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RadLonghammer
04-27-2013, 08:01 AM
I'm writing this because there's been a great deal of discussion regarding probabilities and odds in the forum lately. Because I have a suspicion that some people who read these boards are younger folks, and folks that might one day wander into a casino, I want to make sure that they're exposed to accurate info with regard to statistics.

The first thing to understand is that for the chance of something happening to be gleaned from observed instances, the sample size has to be HUGE. Not in the tens, hundreds, or even thousands.

Think of a coin flip. We all know that the chance of landing heads is 50% If we flipped a coin 1000 times, however, it's quite easy to get a result on the order of something like 550 heads and 450 tails.

Clearly, this hypothetical (but completely reasonable result does NOT mean that the coin has a 55% probability of turning up heads. We know better.

In fact, it would take hundreds of thousands, even millions of trials to overcome random chance, and get results that mirror the true probability of the event.

Secondly, understand that all random events are independent events. The result of the first trial in no way affects the result of the second trial. If your coin comes up tails seven times in a row, the next flip is still 50% likely to be heads. You are not "due" any result. The coin will do what the coin will do.

Finally, the idea that something is guaranteed to happen because you've tried it a certain number of times is completely inaccurate.

Suppose you were rolling a 10 sided die, and needed the number 7 in order to win. All other numbers lose. You know the probability of rolling a 7 is exactly 1 in 10, or 10%. It is completely wrong, however, to assume that if you get to roll the die 10 times, you will roll at least one seven. The odds of NOT rolling a 7 in 10 tries are actually much higher than you might believe.

To find the chances of NOT rolling a 7 in 10 successive tries, we must first find the chance of failure on a single try. The chance of failure is 1 minus the chance of success. In this case, 1 - .10 = .90 So, we have a 90% chance of failure on a single try. When we have 10 tries, we simply multiply the failure rate by itself 10 times.

In this case .90 x .90 x .90 x .90 x .90 x .90 x .90 x .90 x .90 x .90 = .3487 or 34.87%

That means that our 10 tries don't guarantee us a success at all. In fact we'll fail to hit that win 34.87% of the time when making 10 roll attempts!

So please, don't let anybody, no matter how well intentioned, convince you that trying something a certain number of times will guarantee success. That's just not how the math works.

Harvey Guo
04-27-2013, 08:18 AM
I would say all we talking about is inaccurate, because the number of chests open is limited. But this does not influence us to gain a range of result.
As you like to use coins like example, 10, 100, 1,000, would be different, that's true
But reality is not a precisely math class, there are many variables, once GREE downgrade or upgrade, every thing change completely. You cannot assume that we all together to open thousand or even ten thousand chest to prove the more accurate probability, that is not what math work to reflect the reality.
What math help us here is to gain a range probability which close to the real probability, so that people will get an knowledge to understand how much money they will need to spend, help them to judge worth or not, prevent them loosing blood and disappointing.
Like 10, 100, 1,000 again, when we open 10, maybe the probability can be far inaccurate, but when we open 100 chests, the result is pretty enough to tell us something, we no need to spend money to try 1,000 or more.
Again, ex. 1000 chest would be a certain gain, just describe how hard to gain one, we both know he can gain before this number, or later this number.
So over chasing the precisely number probability would not the wise choice for helping people to understand the meaning or judge worthwhile about opening chest.

DreamM0d3
04-27-2013, 09:14 AM
Actually I kinda agree with Radlonghammer as far as the way chests work. You could treat getting a specific armor or not as a Bernoulli Trial where each instance is independent of one another. I believe many people have the wrong concept of how the chests work. People are under the impression that if you buy like say 500 chests, at least one of the chests should be or will be a legendary armor. However, this is not a case where its a bag of many black balls and you repeatedly draw balls without replacement and eventually hope to draw a white ball. If one wants to use his ball model to explain further, in reality its still drawing balls just that every time you draw a ball, be it black or white, you put it back into the bag and try your luck again. That is why it seems that the chances to get a legendary is so abysmal.

