theymos
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August 02, 2019, 10:15:50 PM 

~0.2% chance of that happening two months in a row. Eventually once we get to 250 candidates (or whatever theymos' expectation was) it will be much more frequent.
If you're looking at a particular person, their chance of being excluded in both a month with 104 eligible and the next month with 106 eligible is ~0.2%. But the chance that any one or more people already excluded in the first month are also excluded in the second month is, I believe, 1  [(102 choose 100) / (106 choose 100)] = 99.9997%

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fillippone
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August 02, 2019, 10:54:43 PM Last edit: August 03, 2019, 12:08:21 AM by fillippone 

~0.2% chance of that happening two months in a row. Eventually once we get to 250 candidates (or whatever theymos' expectation was) it will be much more frequent.
If you're looking at a particular person, their chance of being excluded in both a month with 104 eligible and the next month with 106 eligible is ~0.2%. But the chance that any one or more people already excluded in the first month are also excluded in the second month is, I believe, 1  [(102 choose 100) / (106 choose 100)] = 99.9997% I might be hugely wrong here: Probability of a single user being excluded from the two DT1 round as defined (100 out of 104 and 100 out of 106) is correct as l’you already found: 4/104*6/106~0,2%. Probability of any user excluded from first selection to be excluded also from second one: 1(100/106)^4~20.79% Please check me EDIT: typo on the first result EDIT: already spotted by Quickseller EDIT: after a little mumbling on Quickseller observations, I stand with my answer. Tomorrow I will double check.




Quickseller
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~0.2% chance of that happening two months in a row. Eventually once we get to 250 candidates (or whatever theymos' expectation was) it will be much more frequent.
If you're looking at a particular person, their chance of being excluded in both a month with 104 eligible and the next month with 106 eligible is ~0.2%. But the chance that any one or more people already excluded in the first month are also excluded in the second month is, I believe, 1  [(102 choose 100) / (106 choose 100)] = 99.9997% The chances of any one or more people already excluded in the first month also being excluded in the second month (when there are 104 eligible in the 1st month and 106 eligible in the next month) is: 4 * [1(100/106)], or ~22.4% In other words, it is the chances of a single individual person being excluded in the second month, times the number of people excluded in the 1st month. edit: I might be hugely wrong here: Probability of a single user being excluded from the two DT1 round as defined is 4/104*6/106~0,02% Your formula: 4/104*6/106 is correct, however you converted into a percentage incorrectly, the chances of a person being excluded two months in a row, one with 104 eligible people and the other with 106 eligible is 0.217% Probability of any user excluded from first selection to be excluded also from second one:1(100/106)^4~20.79%
Your exponent should be a multiplication, and there should be an additional bracket because of the order of operations.

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theymos
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August 03, 2019, 12:22:11 AM 

The chances of any one or more people already excluded in the first month also being excluded in the second month (when there are 104 eligible in the 1st month and 106 eligible in the next month) is: 4 * [1(100/106)], or ~22.4%
Damn it, I simulated it, and you seem right. I suppose that my model of the situation was wrong because it actually does matter that the first month has already happened, whereas I was trying to eliminate the specificity of this.

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fillippone
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August 04, 2019, 10:09:06 PM Last edit: August 05, 2019, 01:10:40 AM by fillippone 

The chances of any one or more people already excluded in the first month also being excluded in the second month (when there are 104 eligible in the 1st month and 106 eligible in the next month) is: 4 * [1(100/106)], or ~22.4%
Damn it, I simulated it, and you seem right. I suppose that my model of the situation was wrong because it actually does matter that the first month has already happened, whereas I was trying to eliminate the specificity of this. Guys I am again on this. I thought about this problem quite extensively during this weekend on the italian riviera. I think Quickseller formula is not correct as it does allow repetition, while we must find a solution without repetition (if a user is selected, it cannot be taken out again on the same round). I think Theymos was then on the right path using binomial coefficients, so I am going to use the same technique. The right probability of any of the 4 excluded in the first round to be excluded in the second round is equal to 1  the probability of everyone of such 4 to be selected: 1C(100,4)/C(106,4)=0.210654248 another less intuitive method give the same exact result: 1C(102,6)/C(106,6)=0.210654248 (probability of being amongst the 6 excluded from the second extraction chosen by the 100 selected from the first extraction + the 2 new addition). I am almost sure about this, but please double check me again. Theymos said he simulated and got a result very similar to Quickseller, this scares me, also because I saw LoyceV and other heavyweight meriting previous solution... shall I go back to school? EDIT: Forgot to mention, but clearly an hypothesis here: every candidate on the first round is a candidate also for the second round. This simplifies calculations, when we agree on the solution, we'll be able to remove this hypothesis.




