where u getting this number? ur number is like the bloated chess possiblities. People think chess is 16x16x16..... possibilities, when it's actually 10x10x10....by 30th number it's already end-game.
Dota is like the same. Top 25 heroes are picked more than the bottom 80+ heroes. Heck the top 5 are picked more than the bottom 40 heroes etc... factor in CM mode with bans, no mirror match, general weakness and no all INT/STR lineup and u gotten urself like at most 1,000 possible lineup.
![[Lk].Zano](https://steamcdn-a.akamaihd.net/steamcommunity/public/images/avatars/b9/b98e01ce6ef4a5e926a44cdd1564d0e8e5fbfa36_full.jpg "[Lk].Zano")
Well, it's better to get some identical games than to end up with a Void, Antimage, Medusa, Phantom Assassin and Ursa in the same team just because it hasn't been done before.
"where u getting this number? ur number is like the bloated chess possiblities. People think chess is 16x16x16..... possibilities, when it's actually 10x10x10....by 30th number it's already end-game."
Seriously? If you are going to question the math, I suggest you do your own math first rather than just assume it is incorrect. Also accounts for dire vs radiant.
http://www.reddit.com/r/DotA2/comments/27y8vq/at_107_heroes_there_are_8854617997445220_possible/
I'll do it late but it should be something like this right? 107 x 106 x 105.....or 1.2368^22 choices? Haven't done math in awhile what's the 102? Also does this formula factor in that you can't have mirror mode/duplitcates?
No the equation is correct and so is concede, I don't think making arguments for the sake of it is worth it. We will just have another thread where some kid who goes to a "top university" thinks that dotabuff is doing stuff wrong.
Interesting stuff though
@Madao! no that is not the equation (the one you posted). If i were you i would delete that post cause it only shows how big of a fucking retard you are, equaling a "F"ailure math 1/statistics you garbage seeking attention retard.
Why is it being divided by 5!*102? I understand the 102, but why 5!?
Is that to remove the different combinations of the 5 heroes? (The order)
There would be significantly less viable matchup combinations however. How often do you see 10 carries in tournaments? 9 Carries? Etc.
But yes, cool thought.
(It actually wouldn't even be that hard to figure out, just make a pool of carries/supports/mids/offlanes or whatever, then make up a list of viable combinations ie: 1 carry, 1 mid, 1 offlane, 2 supports // 2 carries, 1 mid, 2 supports, etc. and then multiply everything together)
That would be interesting to see if anyone was bored enough to write it up.
Actually to make it easier you can just negate off non-viable combinations, like 4-5 carries or whatever.
@links
I already posted it, and I was not the one that did the math for it originally. Like the title says "from reddit"
I made a thread about this a while ago from an even older reddit thread when there was only 98 heroes.
8.85 quadrillion is wrong because your math assumes team X vs Y is a different match up than Y vs X, so you have to divide by 2. You end up with 4.42 quadrillion. So... all of those numbers you made above -> divide by 2.
The math:
(107 choose 5) * (102 choose 5) * 0.5 = 4.42 quadrillion OR
(107 choose 10) * (10 choose 5) * 0.5 = 4.42 quadrillion
112 heroes = 7.13 quadrillion
Omg cus there's practical difference between 4 quadrillion and 7 =p
It is interesting but it's also kind of like listing the number of possibilities in march madness. You're never going to see 4 16 seeds in the final four, just won't happen. Just like dota will never see chen, io, visage, es and et team (the 5 least played this month). Unless someone goes out to make that team right now just to troll me. What's kind of funny is the next bottom 5 if we're going for a full match, really wouldn't be *that* bad- beastmaster, leshrac, brood, lone druid, naga. You could do LD mid, brood offlane, tri lane naga, lesh, bm. Not terrible, good push team.
Umm, another remark: what if the colour of the hero matters? you can have about 100 different matchups with the same 10 heroes, just by changing their colours.
I think this is counted in the calculation, so prolly it's A LOT LESS than that brazillion (#world cup) amount of matchups.
If the color of the hero matters then that is a permutation, so it would be:
(107 p 10) = 127.5 quintillion
which means X vs Y is different than Y vs X
team X vs Y and team Y vs X are different because dire and radiant sides are not identical.
but it isn't, because a tinker on radiant is not the same as a tinker on dire for example. Their potential to farm and perform is different.
but you said match up combinations. everyone who says match up thinks "ne vs ud", "terran vs protoss", spawns don't matter. anyways our math is correct however you want to interpret it
^well in starcraft the spawns are identical (assuming cross spawns). Same as in league.
In Dota, the spawns are not identical.
112 is including not released right..?
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"Eight quadrillion, eight hundred fifty four trillion, six hundred seventeen billion, nine hundred ninety seven million, four hundred forty five thousand two hundred and twenty is a number that accounts for which fountain each team spawns. There have been a total of about 715 million matches, which is only 8*10-6 % of the total.
If each game lasted 30 minutes, and every matchup were played in order, it would take 505,054,642,793 years. If you live to be 80 years old, this would take you 6,313,183,035 lifetimes. That's 36.6 times as old as the universe.
However, identical games have most likely already occurred due to the presence of popular and unpopular heroes."