Ask a simple question, get a simple answer

[russianspy1234]

I try a fast calculation, it should be 0.8^4 = 0.4096, that means 40.96%
The other case should be 0.6^4 = 0.1296, that means 12.96%

If i made errors, someone point out please!

That's the odds of winning 4 in a row with the given win percentages, and is correct.  It's not actually the answer to his question, though

I'll have to try and remember how to answer his exact question with statistics; I can't recall off the top of my head just now.  Failing that, a simple RNG computer program could be written to figure it out, which would be about the size of this post.

my gut says to just multiply that percentage by the number of sets of 4 (37).
...except that doesnt take into account the fact that if you win 4, the count resets, so multiply the 40.96 by .2 to make it so you lost the previous game, that yields 3 which seems a little low...

[Jangoo]

I don't really understand your calculation but:
2 would be the lowest possible number of streaks.
If the streak is broken at the fourth game every time that would give you:

4games*8(losses at 4th game)=32
That leaves 8 straight wins = 2 streaks at the end of the set

On the other hand, 8 streaks is the highest possible number ...

So, yeah, intuitively, 3 seems a bit low. I also find it hard to believe that the expected number of streaks will be an even value ...

[russianspy1234]

I don't really understand your calculation but:
2 would be the lowest possible number of streaks.
If the streak is broken at the fourth game every time that would give you:

4games*8(losses at 4th game)=32
That leaves 8 straight wins = 2 streaks at the end of the set

On the other hand, 8 streaks is the highest possible number ...

So, yeah, intuitively, 3 seems a bit low. I also find it hard to believe that the expected number of streaks will be an even value ...

it was 2.9 or so when i did my math so i just rounded up.  i dont see how the lowest number of streaks can be anything other than 0...

[Jangoo]

Because at a win-rate of 80%, in 40 games, you only got 8 losses at your disposal to break streaks. 

Like the first example shows, you "run out of" losses to break it by game 32. After that, its 8 straight wins ...

Now for only 60% win-rate, it's a different story and 0 streaks is well possible.

[dragonsdemesne]

Question(s):
If I play a deck with an 80% win-rate over 40 games,
How many streaks of at least 4 wins can I expect?
How many would it be, if my win-rate is only 60%?

I just wrote a little MATLAB program to figure this out.  It's 17 lines long.

If you play 40 games, and your win rate per game is 80%, then on average you will have about 5.55 streaks of 4.
If you play 40 games, and your win rate per game is 60%, then on average you will have about 2.38 streaks of 4.

Due to the fact that I did this with random simulation (of 1 million games) there may be a small error.  I ran it a few times, and it's within 0.01 each time, so it's good enough for these purposes.

edit: just realized that this doesn't take into account the problem that occurs if your 37th game is a loss and so your last 3 games are irrelevant.  Fortunately, this will only have a minor impact on the final result, lowering it slightly.

[russianspy1234]

Because at a win-rate of 80%, in 40 games, you only got 8 losses at your disposal to break streaks. 

Like the first example shows, you "run out of" losses to break it by game 32. After that, its 8 straight wins ...

Now for only 60% win-rate, it's a different story and 0 streaks is well possible.

an 80% win rate overall does not guarantee an 80% win rate over 40 games.

Question(s):
If I play a deck with an 80% win-rate over 40 games,
How many streaks of at least 4 wins can I expect?
How many would it be, if my win-rate is only 60%?

I just wrote a little MATLAB program to figure this out.  It's 17 lines long.

If you play 40 games, and your win rate per game is 80%, then on average you will have about 5.55 streaks of 4.
If you play 40 games, and your win rate per game is 60%, then on average you will have about 2.38 streaks of 4.

Due to the fact that I did this with random simulation (of 1 million games) there may be a small error.  I ran it a few times, and it's within 0.01 each time, so it's good enough for these purposes.

edit: just realized that this doesn't take into account the problem that occurs if your 37th game is a loss and so your last 3 games are irrelevant.  Fortunately, this will only have a minor impact on the final result, lowering it slightly.

good to know, but theres gotta be some kind of formula for this...  guess this isnt such a simple question.

[TheManuz]

Because at a win-rate of 80%, in 40 games, you only got 8 losses at your disposal to break streaks. 

Like the first example shows, you "run out of" losses to break it by game 32. After that, its 8 straight wins ...

Now for only 60% win-rate, it's a different story and 0 streaks is well possible.

an 80% win rate overall does not guarantee an 80% win rate over 40 games.

Question(s):
If I play a deck with an 80% win-rate over 40 games,
How many streaks of at least 4 wins can I expect?
How many would it be, if my win-rate is only 60%?

I just wrote a little MATLAB program to figure this out.  It's 17 lines long.

If you play 40 games, and your win rate per game is 80%, then on average you will have about 5.55 streaks of 4.
If you play 40 games, and your win rate per game is 60%, then on average you will have about 2.38 streaks of 4.

