I was actually going to point that out... Last 30 days if I'm not mistaken...

You are actually arguing something he didn't say, and making a different point then darth at the same time (who just used wrong math to analyze probability).

There is a difference been the odds of a single event, and the odds of a chain of events. KJReed analyzed the chain of events and the probability of it occurring, and correctly stated it bares no influence on the individual events there in. Nor does it impact the odds of his next invasion attempt. However at the exact same time, the odds of the chain of events leading to one more failure in a row would be incredibly small. Has nothing to do with influencing the chance of it occurring whatsoever. Well, other then the law of large numbers, but do we really need to go there?

First, don't go taking my "Kum Ba Yah" moment from me and Darth. I like to think we agreed on this one. bahahaha

Second, you (and KReed and TB) are correct in the scope of your math. But as you mention in the last line, and this is the key part Darth presented too, we would have to talk about numbers on a huge scale to really show a difference in the phenomena.

So, if we go back to the original statement by the topic author, specifically that these 5 out of 7 failed invasions happened over a TWO WEEK period, then there is virtually zero influence that the chain has upon the individual attempts. His concern was that Dan's 90% success rate was incorrect or off in some way (a claim which might very well be true, but not one backed up by the data he was presenting). I pointed out that 5 out of 7 attempts was hardly enough information to draw the conclusion he was making.

And using the gambling illustration just one more time, it is exactly because people start assuming that the probability numbers have shifted in their favor that they keep on tossing away the money. They believe that the next one has to be a winner because the last 10, or 100, or 1000 in the chain was a loser. They are lulled into counting on their probability increase without realizing just how exponential it would have to be to break even.

This has been a fun discussion on the concepts of possible and probable. I got to head back to work now, talk to you later this evening.

0.1^7 = 1 * 10^-7 = 0.0000001 = 0.00001% chance of failing all seven.

( 0.9^2 * 0.1^5 ) * 21 = 0.0001701 = 0.01701% chance of failing five out of seven.

Not sure how relevant this is to the topic right now.. Don't really care.

Basically, each attempt is independent of the other. So for example, I have a 90% chance of invading(hypothetically of course), and I fail it. I try again, and fail. I try a third time and succeed.
I'm trying to say you should treat each invasion attempt independently. Only that attempt matters, no other one does. Sure, it's a bit odd to fail so many attempts, but it has nothing to do with maths.

By that logic, you would never know if there WAS a problem with the RNG being used in the game.

This sample size is too small to make any conclusions from, but if you failed (for an extreme example) 100 90% attempts in a row you could certainly have enough to ask a reasonable question about the games chances.

(Now before someone argues with me, I didn't claim it would be a scientifically significant sample, it's not, but that would be more then enough for making an observation and asking a question about).

With Maths, the values are independent of one another. I simply calculated the chance of failing 5/7 times or 7/7 times. Maths still works when the values are independent. Dice rolls are independent of one another, but it's one of the most commonly used examples (In the UK at least) when teaching statistics.

i hear these arguments all the time with online poker sites and they just don't hold water. yes, dice rolls are independent. however, GL's 'dice rolls' apply to EVERY player simultaneously. so, the odds calcs based on an individual player's experience are misleading, because while any player rolling those GL dice for themselves may see a sample variation from the expected success rate, the success rate for ALL the players in total will even out if the RNG is working properly. it is this reality that allows players who can multi-table online poker to succeed, as the variance on any given table gets evened out as more tables are played simultaneously.

+1

There is a point though with a big enough sample size you can still conclude that it is not working. 7 isnt big enough but lets say 100 in a row 90% fails? that would be enough to question the validity of the formula.
And RNG doesnt really apply as much to poker as alot of its effects can be cancelled out by player ability.

Dear OP what I have managed to wrap my head around in this thread is that the system is fine you were just unlucky.

Classic example of the Gambler's Fallacy if I ever saw one...

You should have no argument with this. A 66% chance vs a 33% chance will go to the 33% 1/3 of the time (decimals are implied) If you only have that chance once and loose it, the net result is a complete loss. If you take the same chance 100,000 times (somewhere close to a years worth of online poker multi tabling), you will expect to win 66% of the time within one standard deviation. The goal of both the skilled poker player, and "the house" for gambling, is to take that favored chance as many times as possible, thus profiting, and so what if you loose some of the time. (You do the same thing every time you hack/raid/invade, so what if it fails some of the time as long as it works for you most of the time?).

If, on the other hand, you only won 20% of the time in this scenario, you would have serious, and legitimate questions. That is the difference between the chance of an individual occurrence and a statistical trend.

The Gambler's fallacy, also known as the Monte Carlo fallacy (because its most famous example happened in a Monte Carlo Casino in 1913), and also referred to as the fallacy of the maturity of chances, is the belief that if deviations from expected behaviour are observed in repeated independent trials of some random process, future deviations in the opposite direction are then more likely.

Now back to the scheduled program...

Either way, any individual player has that chance of failing 5/7 invasion attempts or all 7 invasion attempts. If the values are independent, it does not matter how many people are rolling dice with you, that's still the chance. As I've shown, it is a very low chance of it occurring.

Fancy way of saying some people believed you were more likly to win after you lost a bunch of times.

What senator is actually saying is if the odds are in your favor by playing more times I have less of a chance of losing money because with more games played the actual percentages of win and lose will approach the expected percents.