Once again, this goes out mostly to the younger players who do not understand probability. As for older players , I believe they should be able to decide if the opportunity cost is worth it before they give in to the temptation of spamming chests.

Harvey Guo
04-27-2013, 10:00 AM
Probability is a number, depends how you treat it.
Both of us know we should not spend gems on trying to gain that so-called legendary, after 3 big gem spenders, we can see nearly 10,000 gems can only gain one. That's pretty enough to reflect how low the probability is, people should not gamble on this. There is no need to 10 or 100 times more experiment to test more accurate number of probability, result is pretty enough for reflecting how risky to spend such gems on that.
For the nemesis, same thing, after nearly thousand chests opened by many people, we can find the probability would be between 1/11 to 1/12 maybe the real probability is 1/11.5 or 1/11.3 but what does the meaning of accurate? We should already have a concept of how hard it is, we knew GREE downgrade the probability, that's enough for people to understand. open 11 or 12 chest, maybe will gain one, some people may open 6 to gain, some people may open 18 to gain, the average number is between 11 to 12, that's it.
zhy said former people normally will gain the armor about spending 400 gems, that is nothing wrong. It is just a range of people average spending gems to gain that, no one said it is a sure thing, some of them spend 100, another may spend 700, average same thing.
For teaching young people, I would rather directly tell them like zhy way, not a math probability class. Make the thing easier not complex.
Just tell them this item may need you spend 1,000 gems to gain, but no guarantee, just like fusion depends on luck, right combination may gain different result, just the result now become the real money.
Everything has its risk, let them know first, then let them make their own choice. Pain is always a good teacher for growing up.

Actually I kinda agree with Radlonghammer as far as the way chests work. You could treat getting a specific armor or not as a Bernoulli Trial where each instance is independent of one another. I believe many people have the wrong concept of how the chests work. People are under the impression that if you buy like say 500 chests, at least one of the chests should be or will be a legendary armor. However, this is not a case where its a bag of many black balls and you repeatedly draw balls without replacement and eventually hope to draw a white ball. If one wants to use his ball model to explain further, in reality its still drawing balls just that every time you draw a ball, be it black or white, you put it back into the bag and try your luck again. That is why it seems that the chances to get a legendary is so abysmal.

Once again, this goes out mostly to the younger players who do not understand probability. As for older players , I believe they should be able to decide if the opportunity cost is worth it before they give in to the temptation of spamming chests.

DreamM0d3
04-27-2013, 10:23 AM
Probability is a number, depends how you treat it.
Both of us know we should not spend gems on trying to gain that so-called legendary, after 3 big gem spenders, we can see nearly 10,000 gems can only gain one. That's pretty enough to reflect how low the probability is, people should not gamble on this. There is no need to 10 or 100 times more experiment to test more accurate number of probability, result is pretty enough for reflecting how risky to spend such gems on that.
For the nemesis, same thing, after nearly thousand chests opened by many people, we can find the probability would be between 1/11 to 1/12 maybe the real probability is 1/11.5 or 1/11.3 but what does the meaning of accurate? We should already have a concept of how hard it is, we knew GREE downgrade the probability, that's enough for people to understand. open 11 or 12 chest, maybe will gain one, some people may open 6 to gain, some people may open 18 to gain, the average number is between 11 to 12, that's it.
zhy said former people normally will gain the armor about spending 400 gems, that is nothing wrong. It is just a range of people average spending gems to gain that, no one said it is a sure thing, some of them spend 100, another may spend 700, average same thing.
For teaching young people, I would rather directly tell them like zhy way, not a math probability class. Make the thing easier not complex.
Just tell them this item may need you spend 1,000 gems to gain, but no guarantee, just like fusion depends on luck, right combination may gain different result, just the result now become the real money.
Everything has its risk, let them know first, then let them make their own choice. Pain is always a good teacher for growing up.

