**KNOWN AW ISSUE**
Please be aware, there is a known issue with Saga badging when observing the AW map.
The team have found the source of the issue and will be updating with our next build.
We apologize for the inconvenience.
Please be aware, there is a known issue with Saga badging when observing the AW map.
The team have found the source of the issue and will be updating with our next build.
We apologize for the inconvenience.
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This is an extrapolation of the fundamental counting principle, which is the foundation of statistics and probability. I'm not going to do it for 250, but I'll illustrate the principle with (six sided) dice. The odds of rolling the same number twice in a row is one in six, not one in 36. Calculation would say the odds of rolling one specific number twice in a row is one in 36, and there are six different numbers, so the odds of rolling the same number twice is 1/36 x 6 = 1/6.
But if you don't trust the calculations, you can just list all possible ways to roll a dice twice, and just visually count the number of times you get two of the same number in a row. Here we go:
1 1 < --- dup
1 2
1 3
1 4
1 5
1 6
2 1
2 2 < --- dup
2 3
2 4
2 5
2 6
3 1
3 2
3 3 < --- dup
3 4
3 5
3 6
4 1
4 2
4 3
4 4 < --- dup
4 5
4 6
5 1
5 2
5 3
5 4
5 5 < --- dup
5 6
6 1
6 2
6 3
6 4
6 5
6 6 < --- dup
There are thirty six different ways to roll dice twice. There are six ways to roll a duplicate. Thus the odds of doing this are six in thirty six, or one in six. That's the definition of probability.
Because each crystal opening is rolled independently, the odds of a champion being a particular champ after rolling that champ are identical to the odds of rolling that champion initially. Someone might argue that the rolls aren't independent because they are generated by random number generator, but that argument fails due to the nature of modern pRNGs. Modern pRNGs are tested to determine if they pass so-called randomness tests across huge numbers of iterations. One of those tests is the correlation test. This is a test to determine if, basically, the RNG is biased to generate the same results repeatedly *or* are anti-biased to generate a different result more often than random chance would dictate duplicate results. Modern pRNGs generally pass these tests (at least within the scope of how they are used in a game like this) and thus the fact that the game uses software pRNGs essentially guarantees that sequential crystal openings will behave as if they were statistically independent to a statistically high degree (certainly far higher than a player could detect a variance from).
It is also worth noting that given the number of crystals that players open in this game, the odds of a player opening two crystals in a row and actually *seeing* two consecutive openings is low. There's a pretty good chance that in between those two openings were other crystals being opened. The sixth anniversary video stated that over 29 billion crystals were opened by players over the history of the game. That is an average of 150 crystals per second. No player is likely to ever *see* two "consecutive" crystal openings. They are consecutive to them, but they are just two out of the hundreds or thousands of crystals opened at that time, and probably not actually rolled "consecutively."
What were the odds of this happening? About one in 7700.
https://forums.playcontestofchampions.com/en/discussion/comment/1493277/#Comment_1493277
In a game with millions of players (over time) this sort of things almost certainly happens all the time. It would be rare to happen to one individual player, but the odds of it happening to someone and then having them post about it is practically a certainty.
Oh man, I really gotta get the Kabam developers to implement that one in the game. The enormous advantage the people who accept the math would have over the players willing to die on the hill of incorrect intuition would be awesome.
In fact, something like the exact opposite is true. Genuinely random sequences contain more consecutive numbers than people intuitively believe should be there. This is so strong of a psychological error that they've done experiments where people are asked to attempt to generate random sequences of numbers and they are trivial to pick out of a set of otherwise randomly generated sequences specifically because they lack repeats at the proper statistical rate.
So it isn't that pRNGs generate repeats more often than they should, it is that people think pRNGs should generate fewer repeats than statistics otherwise dictates they must.
If you've got two crystals and, before you open them, you decide that you want Corvus in the first and Doom in the second, then your odds are (1/250)*(1/250). This is true of any two specific rolls. If you want Night Thrasher followed by Darkhawk, it's (1/250)*(1/250). If you're a masochist and you want Groot followed by OG Iron man, it's (1/250)*(1/250). And if you want Corvus followed by Corvus, it's (1/250)*(1/250).
But that's not exactly what you've described. If you've already opened your Corvus, then the odds that you get Corvus followed by Doom is just 1/250. The odds that you get Corvus followed by any particular champ is 1/250. You've already got Corvus, so the odds that Corvus precedes whomever is your second pull is 100%. It's a fact that you already got him. So the odds that you get that specific champ you want second, after securing your first pick in your first crystal, is 1/250.
behind two doors and a Ghost behind the third?
Game shows you three hidden options. You get to pick one. Before the game shows you what you picked, it opens one option that definitely contain a 3* champ. Then it gives you the option to keep your choice or switch.
Those who switch will have an enormous edge over those who stick. But the people who do stick will be so convinced they are correct to stick many will do so no matter how horrible their results are, then they will descend into crystal manipulation madness convinced the game is cheating them. Meanwhile the people who understand the actual probabilities will be getting 6* champs twice as often as those who stick.
You balance the cost of the crystal as costing about 50% of the relative cost of a 6* crystal. Those who switch come out ahead. Those who don't come out behind. Good math wins. Bad math loses.
This punishes conspiracy theorists with cold hard math. All they would have to do is let go of their conspiracy theories and they would start to win. But most won't.
Or, if we want this probability to converge faster, we could increase the crystals to five choices, or even ten choices.
You have a 1/250 chance of pulling a specific champ. So if you are trying to pull two of a specific champ it would be (1/250)^2.
However, you have 1/1 chance of pulling any champ, and then a 1/250 chance of pulling that same champ again, which makes it a 1/250 chance of pulling two of any champ.
TLDR;
(1/250)^2 chance to pull 2 of a specific champ.
(1/250) chance to pull 2 of any champ.
If the OP is still unconvinced when they get back on the thread, maybe we should direct them to one of the many threads complaining about how hard it is to Dupe champions because there are too many in the crystals...?
To demonstrate this, imagine there were 100 doors, 1 with the prize and 99 with nothing. You randomly pick one, the host then opens 98 doors showing you nothing. He then asks you whether you want to swap.
The chances of you randomly picking the one door with the prize out of 100 is so low, that the host revealing 98 doors without a prize means that the final door he didn’t reveal likely has the prize in it.
The odds were locked in at 1% chance when you selected the first door. So the odds now that the other door contains the prize is 99%. Even though there are two options, it’s not 50/50.
Not only have I pulled the same champ back to back several times... I've pulled a champ 3 times in a row on 2 separate occasions.
Did it suck pulling Cyclops 3 times? Yes.
Was it awesome to pull Corvus back to back to back? Absolutely!!!
That's just how RNG works.
Odds of getting same champ once in a row... well... let's see: 100%. Impossible not to.
Odds of getting same champ twice in a row: 1:200 or .5%
Odds of getting same champ three times in a row: 1:40000 or %.0025
Now obviously the math is a bit more complicated with say a featured cav, as you need to account for the odds of getting a certain starrage, and whether you are talking about the featured champ or some other random champ in the crystal... but the same approach to calculating the odds will apply.
So... take a look at that 0.5%: how many people here have some rarity immortal iron fist, or some other trophy champ that comes in and such rarities... or got the 6 star featured from the featured cav a couple times at some point... those have similar odds, and through sheer number of crystals opened... you got it.
This statistically is no different.