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On June 29 2016 15:18 MooMooMugi wrote:
Anyone good with stats know what are the odds of getting 3 Cloud Drakes in a row? Given that only 3 dragons of each type can spawn per game. Is it (1/3)^3?
Impossible to know without conditional spawn probabilities or looking at actual game data.
If everything is independent (besides the obvious dependencies once you get the chosen 3) then the probabilities depend on how many drakes there are and additionally whether or not you're really asking what the probability of 3 drakes in a row is.
For 3 total drakes/game the probability is 1/36. 1/4 First Drake is Cloud, ->1/3 second, 1/3 third.
For 4 total drakes/game the probability of 3 cloud in a row is 1/36 + 1/54 [First probability plus probability that drake is not picked first BUT also in the 3 selected and then dings 3 times in a row] = about 1.66/36
For 5 total drakes/game the probability would be the above plus 1/81. So about 2.1/36
Those are the "in a row" numbers which are relatively simple. The "total possible numbers" are a bit more complicated because there are a number of dependencies. But it on the surface to me it should be equivalent to the "at least 3" numbers which is the sum of the probabilities of getting 3, 4, or 5 of the same drake given that it was totally independent.
The total probabilities would be 1/36 for 3 total drakes... obviously
For 4 total drakes it would be
1/3*1/3*1/3*2/3*4c3 = 8/81 +
1/3*1/3*1/3*1/3*4c4 = 1/81
*3/4 [probability of selecting cloud of the 3 to choose] = 9/108 = 3/36
For 5 total drakes it would
1/3*1/3*1/3*2/3*2/3 *3/4 *5c3= 40/324
1/3*1/3*1/3*1/3*2/3 *3/4 *5c4= 10/324
1/3*1/3*1/3*1/3*1/3 *3/4 *5c5= 1/324
=51/324 or about 5.666/36
Could have made a mistake here but that seems right to me.
Edit:
On June 29 2016 17:30 Alaric wrote:
Lulu gets hit hard as support too. They give compensation onto the ability she maxes last anyway, and in exchange her poke for the early levels takes a hard beating unless she positions in riskier ways.
If I can't just walk up to them and try trading at level 1 with my Q and passive without getting trashed because I can't use minions to make up for low MS and long animation, I'll call that a nerf anyway.
The only reason you level E last and Q first on support is because the slow duration increases on Q. (OK, poke too). Now that you don't need the slow duration increase playing E max like a Janna makes a lot more sense.
Also... So i totally missed the Censor buff. Man Ardent Censor Shield Karma was fucking hilarious before with the whole "on hit damage for everyone adds up to a ridiculously hilarious amount of damage" but now its going to make her shields stronger too. Ah ha ha ha ha ha.
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Why do people keep using 1/3 in the Drake calculations? We don't know that they predetermine the 3 possible pre-game. It could be that the chance is 1/4 until the third type spawns.
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On June 30 2016 07:43 cLutZ wrote:
Why do people keep using 1/3 in the Drake calculations? We don't know that they predetermine the 3 possible pre-game. It could be that the chance is 1/4 until the third type spawns.
Because it's easier to do it that way assuming independence and equal probabilities. Edit: Which we more or less have to assume if we want to work without any hard data or the given distribution for a number of reasons not worth going into.
Edit: additionally it doesn't matter how they select the overall drakes if each drake has an overall equal chance of being in the game; whatever method they use will sum to 3/4 for each drake.
Probability that you select a specific drake once it has been selected for the game = 1/3.
Probability that you select a specific drake to be in the drakes chosen for a game = 3/4.
So probability you choose the first drake as cloud is 1/3 * 3/4 = 1/4. Probability that you select the first drake as not cloud while cloud is in the game = 2/3*3/4 = 1/2.
Basically it lets me run all the probabilities faster and then multiply by the number of games that would have cloud in them rather than working out each probability and counting by hand.
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On June 30 2016 06:26 Nemireck wrote:Show nested quote +On June 29 2016 17:30 Alaric wrote:
Lulu gets hit hard as support too. They give compensation onto the ability she maxes last anyway, and in exchange her poke for the early levels takes a hard beating unless she positions in riskier ways.