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August 04, 2019, 10:36:06 PM 

The query is: What are the chances that at least one person who was not included in DT1 in July are also not included in DT1 in August. There were 4 people not included in July, there were 106 candidates for DT1 in August with only 100 spots. It is assumed that all 4 people will continue to be eligible in August. The query can be rewritten/simplified as: What are the chances of at least 1 of 4 specific people not being included in DT1 in a month in which there are 106 candidates and 100 spots? You can start by calculating the chances of any one person not being included on DT1 with 100 spots, and 106 candidates with the following formula: 6/106The 6 represents the number who will not get a DT1 spot, and the 106 represents the total number of candidates. The formula is calculated to 5.66%. In other words, there is a 5.66% chance that any one person will not be included in DT1 given 106 candidates and 100 spots. Since there are 4 opportunities for the above outcome to happen, we would multiple the above result by 4. Every candidate has the same chances of being not included, and there may be some months in which more than one in the list of 4 is also not included in the following month I saw LoyceV and other heavyweight meriting previous solution Unless there is a solution in another thread, LoyceV did not merit any previous solution other than mine (he did merit mine). bones261 is the only one who merited the previous solution, but he also gave more merit to my solution.

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fillippone
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August 05, 2019, 12:35:29 AM 

The query is: What are the chances that at least one person who was not included in DT1 in July are also not included in DT1 in August. There were 4 people not included in July, there were 106 candidates for DT1 in August with only 100 spots. It is assumed that all 4 people will continue to be eligible in August. The query can be rewritten/simplified as: What are the chances of at least 1 of 4 specific people not being included in DT1 in a month in which there are 106 candidates and 100 spots? Correct You can start by calculating the chances of any one person not being included on DT1 with 100 spots, and 106 candidates with the following formula:6/106
The 6 represents the number who will not get a DT1 spot, and the 106 represents the total number of candidates. The formula is calculated to 5.66%. In other words, there is a 5.66% chance that any one person will not be included in DT1 given 106 candidates and 100 spots.
correct Since there are 4 opportunities for the above outcome to happen, we would multiple the above result by 4.
Not correct, sorry. Source: Combinatorics/Probability Calculation. I also discussed this solution with some errorproof individual. He agreed on my solution (this is not appeal to authority, this is only to double check my calculations). Every candidate has the same chances of being not included, and there may be some months in which more than one in the list of 4 is also not included in the following month I saw LoyceV and other heavyweight meriting previous solution Unless there is a solution in another thread, LoyceV did not merit any previous solution other than mine (he did merit mine). bones261 is the only one who merited the previous solution, but he also gave more merit to my solution. When I said previous solution I was referring to your solution, of course, the last solution above my post.




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August 05, 2019, 12:54:07 AM Last edit: August 05, 2019, 04:23:37 AM by suchmoon 

If you're looking at a particular person
Yes, the chance of babo being excluded twice in a row. any one or more people already excluded in the first month are also excluded in the second month
Intuitively that chance would be ~100 times greater, i.e. around 20%. Sounds close enough to the debate going on above but they seem to assume that all 104 candidates from the first month are also eligible in the second month, which may or may not be the case.




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August 05, 2019, 01:12:03 AM 

If you're looking at a particular person
Yes, the chance of bobo babo being excluded twice in a row. any one or more people already excluded in the first month are also excluded in the second month
Intuitively that chance would be ~100 times greater, i.e. around 20%. Seems close enough to the debate going on above but they seem to assume that all 104 candidates from the first month are also eligible in the second month, which may or may not be the case. FTFY! poor Babo!




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August 05, 2019, 04:20:32 AM 

FTFY! poor Babo!
Apologies to babo. My excuse is that I was binging Wynonna Earp yesterday.




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August 05, 2019, 08:23:30 AM 

Since we're back at the chances of being included, I'll drop my 2 satoshis: I merited Quickseller's post, but not theymos' post. I thought the 99.99997% looked a bit high, but past midnight I didn't have the time for a proper response. Rough calculationAssuming: the first month 4 people didn't make it to DT1, and the next month 6 people didn't make it. I see no need for a very accurate calculation, so I'm doing a backoftheenvelope calculation with rounding. That means there's a 4% chance for anyone to be excluded in the first month, and 6% the next month. For someone to be excluded 2 months in a row, the chance multiplies to 0.24%. For someone who is already excluded in the first month to be excluded in the second month too, the chance is the same as it is for anyone else to be excluded in the second month: 6%. For one of the 4 users who were excluded in the first month, to be excluded again in the second month, the chance is 4 times higher: 24% (and here the rounding error gets a bit larger but it's still acceptable for the sake of argument).
Wouldn't it be more interesting to look at the actual chances to DT2 that result from the changes in DT1? It only matters who's on DT1 if a DT2member is included by only one (or maybe two) DT1 member(s).




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August 05, 2019, 08:29:04 AM 

I see no need for a very accurate calculation, so I'm doing a backoftheenvelope calculation with rounding.
There's no need for very accurate calculation, but there is a way to do very accurate calculations. This is why I did very accurate calculations!




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August 05, 2019, 08:48:54 AM 

i follow the discussion for pure mathematical interest.




