What Kind of Chance?

[lemur]

A Staff Member told me today that InnoGames does not claim that the percentages it lists for various game prizes represent the probability of a random outcome. He doubts that InnoGames has "ever actually used that particular word" (random) in reference to its events.

The announcement for the 2016 Soccer Cup used the word "chance" many times. The icon used for the "Double Chance" option contains the image of a six-sided die — thereby at least implying a random process. If the chance of winning a prize from any particular attempt is not a random event, then what kind of a "chance" is it?

Is it a chance that is predetermined for the player, regardless of the number of attempts, based on his position in a queue? Is it a chance that is determined by how many attempts have been made since the last prize was awarded? Is it a chance that depends on whether diamonds were used to acquire the chance? What other factors influence this "chance"?


Edit: typo corrected

 

[DeletedUser8152]

Only a person with access to the game code could answer this kind of question. The point I was making is essentially that any "random number generator" on a computer is in fact deterministic. It's just a question of how complicated the algorithm is. So it can't be truly random in an absolute sense.

I would assume though that the outcomes are essentially unpredictable from the point of view of a player, and every time I've checked carefully, the frequencies of occurrence are in reasonable agreement with what they claim. I don't see that anything more than that is needed for the game to work as expected.

 

[DeletedUser9433]

Only a person with access to the game code could answer this kind of question. The point I was making is essentially that any "random number generator" on a computer is in fact deterministic. It's just a question of how complicated the algorithm is. So it can't be truly random in an absolute sense.

I would assume though that the outcomes are essentially unpredictable from the point of view of a player, and every time I've checked carefully, the frequencies of occurrence are in reasonable agreement with what they claim. I don't see that anything more than that is needed for the game to work as expected.

Actually using mouse moves coupled with their pseudo-random number generator will generate a truly random number, since they claim to be able to detect bots they must monitor mouse moves already so Voila, a random number!

 

[lemur]

Only a person with access to the game code could answer this kind of question.

Then let's get that kind of person to answer.

The point I was making is essentially that any "random number generator" on a computer is in fact deterministic.

Why would that be necessarily true? Consider the roulette wheel — a classic gaming device that generates a random number. It cannot be deterministic because there are too many physical factors involved for the operator to determine the outcome. For a computer to generate random numbers, we need a binary roulette wheel or an electronic coin flip. Once a 0 or 1 is generated randomly, any set of random numbers can be created.

For the benefit of anyone reading here, I found this concise introduction to Hardware Random Number Generators.

[T]he frequencies of occurrence are in reasonable agreement with what they claim.

Composite frequency is not the issue. The question ("What kind of chance?") is whether each trial is a fair one. What I have observed many times is Player 1 failing to win a prize despite dozens of attempts, followed immediately by Player 2 winning the prize with one attempt. At various times, I have been in either role. Such a process may adhere to the posted frequency, but each particular attempt to win the prize does not appear to have an equal probability of success.

 

[DeletedUser20367]

The old Atari computers used to have an actual random number generator based on (I think) the fluctuations in the electrical current.

 

[DeletedUser25273]

The roulette wheel is not a (very) random process, but is theoretically (and actually somewhat practically) to a large degree predictable. Years ago someone I knew developed a system that would, with a few simple speed/timing measurements, predict with about a 50% accuracy which quadrant of the wheel the ball would land. At least then, the croupier would spin the wheel as throw the ball, and people had a few last seconds to place their bets (as long as the ball was on the top track). A couple of measurements of the wheel and the ball passing a fixed point on the table and he could predict where the ball was going to land (after calibrating to the table) with fairly good accuracy.

He asked me if I could help miniaturize it enough that it could be made small enough to be concealable at a casino. I declined, as I know what sort of people that could get me involved with, not my cup of tea. but does show that 'true randomness' is harder to find then it might seem. Even systems which use things like radio-active decay need some post processing to 'whiten' the noise.

 

[lemur]

For the past week I have been playing this game on several worlds. It often seems to me that the "chance" to win a prize is not determined by attempts that each have a random probability. There seems to be some other method involved.