That said, I still think a lot can be done to avoid this so called growing pains because you can always learn from the experiences of others. I suppose that the main point is that players have to understand opportunity cost. Is spending that many gems justifiable when you could have used the money on other things like new clothes or gadgets. Of course I understand that everyone has a different value system. It really boils down to one's satisfaction level of the status quo. If you just look at many experienced players like zhy, me, you or others. We do not possess these so called legendary or DPC ultra rare+ armors but we still do so well and we frankly do not miss out much. We are still capable of dominating the leaderboards if we really wanted to. Is it necessary to spend so much money on one armor that is perhaps only about 100 points stronger than the rest when you could have used that amount of gems to upgrade your base and farm for all the other level 70 craftable armors in the game (which are still very strong IMO). Besides, based on the trend that boss armors are coming out, I see the gap slowly narrowing.

RadLonghammer
04-27-2013, 10:30 AM
Actually I kinda agree with Radlonghammer as far as the way chests work. You could treat getting a specific armor or not as a Bernoulli Trial where each instance is independent of one another. I believe many people have the wrong concept of how the chests work. People are under the impression that if you buy like say 500 chests, at least one of the chests should be or will be a legendary armor. However, this is not a case where its a bag of many black balls and you repeatedly draw balls without replacement and eventually hope to draw a white ball. If one wants to use his ball model to explain further, in reality its still drawing balls just that every time you draw a ball, be it black or white, you put it back into the bag and try your luck again. That is why it seems that the chances to get a legendary is so abysmal.

Once again, this goes out mostly to the younger players who do not understand probability. As for older players , I believe they should be able to decide if the opportunity cost is worth it before they give in to the temptation of spamming chests.

Thanks for picking up what I'm putting down, man!

I like to use the "deck of cards" example. If you're drawing from a 52 card deck in hopes of pulling the Ace of Spades, and each successive try diminishes the deck by one card, further attempts increase your odds from 1/52, to 1/51, to 1/50 and so forth. Even if the Ace of Spades is the very last card in the deck, you DO reach a point where you're guaranteed to draw it.

If, on the other hand, the deck is reshuffled after each attempt, which is properly analogous to the Chance Chests, you NEVER reach a point of absolute guarantee, you simply approach it. Successive tries represent an exponential decrease in the probability of failure, but if viewed graphically, the failure rate NEVER touches the X-axis that would represent a zero failure rate. Exponential shrinkage works, after all, in precisely the opposite manner of exponential growth.

Harvey Guo
04-27-2013, 10:38 AM
Actually, the fact of people can learn from others are vary, especially for young people or someone who always make same mistake.

For example, we can learn how girls use man to reach their goals from our friends, we do not need to really find a that type girl friend to really taste that pain. But for some people, they may never learn the lesson, because they are lack of observation...Even they failed again again again, they never learn from the mistake...They probably just feel they are unlucky...

And for the same target, same thing, different people would treat differently. Some people believe they have a magic power to manipulate the probability, image they can win the gamble or lottery etc. so they spent huge amount money on and failed...No matter how we persuade him, he just never listen from others or never learn from other people's failure experiences...Because he will think he is unique and different than other, he can make it. Otherwise, why after 4,200 gems spent and failed, still many people spent larger amount money to try their luck instead of learning from former.

People are not completely rational, for a same probability, different people may make different choice. For risk adverser, 30% failure can be too high, for risk taker, their tolerance may up to 60%, so people's choice are vary....If every one like us do not or buy less gem, probably GREE will fall soon.

People are who they are. So most of time, I would just provide suggestion, but not interfere people's choice. Although we know a better way, but who knows other people may want play in another way.


