you are in the same bracket as them, your game just matched them, so it's gonna match same people most likely atleast 2 I have noticed.
It simply means that you play in a similar skill bracket as them. I got matched 2 games in a row with the artist from Nerfnow and 2 of her friends on the US server. The odds of that happening are low, but because no one else was playing in that skill braquet, it just matched us again.
1.6% is not that rare. I just lost to an Orge Magi who got four 4x multies in one team fight to win the game. The odds of that are 1/1296 or less than 0.1%.
But really the matchmaking setting you up that way is much more likely than you are estimating. Since you played one game with them you know they are going to match up with you. And since your game just ended and you all just re-qued...well. The real numbers in any given 2-3 minutes search time in US, and one mode at your MMR it should almost be a surprise if you did not get several of the same players the next game.
There were about 3.2 million dota 2 games last week. Thats about 19,000 per hour or 950 starting during a 3 min que time. If only 1/5 are on US servers and 1/5 of that are in your chosen mode, then you are down to about 38 games. Matching your MMR as well and its really fairly likely that you will get the same people again if they re-que right away and you do also. Having at least 1 player from the previous game would be almost certain if everyone re-qued. Only reason it doesn't happen more is lots of people don't immediately play another game.
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Just a few days ago. I noticed me and along with others who I joined, are playing the same group of people. Say 2-3 games in a row with 2-3 same individuals... Then I join another matchmaking, with 4-5 people who also played together earlier and they talk about, "being in the same 2-3 games before".
So anyways I have really low math crap, but I hope you guys like my estimation.
Let's say the average size of the dota community who are online 220,000... Let's round that off to 200,000 people online. Let's say 1/5 are afk, with their computers on. 1/5 are waiting for friends, 1/5 are in-game, 1/5 are almost done and finally 1/5 or 20% are ACTUALLY queuing for a game. That's a pretty reasonable estimation, so 40,000 people looking for a game a any given time.
Ok now regions, to be fair and generalizing. Most players will only queue up 2 regions. Especially in the USA. So round up 9 regions for sake of numbers to 10. That's 4,000 x 2 or 8,000 active players. Ok, now there are a whole bunch of unknowns but for the sake of DBR. 5 ranks (bronze, silver, gold, platinum & diamond).. So if there are equal amounts of each rank you get 1,600 players who are around your ranking.
Lastly there are 3 types of game modes people play the most. AP, AR & the rest. Most pubstomp AP players don't like the luck of AR mode. Well all enjoy those drow/troll/PL AP pubstomp games. Most AR players love the extra gold. Then the rest fit in the last category. Further reduces the odds to 533 people.
So would the odds of playing same people twice is 1.6%? Would the odds of playing same 5 people be 8%.
Anybody who can provide me with a better odds formula or generalization, feel free to add.