If I can't just walk up to them and try trading at level 1 with my Q and passive without getting trashed because I can't use minions to make up for low MS and long animation, I'll call that a nerf anyway. It's like, they wanted to make Lulu viable as support without affecting her Solo game. So they nerfed her laning as support with the Q nerf, in trade for a buff to Allied Whimsy... the spell that I USUALLY use on an enemy champion to keep my ADC alive... Nothing makes sense about the Lulu changes...
I think if they had put the aspd buff on e it would have so much more synergy, but that might have been still good top so rip
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On June 30 2016 00:21 Scip wrote:Show nested quote +On June 29 2016 21:15 PrinceXizor wrote:On June 29 2016 20:38 Scip wrote:
since when can only 3 types of drakes spawn in a given game.
Also, why?
Also, the chances of seeing 3 cloud drakes in a 5 drake game are lower than that, because to see 5 drakes the first drake has to be killed realistically like before 8 minutes, which means the first drake is almost certainly fire.
Cloud drake is the evolutionarily most advantaged drake. It was added shortly after the specialized drakes so that people could be aware of what drakes are going to be played with in the game. rather than praying for the right one each spawn. That is a pretty strange decision so if I see the first drake I know that there's 1/3 chance it will repeat and that it's 2/9 chance any one other dragon will spawn not exactly probabilities that'd influence my decision making. Might as well be 1/4 for each lol.
Riot's justifications aren't exactly based on experience from high level play. All they get is the couple diamond players that play for them, and then the test group pros that come in say stuff and then half of it gets ignored (scarra). but yeah it's a bit silly. oh well though gotta live with it.
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Yay Syndra bug fixes. Literally the one change that would make league better for Syndra players is ensuring her E is 100% reliable.
That Ryze ult is like Urgot tier of ult mismatching. There's a yet to be made support champ crying already.
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On June 30 2016 07:50 Goumindong wrote:Show nested quote +On June 30 2016 07:43 cLutZ wrote:
Why do people keep using 1/3 in the Drake calculations? We don't know that they predetermine the 3 possible pre-game. It could be that the chance is 1/4 until the third type spawns. Because it's easier to do it that way assuming independence and equal probabilities. Edit: Which we more or less have to assume if we want to work without any hard data or the given distribution for a number of reasons not worth going into. Edit: additionally it doesn't matter how they select the overall drakes if each drake has an overall equal chance of being in the game; whatever method they use will sum to 3/4 for each drake. Probability that you select a specific drake once it has been selected for the game = 1/3. Probability that you select a specific drake to be in the drakes chosen for a game = 3/4. So probability you choose the first drake as cloud is 1/3 * 3/4 = 1/4. Probability that you select the first drake as not cloud while cloud is in the game = 2/3*3/4 = 1/2. Basically it lets me run all the probabilities faster and then multiply by the number of games that would have cloud in them rather than working out each probability and counting by hand.
There are quite a few games where only 1 or 2 drakes spawn. Moreover, your math is working backwards, almost like a monte hall question where you are acting as if you already know the "not spawning" dragon. But for the majority of dragons that spawn you do not know which type will not be spawning in the game, so the math and the logic are different.
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On June 30 2016 10:27 cLutZ wrote:Show nested quote +On June 30 2016 07:50 Goumindong wrote:On June 30 2016 07:43 cLutZ wrote:
Why do people keep using 1/3 in the Drake calculations? We don't know that they predetermine the 3 possible pre-game. It could be that the chance is 1/4 until the third type spawns. Because it's easier to do it that way assuming independence and equal probabilities. Edit: Which we more or less have to assume if we want to work without any hard data or the given distribution for a number of reasons not worth going into. Edit: additionally it doesn't matter how they select the overall drakes if each drake has an overall equal chance of being in the game; whatever method they use will sum to 3/4 for each drake. Probability that you select a specific drake once it has been selected for the game = 1/3. Probability that you select a specific drake to be in the drakes chosen for a game = 3/4. So probability you choose the first drake as cloud is 1/3 * 3/4 = 1/4. Probability that you select the first drake as not cloud while cloud is in the game = 2/3*3/4 = 1/2. Basically it lets me run all the probabilities faster and then multiply by the number of games that would have cloud in them rather than working out each probability and counting by hand. There are quite a few games where only 1 or 2 drakes spawn. Moreover, your math is working backwards, almost like a monte hall question where you are acting as if you already know the "not spawning" dragon. But for the majority of dragons that spawn you do not know which type will not be spawning in the game, so the math and the logic are different.
