EPTEither way, the number is indeed somewhat beyond belief. Also, teams occasionally run as few as 0 cores (TI3 grand finals game 1) to as many as 4 although it's possible you wouldn't qualify all those cores as "carries".
General Discussion - Page 3588
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Sn0_Man
Tebellong44238 Posts
Either way, the number is indeed somewhat beyond belief. Also, teams occasionally run as few as 0 cores (TI3 grand finals game 1) to as many as 4 although it's possible you wouldn't qualify all those cores as "carries". | ||
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Unleashing
Denmark14978 Posts
On August 15 2013 04:03 Hertzy wrote: I just started wondering how many unique lineups there can be. An upper limit I can come up with is the number of heroes, 102, over ten. The result is a bit over twenty one trillion. Accounting for the facts that there are 49 carries and that a lineup will contain from one to (greedy) three carries, I pared it down.... to eighteen trillion and a bit. Then you're forgetting that some heroes have multiple uses and a line-up with 3 heroes + windrunner and shadow demon might have run shadow demon as a mid and windrunner as a support or the other way around, which to me is a different line-up. Obviously that's semantics though. | ||
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Incze
Romania2058 Posts
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LuckoftheIrish
United States4791 Posts
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Hertzy
Finland355 Posts
So, the octave code I used looks like + Show Spoiler [code] + heroes=102; carries=49; noncarries=heroes-carries; upper_limit=0; for i=2:6 upper_limit=upper_limit+(bincoeff(carries,i)*bincoeff(noncarries;10-i) ) ; end; | ||
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Unleashing
Denmark14978 Posts
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Yoshi-
Germany10227 Posts
So if anything it should be 102C5 * 97C5 / 2. http://www.wolframalpha.com/input/?i=((102 choose 5) * (97 choose 5)) / 2 Dunno if that is correct, I might not be able to do proper math atm. | ||
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Hertzy
Finland355 Posts
On August 15 2013 04:28 Unleashing wrote: But if you disregard positions then why care about the amount of carries? As you yourself said, it's a matter of semantics whether or not swapping the trilane and midlane carries is a new lineup. I'm leaning towards "no". Essentially, anything happening after picking the fifth hero is not factored in to the calculations. | ||
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Yoshi-
Germany10227 Posts
On August 15 2013 04:33 Hertzy wrote: As you yourself said, it's a matter of semantics whether or not swapping the trilane and midlane carries is a new lineup. I'm leaning towards "no". Essentially, anything happening after picking the fifth hero is not factored in to the calculations. Are you responding to me? 102 choose 10, implies that the matchup ABCDE VS FGHIJ is the same as ABCDF VS EGHIJ, but obv those matchups are not the same. | ||
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Unleashing
Denmark14978 Posts
There are carries that can support and supports that can carry without being listed as such in the heropedia. It's very possible to have a line-up with 5 heroes listed as 'carries' by valve or have a lineup with no heroes listed as a carry by valve.. Edit: Gyrocopter isn't even listed as a carry. Probably plenty more inaccuracies/flaws. | ||
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Mafe
Germany5966 Posts
On August 15 2013 04:30 Yoshi- wrote: 102C10 is wrong, because this would imply that it doesn't matter which side picks which hero. So if anything it should be 102C5 * 98C5 / 2. http://www.wolframalpha.com/input/?i=((102 choose 5) * (98 choose 5)) / 2 Dunno if that is correct, I might not be able to do proper math atm. If it's correct depends on what you want to calculate, but this is exactly the number for possible all possibly pickable lineups, withour any further restrictions (such as a limited number of carries); and also not counting matchups twice, as they could switch radiant and dire. My web calculator say it's 2683908481910040, which I guess tells me I should better use wolframalpha in the future. edit: or no; I think your calculation should be 102C5 * 97C5 /2 instead. | ||
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Yoshi-
Germany10227 Posts
On August 15 2013 04:38 Mafe wrote: If it's correct depends on what you want to calculate, but this is exactly the number for possible all possibly pickable lineups, withour any further restrictions (such as a limited number of carries); and also not counting matchups twice, as they could switch radiant and dire. My web calculator say it's 2683908481910040, which I guess tells me I should better use wolframalpha in the future. You get 2683908481910040 because you used 97C5, I used 98C5, which is wrong, your 97C5 is correct.(I had this right and then edited for we reason) | ||
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Hertzy
Finland355 Posts
On August 15 2013 04:35 Yoshi- wrote: Are you responding to me? 102 choose 10, implies that the matchup ABCDE VS FGHIJ is the same as ABCDF VS EGHIJ, but obv those matchups are not the same. No, you managed to slip a post in while I was typing. Actually, I think you were right, other than using 98 instead of 97. So now I'm going with + Show Spoiler [code] + N=0; for i=1:3; for j=1:3; N=N+(bincoeff(carries-i,j)*bincoeff(noncarries-5+i,5-j))*(bincoeff(carries,i)*bincoeff(noncarries,5-i))/2; end; end; Which is giving me 1.74*10^15 possible matchups. EDIT: Good point about the switched lineups, you need to divide it by two RE-EDIT: Fixed a copypaste error that was throwing the result off | ||
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FairForever
Canada2392 Posts
On August 15 2013 04:30 Yoshi- wrote: 102C10 is wrong, because this would imply that it doesn't matter which side picks which hero. So if anything it should be 102C5 * 97C5 / 2. http://www.wolframalpha.com/input/?i=((102 choose 5) * (97 choose 5)) / 2 Dunno if that is correct, I might not be able to do proper math atm. This is correct - under the assumption you don't care which side is Radiant and which is Dire. Could be twice this amount if the side matters as well (as in, a given match would be different if played as one side Rad one side Dire as opposed to vice versa). | ||
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Qbek
Poland12923 Posts
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Incze
Romania2058 Posts
I'm not complaining, combinatorics was among my favourites | ||
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Hertzy
Finland355 Posts
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Emnjay808
United States10666 Posts
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Yoshi-
Germany10227 Posts
On August 15 2013 05:07 Emnjay808 wrote: Wtf is happening. Too early for school guys. There is always time for math | ||
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Targe
United Kingdom14103 Posts
On August 15 2013 04:57 Incze wrote: Since when has the GD thread become the Math thread? I'm not complaining, combinatorics was among my favourites I always hated this stuff. | ||
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