Due to the fact that I did this with random simulation (of 1 million games) there may be a small error.  I ran it a few times, and it's within 0.01 each time, so it's good enough for these purposes.

edit: just realized that this doesn't take into account the problem that occurs if your 37th game is a loss and so your last 3 games are irrelevant.  Fortunately, this will only have a minor impact on the final result, lowering it slightly.

good to know, but theres gotta be some kind of formula for this...  guess this isnt such a simple question.

This is a really interesting question, but unfortunately my math isn't strong enough!
I hope someone could give us the formula and explain it!

[Jangoo]

@dragonsdemesne

Thanks dude! Can you run it for 50% and 70% as well? *cough


Anybody wondering: You guessed right, this is of course to estimate how profitable Arena-farming really is. 

[artimies7]

Is my Compendium a real compendium, or is it just a big list?

[dragonsdemesne]

@dragonsdemesne

Thanks dude! Can you run it for 50% and 70% as well? *cough

Very easy; I only have to change one number in the program to change the win percentage.  Similarly, to do it for 6,5, or 3 streaks for the other arena leagues, I only need to change 1 number. 

I also thought of a way to remove the slight error due to the problem I mentioned in my last post.  Instead of using one streak of 1000000 games as I did before, I use 25000 streaks of 40 games.  This may seem like a subtle difference, since it's still 1 million games, but it (finally!) answers the exact question asked. 

As I mentioned, because of this, it removes a few of the streaks and thus lowers the old numbers i had for 80% and 60% slightly, the reason being that what my old method's mathematics actually calculated was the case where if you finished the 40 games, and you had some rings lit, you would play a few more games to finish that streak until you either got a rare spin or lost a game.  (which is probably what you'd do in real life, but whatever :p )

If you play 40 games, and your win rate per game is 90%, then on average you will have about 7.32 streaks of 4.
If you play 40 games, and your win rate per game is 80%, then on average you will have about 5.30 streaks of 4.
If you play 40 games, and your win rate per game is 70%, then on average you will have about 3.60 streaks of 4.
If you play 40 games, and your win rate per game is 60%, then on average you will have about 2.26 streaks of 4.
If you play 40 games, and your win rate per game is 50%, then on average you will have about 1.26 streaks of 4.
If you play 40 games, and your win rate per game is 40%, then on average you will have about 0.59 streaks of 4.
If you play 40 games, and your win rate per game is 30%, then on average you will have about 0.21 streaks of 4.
If you play 40 games, and your win rate per game is 20%, then on average you will have about 0.05 streaks of 4.
If you play 40 games, and your win rate per game is 10%, then on average you will have about 0.003 streaks of 4.
If your win rate is less than 10%, you need to find a new deck!

I ran these a couple times each, and the numbers again vary by about 0.01 or so, but they give a good enough idea.  Increasing N in the code below will get a more precise number, at the expense of having the program take longer to run.

MATLAB code for the uber geeks:
N=25000;
B=zeros(1,N);
streak = 0;
rarewin = 0;
rarewinsum = 0;
for I = 1:N
    for I=1:40
        B(I) = rand;
        if rand < 0.8
            streak = streak + 1;
            if streak == 4
                streak = 0;
                rarewin = rarewin + 1;
            end
        else
            streak = 0;
        end
    end
        streak=0;
        rarewinsum = rarewinsum + rarewin;
        rarewin=0;
end
rarewinsum/N

-Increase N to increase the simulation accuracy.  (and require more CPU time to run; right now it takes my dinosaur computer about a second)
-On the line " if streak == 4" the 4 represents how long the streak needed is.  So for bronze, you'd make this a 6, for silver a 5, for plat a 3.
-On the line " if rand < 0.8" the 0.8 in this case represents a deck with a win rate of 0.8, or 80%.  Change this to match the win % you are looking for.
-On the line "for I=1:40" the 40 represents the 40 games.  Change this to change the number of games played in one sitting.

This is a really interesting question, but unfortunately my math isn't strong enough!
I hope someone could give us the formula and explain it!

Sadly, I only ever took one statistics class in university, so my programming skills are stronger than my statistics skills, and I don't know how to come up with an exact formula.  I could probably dig around in my books and figure it out, but it would require devoting several hours to the problem, whereas the program above took me maybe 15 minutes max to think up, write, run, and post about.

[DarknessDemon]

Did the original black hole only drain 2 from each element?

[FlarePod]

Ive got a quick little question about the spins
I am currently farming AI3, slowly but steadily making my way to a false god deck.
Ive noticed the spins has a certain nature to make me win some cards more then others
It may be pure coincidence, or maybe there is something about it.. A rare scale perhaps?
For instance- If i had kept all my Blessings, i would have had over 30 of them.
Then again, from the same AI3, i would get about 5 pegasuses or Wyrms. Is there more then just 2 rarity scales? Because i thought there basicly was the common cards you could buy from the Bazar, and there rare cards you could only get from oracles or spins (Or Redeem codes i guess).

Same with weapons. I tend to get A TON of pharaos. And i really mean it. ive gotten about 20 of them, and its not even exadurating. Though on the other side, out of probably all the 200 matches ive had with the aether AI3, ive never got a single lobotomizer.  (Ofcourse, this is the weapon i need.. Oh the gruesome fate)

Really aprreciate any answers.