That is only due to players not pursuing the objective. Fact if every time a dragon dies before one would spawn at 35 minutes it could be one of three types.
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That Ryze ult is like Urgot tier of ult mismatching. There's a yet to be made support champ crying already.
It also seems horrifically broken. The video looks like its 3s from cast to "ryze is under your tower with his jungler ganking you"
Like a jungle ryze could blink from jungle to next to you during the space of a single morgana root.
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On June 30 2016 10:27 cLutZ wrote:Show nested quote +On June 30 2016 07:50 Goumindong wrote:On June 30 2016 07:43 cLutZ wrote:
Why do people keep using 1/3 in the Drake calculations? We don't know that they predetermine the 3 possible pre-game. It could be that the chance is 1/4 until the third type spawns. Because it's easier to do it that way assuming independence and equal probabilities. Edit: Which we more or less have to assume if we want to work without any hard data or the given distribution for a number of reasons not worth going into. Edit: additionally it doesn't matter how they select the overall drakes if each drake has an overall equal chance of being in the game; whatever method they use will sum to 3/4 for each drake. Probability that you select a specific drake once it has been selected for the game = 1/3. Probability that you select a specific drake to be in the drakes chosen for a game = 3/4. So probability you choose the first drake as cloud is 1/3 * 3/4 = 1/4. Probability that you select the first drake as not cloud while cloud is in the game = 2/3*3/4 = 1/2. Basically it lets me run all the probabilities faster and then multiply by the number of games that would have cloud in them rather than working out each probability and counting by hand. There are quite a few games where only 1 or 2 drakes spawn. Moreover, your math is working backwards, almost like a monte hall question where you are acting as if you already know the "not spawning" dragon. But for the majority of dragons that spawn you do not know which type will not be spawning in the game, so the math and the logic are different.
The monte hall problem requires that the opened door is not random. That the show runner knows which door does not have the money and always opens the one without.
Working backwards* would be just fine if Monte opened the door at random (and such had a chance of opening the door with the money) and so then the probability would not change and it would be 1/3 for the door you have 1/3 for the unopened door and 1/3 for the door monte opened. (In this situation if monte does not open money then it's 1/2 1/2 as people incorrectly guess)
So the math and the logic aren't different. Unless the distribution is not uniform or if the conditional probabilities are not the same as the unconditional. But well that was my caveat where I said we couldn't work it in that instance.
If you want to do a full count to show I am wrong go ahead. I am not mistake proof. But be thorough; it's very easy to mess up a full count.
*well rather working transitively. Independence implies multiplication implies transitivity.
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The math is hard because its conditional probability. It can go Cloud>Cloud>Fire>Fire and the chance for the next one being cloud is 1/4, conversely if it gets Cloud>Fire>Water the chance the next is cloud is 1/3.
The reason I brought up Monte hall is because when you use the 1/3 number you are assuming the "only 3 Drake's per game" rule (akin to opening the door) has been invoked, but it's never invoked till the fourth spawn, and often not until much later.
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On June 30 2016 15:41 cLutZ wrote:
The math is hard because its conditional probability. It can go Cloud>Cloud>Fire>Fire and the chance for the next one being cloud is 1/4, conversely if it gets Cloud>Fire>Water the chance the next is cloud is 1/3.
The reason I brought up Monte hall is because when you use the 1/3 number you are assuming the "only 3 Drake's per game" rule (akin to opening the door) has been invoked, but it's never invoked till the fourth spawn, and often not until much later.
It doesn't matter when it's invoked because it has to be invoked. You cannot have all four types of drakes in a game.
The monte hall works not because there is some rule later that is going to be invoked. But because if you do not pick the right option(which occurs with probability 2/3) with probability 100% monte opens a door with nothing behind it. Because he knows and chooses. That being the important part.