Sometimes it seems that the "chance" to win a prize is a probability per player that mostly ignores the number of attempts. Once you have been designated a "loser" by the program, it doesn't matter how many shots you take — perhaps until the prize gets sufficiently large. Players operating under the assumption that each attempt were a random probability would be very tempted to purchase more shots with diamonds.

That would explain the profusion of ridiculously high scores:

Example 1

On Langendorn the high score this week is 2350 in my neighborhood. I was one of the players involved in that fiasco. I took 30 shots (supposedly at 5% odds apiece) and used the "double chance" option with 5 of them. My particular failure is nothing spectacular — because if each attempt were random, then the probability would be 16 percent.

But what was the total probability of reaching 2350 if each attempt were a random trial? Well, a grand total of 150 shots were taken. As the jackpot climbed well over 1000, let's conservatively assume that 15 other attempts also used the "double chance" option — even though it could have been more.

In that case, here is the probability of 150 missed shots:

0.95^130 * 0.9^20 = 0.000154​

... or 1 chance in 6500 for that amount of neighborhood futility.

Example 2

On Sinerania this week, the jackpot for the goal with a "10 percent chance" reached 640. Let's conservatively assume that 10 attempts used the "double chance" option. Here is the probability of 57 missed shots:

0.9^47 * 0.8^10 = 0.000759​

... or 1 chance in 1320.

Example 3

On Mount Killmore this week, the jackpot for the goal with a "20 percent chance" reached 195. Here is the probability of 31 missed shots:

0.8^31 = 0.00099​

... or 1 chance in 1009.

————————————————————

So the question remains. When InnoGames tells us that we have a "chance" to win a prize, exactly what kind of a chance is that?

 

[DeletedUser8152]

Sometimes it seems that the "chance" to win a prize is a probability per player that mostly ignores the number of attempts. Once you have been designated a "loser" by the program, it doesn't matter how many shots you take — perhaps until the prize gets sufficiently large. Players operating under the assumption that each attempt were a random probability would be very tempted to purchase more shots with diamonds.

I doubt that is true, because I have won some pretty big jackpots after having taken many shots on them first.

But what could be the case is that the average chance to win the jackpot is 5%, but that any particular jackpot might have a higher or lower probability. So maybe some of the "5%" jackpots have only a 1% chance to win, while others have a 10% chance. That doesn't belie the claim that there is a 5% chance per shot, it would just mean that you get that when you average over many jackpots.

That would explain why the prizes go so high as often as they do; I agree that it is otherwise hard to understand. But then, I don't really know how many times per week the jackpot is won, to say how large a max jackpot ought to be.

But even if this is true (which of course I don't know), I'm not sure it would change my strategy.

 

[lemur]

But what could be the case is that ... any particular jackpot might have a higher or lower probability....
That would explain why the prizes go so high as often as they do.

Yes, I agree. Interesting ...

 

[DeletedUser9433]

Thanks for the math Lemur, I was curious as to how unusual those large jackpots should be.

 

[DeletedUser25273]

I some times wonder if the 5% might mean that it is winnable 5% of the time, like 1 minute every 20 or something like that at times, or some other unusual pattern. That would also say it would be best to spread out your shots.

 

[DeletedUser8152]

OK, I bet this is how they do it. When a new prize starts (right after someone wins), I bet the server determines right then how many shots it will take to win the prize. Ie, it uses a random number to determine that the 10th shot will win that prize. That way it doesn't have to calculate random numbers every time someone takes a shot, and it doesn't risk the problem where two shots come in at almost the same time and the first shot wins before the second shot has resolved, or perhaps even the second shot resolves before the first.

A small piece of evidence for that is in the old Easter events, where the number of eggs you got from a collection was random, but if the game glitched and reloaded so you had to collect again, you always got the same reward as you got the first time.

If this is true, then they can use whatever distribution they like for the probability of which shot will collect. It doesn't have to be Poissonian like we might assume, maybe they want to have a longer tail so that big jackpots are more likely. The only thing they need to do to be honest is to make the average number of shots needed work out right. So it might be more likely to win right away, but also more likely to go a long time.

And I bet then that the 2x button just makes your next shot count as two attempts at once.