That said, I still think a lot can be done to avoid this so called growing pains because you can always learn from the experiences of others. I suppose that the main point is that players have to understand opportunity cost. Is spending that many gems justifiable when you could have used the money on other things like new clothes or gadgets. Of course I understand that everyone has a different value system. It really boils down satisfaction level. If you just look at many experienced players like zhy, me, you or others. We do not possess the these so called legendary or DPC ultra rare+ armors but we still do so well and we frankly do not miss out much. We are still capable of dominating the leaderboards if we really wanted to. Is it necessary to spend so much money on one armor that is perhaps only about 100 points stronger than the rest when you could have used that armor of gems to upgrade your base and farm for all the other level 70 craftable armors in the game (which are still very strong IMO). Besides, based on the trend that boss armors are coming out, I see the gap slowly narrowing.

DreamM0d3
04-27-2013, 10:53 AM
Actually, the fact of people can learn from others are vary, especially for young people or someone who always make same mistake.

For example, we can learn how girls use man to reach their goals from our friends, we do not need to really find a that type girl friend to really taste that pain. But for some people, they may never learn the lesson, because they are lack of observation...Even they failed again again again, they never learn from the mistake...They probably just feel they are unlucky...

And for the same target, same thing, different people would treat differently. Some people believe they have a magic power to manipulate the probability, image they can win the gamble or lottery etc. so they spent huge amount money on and failed...No matter how we persuade him, he just never listen from others or never learn from other people's failure experiences...Because he will think he is unique and different than other, he can make it. Otherwise, why after 4,200 gems spent and failed, still many people spent larger amount money to try their luck instead of learning from former.

People are not completely rational, for a same probability, different people may make different choice. For risk adverser, 30% failure can be too high, for risk taker, their tolerance may up to 60%, so people's choice are vary....If every one like us do not or buy less gem, probably GREE will fall soon.

Yes its like I said in my previous post about everyone having different value systems and perspective. We can have many discussions here but ultimately the players still make their own choices. Nevertheless, a smart player will make use of the forums to observe the trends from all the other players before taking the plunge. And I believe we have already shared enough for them to make their informed choice. Im also not saying that one should stop spending gems on chests because Im perfectly fine opening chests. Its just that one's gotta know the odds before expecting too much.

Harvey Guo
04-27-2013, 11:04 AM
That's true.
I believe that many people like me has a habit of trying to maximum performance in gaming without spending a penny, that's kind of achievement.

Let's change they subject. Have you maxed out your Regalia+? It is superb in arena, you can kill many people with 1 shot or maximum 2 shots. I would have further test about this armor to against Starmetal+ etc.
Yes its like I said in my previous post about everyone having different value systems and perspective. We can have many discussions here but ultimately the players still make their own choices. Nevertheless, a smart player will make use of the forums to observe the trends from all the other players before taking the plunge. And I believe we have already shared enough for them to make their informed choice. Im also not saying that one should stop spending gems on chests because Im perfectly fine opening chests. Its just that one's gotta know the odds before expecting too much.

DreamM0d3
04-27-2013, 11:12 AM
That's true.
I believe that many people like me has a habit of trying to maximum performance in gaming without spending a penny, that's kind of achievement.

Let's change they subject. Have you maxed out your Regalia+? It is superb in arena, you can kill many people with 1 shot or maximum 2 shots. I would have further test about this armor to against Starmetal+ etc.

Hmm my regalia is still level 1 although its already the + version. Im not a big fan of offensive armors but I really like the uniform look of regalia. Moreover I have recently maxed out my Infernal Lord. I was actually hoping that they came out with a new water/spirit or fire/air armor but oh well.

Harvey Guo
04-27-2013, 11:22 AM
Hmm my regalia is still level 1 although its already the + version. Im not a big fan of offensive armors but I really like the uniform look of regalia. Moreover I have recently maxed out my Infernal Lord. I was actually hoping that they came out with a new water/spirit or fire/air armor but oh well. Water/Spirit should be the next week boss armor. Water/Fire is also needed (poor steampower+...so cool looking).
Recently I keep fusing 1 star uncraftable armor to gain 50EP, cost too much golds...I now even using lv70 armors as the final material to upgrade my armor from lv67 to lv70 directly:)
Because there is nothing good armor can be gained though fusion (even sky guardian).