Suppose that it's cloud/cloud/fire/fire the next one could be any one of the four yes and even with probability 1/4. But overall the count will be the same as if you clipped in the front. All you're doing is organizing the count in a way that muddies the water because you're looking at a total divisor that includes sequences like ffeoo. Whereas I am not and then am correcting for it later.
Don't believe me? Do a count.
Edit:
Hard count should look like this so my estimate had some error in it by assuming a conditional probability which may or may not exist.
ccc- ee,ef,eo,ff,fe,fo,oo,of,oe = 9. Plus any order = 9 x 5c3
cc-eee, eef, eeo, and so on = 21 plus any order = 21 x 5c2
c-eeef, and so on = 42. Plus any order 42 x 5c1
eee-ff,fo,oo,of = 4 plus any order 4 x 5c3
ee-fff and so on = 8 plus any order 8 x 5c2
e-fffo and so on = 8 plus any order 8 x 5c1
fff-oo = 1 plus any order 5c3
ff-ooo = 1 plus any order
10+10+40+80+40+210+210+90=90/690 as our count. 4.6/36 or so.
Unless I double counted somewhere which is a possibility.
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Testing math brb.
Math is different depending on when it determines the pool, either on game start or on kill with discards of invalid options if the problem arises.
Given that we want the probability of 3 air dragon's in a row.
For just the 3 dragon case, it's 1/36 (3.7%) vs. 1/64(1.56%), which should be pretty self-explanatory. In the 4 dragon case, it's 4/105 (3.81%) valid spawn configurations vs. 6/252 (2.38%)
5 dragon case is 12/210 (4.14%) and 27/964 (2.80)%
Given enough of a sample size, it could be figured out.
EDIT: forgot the 4/3 for initial chance to spawn on fixed pool, should be final math now.
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Czech Republic11293 Posts
On June 30 2016 15:41 cLutZ wrote:
The math is hard because its conditional probability. It can go Cloud>Cloud>Fire>Fire and the chance for the next one being cloud is 1/4
how do you know it works this way, source?
it could be this
it's 1/3 the next one is air, 1/3 the next one is fire, 1/6 the next one is water and 1/6 the next one is earth.
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On June 30 2016 17:12 Scip wrote:Show nested quote +On June 30 2016 15:41 cLutZ wrote:
The math is hard because its conditional probability. It can go Cloud>Cloud>Fire>Fire and the chance for the next one being cloud is 1/4 how do you know it works this way, source? it could be this it's 1/3 the next one is air, 1/3 the next one is fire, 1/6 the next one is water and 1/6 the next one is earth.
AFAIK nobody has ever said how they determine the pool, on kill or on game start, which means there are 2 valid solutions to the problem until otherwise noted.
I'm sure if you had dragon spawn data from thousands of games, you could figure out which given the rather large difference in outcome chance, but who has time for that?
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Czech Republic11293 Posts
On June 30 2016 17:18 Amui wrote:Show nested quote +On June 30 2016 17:12 Scip wrote:On June 30 2016 15:41 cLutZ wrote:
The math is hard because its conditional probability. It can go Cloud>Cloud>Fire>Fire and the chance for the next one being cloud is 1/4 how do you know it works this way, source? it could be this it's 1/3 the next one is air, 1/3 the next one is fire, 1/6 the next one is water and 1/6 the next one is earth. AFAIK nobody has ever said how they determine the pool, on kill or on game start, which means there are 2 valid solutions to the problem until otherwise noted. I'm sure if you had dragon spawn data from thousands of games, you could figure out which given the rather large difference in outcome chance, but who has time for that?
Sufficiency does
has he been around here lately?
Also, it makes me sad I can't roleplay Luka, collect the 4 elemental spirits to obtain the power to challenge the monster king 
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I have seen the light, riot games is the best company of all time and they never do anything wrong or bad. I have taken this last month to reflect on what an amazing company they are and I hope I can aspire to be as great as them one day. I will never doubt any of their flawless decisions again and anyone that talks bad about Riot Games will definitely be getting a piece of my mind because they are the best company to ever exist.
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when rerolling 3 skin shards to get random skin is it only for champions i already own or for every champ in game ?
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VA is there a story behind that? Lol.
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EPT
