In my opinion, two different statements are considered, both of which are correct and are unintentionally mixed, which is why they lead to different opinions.
I have to disagree, akaki put and end to all speculation by saying
[chance with 50 PH/s for 3h] > [chance with 25 PH/s for 6h] > [chance with 5 PH/s for 30h]
The quoted statement is just wrong, the correct statement would be
[chance with 50 PH/s for 3h] = [chance with 25 PH/s for 6h] = [chance with 5 PH/s for 30h]
or
[chance with 50 PH/s ] > [chance with 25 PH/s ] > [chance with 5 PH/s ]
What akaki meant is that the odds calculation related to the block is correct. To illustrate it in another example: you have a dice and the goal is to roll a six. You are only allowed to roll once every 10min. To the question "What is the chance to roll a six?" the correct answer is always the same, it is "1/6", so the probability is 0.16667 % to roll a six. Just because you are allowed to roll again the dice 10min later, it does not mean that the probability to roll a six increases. It always and steadily remains 1/6.
I don't think this is what he meant, but anyways, this illustration is wrong, there is no such thing as "roll once every 10 min" you roll as often as you can, it's just that difficulty that "ensures" you only get 2016 six in 2 weeks assuming you don't increase the rolls.
What the creator of the solochance.com website and many others do is: they multiply/divide the probability of a block hit (related to the block) by the number of 10min periods and thus mix the result with time. However, the time factor has no consideration in the probability calculation. The result of the thus faked probability is thereby glossed over.
The numbers on solochance.com are perfectly correct, looking at akaki post history, I am surprised to why he is confusing himself, he seems to be pretty good at math, maybe missing the logic.
Let's clear up some confusion:
The difficulty adjusts based on the time it took to solve the previous 2016 blocks (more like 2015 blocks due to some bug in the code but can be ignored for now)
So, if the difficulty of the previous epoch was 10 units, and the time it took to solve 2016 blocks was 2 weeks, the difficulty will stay at 10 units, this brings the question, how did the pace of finding blocks get to exactly 2 weeks or 10 minutes average block time? it's because the NUMBER of hahses produced by miners remained the same.
So epoch A had a diff of 10 units and the number of hashes was 1000, based on the difficulty of 10 those 10000 shares can only possibly find 2016 blocks in a period of 2 weeks/avg block time was 10 mins.
see that 10 units of difficulty couldn't care less how the 1000 hahses were generated, if all the miners shutdown their gears for 13 days and do manage to hash 1000 hashes on the 14th day, the block average will still be 10 mins and thus no diff change will accur.
using the dice analogy, you are required to roll 6 at the first epoch, the protocol wants you to hit just one 6 every 10 mins, if you manage to hit more 6s in under 10 mins, the requirement will change, and you are now forced to roll two 6s in a row, now that will need 10 mins to happen, if you do more rolls and manage to hit two 6s in less than 10 mins you will be required to roll three 6s and so on.
while rolling a die every time is an independent event, you will still hit a 6 on average every 6 rolls, you can test it yourself, roll a dice 60000 times and you will likely get 10000 six
,
Still at the dice analogy, the bitcoin dice is actually 2^256, the number of dice sides that can solve a block is determined by the difficulty/target, simply put, with the current difficulty of 37.89T every hash has 1 in 37,885,054,421,573 chance of hitting a block.
let's do more math for fun, the time it takes you to find a block is
time in seconds = difficulty * 2^32 / hashrate in seconds
with 50PH the equation is
((37885054421573 * 2^32 / 50000000000000000) / (3600)) = 903 hours
on average to hit a block, let this 903 hours sink in for a while because we will use it later, and by the way, the division by 3600 is just to convert seconds to hours.
so the above equation suggests that IF you hash 50,000,000,000,000,000 (50PH) every second for 903 hours, you are likely to hit a block, that is 50000000000000000*60*60*903 hashes in a total of 162,540,000,000,000,000,000,000 hashes submit over the period of 903 hours gets you a block on average.
*(60*60 to convert seconds to minutes > minutes to hours )
Now let's say I want to produce the same hashes in just 9.03 hours instead of 903 hours, 9.03 hours has 32,508 seconds, so 162,540,000,000,000,000,000,000/32,508 = 5,000,000,000,000,000,000 hashes/second ( 5000PH)
using the same equation above we now have
((37885054421573 * 2^32 / 5000000000000000000) / (3600)) = 9.03 hours.
now just for fun, I want to produce the same number of hashes over the course of 9,030 hours, without doing any more equations, I know I can just hash at 5 peta hash/second for 9,030 and still get the same result as 50PH over 903 hours, but while the calculator is still open, why not?
5 petahash = 5000000000000000
((37885054421573 * 2^32 / 5000000000000000) / (3600)) = 9039 hours.
Notice how everything here revolves around the total number of hashes (162,540,000,000,000,000,000,000), if I hash them at a rate of 50PH/S i need 903 hours, if I hash them at 5000PH/second all I need is 9.03 hours, if I hash them at 5PH/second I'll need 9039 hours.
By now, it should be clear that it's all about the TOTAL NUMBER of hashes you submit, so back to Nicehack or any rental services, you actually pay per HASH, when you go buy those 162,540,000,000,000,000,000,000 hashes on nice hash you will pay x BTC and it's up to you how fast you want to "consume" them.
for economical reasons and supply/demand, it's sometimes wiser not to put massive orders in the order book as that could trigger a price increase.
Also, it's perfectly fine and correct to say
for example that there are 144 blocks mined each 24h (=1 each 10 min) and thus if we run the miner 24h non-stop we multiply our chances by 144.
akaki insisted that you can't say so, not sure what's the reasoning behind it, the difficulty does keep block inteverals at 10 minutes average, so using 144/day to get a daily chance for x hashrate/second is perfectly correct.
even though Willi's 20 P "go big or go home" is very hard to ignore. 
), that would be really awesome.
If you like to fill the 3 slots of run #10 then send 0.003 BTC to bc1qtyvxwhwctneje9zjvqkzvp6yqtnqc3xs0sf6vd with the filled template that contains your name, your stake, TXid, your payout address and your vote for the desired hash rate. Looking forward to your deposit and hopefully we could launch run #10 soon ... 