multiplied a few million more. I didn't think of that. you're right! I believe there was no 2 similar games. but who knows? :)
minhtuan | 2015-09-08 05:25:50 |
... I didn't think of that. you're right! I believe there was no 2 similar games. but who knows? :)
Of course after a few billion games, you may play the same game again. Or after a hundred billion games...
CyberneticPony | 2015-09-08 12:40:25 |
The mana distribution is randomized each time too, so the number of possible positions would be multiplied by a few millions more. It's not fully random though, it has some fixed rules. Both players will always start at 2 special mana. (Although 1st turn player doesn't get growth.) A player will always be able to play his gen 1st turn.
I haven't spotted any other rules yet, it'd be great if someone knows them to inform me. Modified by CyberneticPony on 2015-09-08 12:41:06 Wavelength | 2015-09-08 16:23:10 |
I don't know any hard and fast rules for mana start, but I've noticed the 6-5-4-3-2 (in any order) mana start come up pretty often.
Also, I believe the second player always starts his first turn with 4 more mana total than the first player (after getting his first turn growth).
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