 

[DeletedUser13838]

OK, I bet this is how they do it. When a new prize starts (right after someone wins), I bet the server determines right then how many shots it will take to win the prize. Ie, it uses a random number to determine that the 10th shot will win that prize. That way it doesn't have to calculate random numbers every time someone takes a shot, and it doesn't risk the problem where two shots come in at almost the same time and the first shot wins before the second shot has resolved, or perhaps even the second shot resolves before the first.

A small piece of evidence for that is in the old Easter events, where the number of eggs you got from a collection was random, but if the game glitched and reloaded so you had to collect again, you always got the same reward as you got the first time.

If this is true, then they can use whatever distribution they like for the probability of which shot will collect. It doesn't have to be Poissonian like we might assume, maybe they want to have a longer tail so that big jackpots are more likely. The only thing they need to do to be honest is to make the average number of shots needed work out right. So it might be more likely to win right away, but also more likely to go a long time.

And I bet then that the 2x button just makes your next shot count as two attempts at once.

I had an issue I contacted support about in which I won a prize with a large jackpot but got the minimum. Per support, the logs showed someone winning with the exact same time stamp as me but since they came before I did they got the larger prize.

Your explanation could be right but ultimately it doesn't matter when the random numbers are drawn. Pretty much all the analysis done in these threads makes the assumption that each trial is independent. I made the case in the easter event that this assumption is probably false and I don't believe it's true in this event either. I still play the odds based on expected value.

 

[DeletedUser8152]

Yes, it's an interesting question of whether you should change your strategy if, for instance, you knew this was true.

 

[DeletedUser26154]

someone winning with the exact same time stamp as me but since they came before I did they got the larger prize.

It's why I start my name with the letter A. We're also first seen in the phone book.

 

[DeletedUser13838]

Support said that despite the same timestamp, the other person must have won before me by milliseconds (ie it's not alphabetical)

 

[lemur]

So it might be more likely to win right away, but also more likely to go a long time.

That still does not explain the remarkable number of times that a player new to the bidding wins the prize with only one shot.

Repeating what I wrote above ... I have observed many times that Player 1, failing to win a prize despite dozens of attempts, is followed immediately by Player 2 winning the prize with one attempt.

The more I play this contest, the more it seems that the deck is stacked, so to speak. The speculation about what is "behind the curtain" is interesting, but I still don't have a definitive answer to my question. An answer from one of the "wizards" would seem most appropriate.

InnoGames is being far too casual in its use of the term "chance" here. If the "double chance" is actually two chances with the same odds — rather than the common perception of doubling the probability of a single chance (since only a single shot is taken) — then I would say that players are being deceived, even if the deception were not intentional.

 

[DeletedUser9433]

I'm not sure how you know either how many times a new player wins the cups or that they are new to the race and win with a single shot, you can only have anecdotal evidence and online that isn't very reliable.

 

[Algona]

This post is strictly in regards to If this quote were true. /me equips tinfoil hat.

And I bet then that the 2x button just makes your next shot count as two attempts at once.

Why aren't players occasionally winning 2 pots with the one Double Chance shot?

Why isn't the pot increased from the extra missed shot?

Cruddy programming or design? Would INNO intentionally screw players this way?

Did my Sarcasm Detectoromatic give a false reading?

 

[DeletedUser8152]

That still does not explain the remarkable number of times that a player new to the bidding wins the prize with only one shot.

Repeating what I wrote above ... I have observed many times that Player 1, failing to win a prize despite dozens of attempts, is followed immediately by Player 2 winning the prize with one attempt.

Like Jenny, I don't see how you can determine when this happens. I can't say I've seen any evidence of it.

InnoGames is being far too casual in its use of the term "chance" here. If the "double chance" is actually two chances with the same odds — rather than the common perception of doubling the probability of a single chance (since only a single shot is taken) — then I would say that players are being deceived, even if the deception were not intentional.

First remember this is just speculation. But second, if this is how it works then there is nothing deceptive or unfair about it. If you hit the double chance button then your chance of winning would be twice as large, on average.

An answer from one of the "wizards" would seem most appropriate.

What wizards? If you are hoping for a game developer to come on and tell you how it works, I'm afraid that won't happen, the developers are not involved with the forums.