[NXT] nxtpool.com - first forging NXT pool [161 KNXT] - closed

[Come-from-Beyond]

It means:

Yes I have lost coefficient calculation.
Benefit somewhat less than I expected.
For 1 million in a single splitting the difference is 0.03% (and here I quoted Come-from-Beyond)
For 50 millions in a single splitting the difference is 1.27%

And now I say that for 200 millions (20%) in a single splitting the difference is 5.26% (20%/19%)

Where is the lie?

Alice owns N, Bob owns N/2 + N/2 (==N).

Let's assess Bob's chance to hit target assuming that base target is such that Alice hits it within 1 minute (say, 0.001 probability):

Every of the accounts has 0.0005 chance to hit the target (0.001 * N/2 / N)
Chance that none of the accounts does it == (1 - 0.0005) * (1 - 0.0005) = 0.9995 * 0.9995 = 0.99900025
Chance that any of the accounts does it == 1 - 0.99900025 = 0.00099975

Thus the combined stake does have advantage which proves Dervish point of view. Let's calculate this advantage:

Alice / Bob = 0.001 / 0.00099975 = 1.000250062515629

Thus Alice quotient of advantage = 1.000250062515629 - 1 = 0.0003 = 0.03%

Max value of advantage quotient can be reached if Bob splits all his coins among very big number of accounts. It will be close to 0.05% in this case.

PS: 0.05% advantage is compensated by dispersion and can work only in very long run which doesn't make sense coz currency where stakeholders don't spend coins will die much earlier.

[1715223637]

1715223637

[BitThink]

It means:

Yes I have lost coefficient calculation.
Benefit somewhat less than I expected.
For 1 million in a single splitting the difference is 0.03% (and here I quoted Come-from-Beyond)
For 50 millions in a single splitting the difference is 1.27%

And now I say that for 200 millions (20%) in a single splitting the difference is 5.26% (20%/19%)

Where is the lie?

Alice owns N, Bob owns N/2 + N/2 (==N).

Let's assess Bob's chance to hit target assuming that base target is such that Alice hits it within 1 minute (say, 0.001 probability):

Every of the accounts has 0.0005 chance to hit the target (0.001 * N/2 / N)
Chance that none of the accounts does it == (1 - 0.0005) * (1 - 0.0005) = 0.9995 * 0.9995 = 0.99900025
Chance that any of the accounts does it == 1 - 0.99900025 = 0.00099975

Thus the combined stake does have advantage which proves Dervish point of view. Let's calculate this advantage:

Alice / Bob = 0.001 / 0.00099975 = 1.000250062515629

Thus Alice quotient of advantage = 1.000250062515629 - 1 = 0.0003 = 0.03%

Max value of advantage quotient can be reached if Bob splits all his coins among very big number of accounts. It will be close to 0.05% in this case.

PS: 0.05% advantage is compensated by dispersion and can work only in very long run which doesn't make sense coz currency where stakeholders don't spend coins will die much earlier.

Ok, Now I understand better.
After split to two equal parts, p = 1 - (1 - P/2) * (1 - P/2) = 1 - (1 - P + P^2/4) = P - (P^2) / 4

So the equation Dervish used was correct.

[Dervish]

The equation for difference is
d=P/p=P/(P-P²/4)=4/(4-P)

for 1% (1 million) d = 4/3,99 = 1,0025 difference 0,025% CFB have rounded it to 0,03%
for 5% (5 millions) d = 4/3,95 = 1,01265 difference 1,265% I have rounded it to 1,27%
for 20% (20 millions) d = 4/3,8 = 1,05263 difference 5,26%

Do you have any reference of p = P-P²/4?

Say if I have all the Nxts, my probability is certainly 1. Then I divide all my coins to two accounts, the probability of one account is (1 - 1/4) / 2 = 3/8 and the sum of my two accounts becomes 3/4? Does that mean there's 1/4 chance no forge in a round?

If I further divide them to 4 accounts, then the forge probability further decreases? So there're more empty rounds? Seems quite hard for me to understand.

Here we make assumption that each b_i > 0.

We need another wallets with non zero balance to consider the way I does and get this equation.

[Come-from-Beyond]

Ok, Now I understand better.
After split to two equal parts, p = 1 - (1 - P/2) * (1 - P/2) = 1 - (1 - P + P^2/4) = P - (P^2) / 4

So what Dervish said was correct.

Dervish overlooked that forging is a Poisson process. That's why he got insane numbers.

[BitThink]

The equation for difference is
d=P/p=P/(P-P²/4)=4/(4-P)

for 1% (1 million) d = 4/3,99 = 1,0025 difference 0,025% CFB have rounded it to 0,03%
for 5% (5 millions) d = 4/3,95 = 1,01265 difference 1,265% I have rounded it to 1,27%
for 20% (20 millions) d = 4/3,8 = 1,05263 difference 5,26%

Do you assume the total coins join forging is 100 millions?

[Dervish]

It means:

Yes I have lost coefficient calculation.
Benefit somewhat less than I expected.
For 1 million in a single splitting the difference is 0.03% (and here I quoted Come-from-Beyond)
For 50 millions in a single splitting the difference is 1.27%

And now I say that for 200 millions (20%) in a single splitting the difference is 5.26% (20%/19%)

Where is the lie?

Alice owns N, Bob owns N/2 + N/2 (==N).

Let's assess Bob's chance to hit target assuming that base target is such that Alice hits it within 1 minute (say, 0.001 probability):

Every of the accounts has 0.0005 chance to hit the target (0.001 * N/2 / N)
Chance that none of the accounts does it == (1 - 0.0005) * (1 - 0.0005) = 0.9995 * 0.9995 = 0.99900025
Chance that any of the accounts does it == 1 - 0.99900025 = 0.00099975

Thus the combined stake does have advantage which proves Dervish point of view. Let's calculate this advantage:

Alice / Bob = 0.001 / 0.00099975 = 1.000250062515629

Thus Alice quotient of advantage = 1.000250062515629 - 1 = 0.0003 = 0.03%

Max value of advantage quotient can be reached if Bob splits all his coins among very big number of accounts. It will be close to 0.05% in this case.

PS: 0.05% advantage is compensated by dispersion and can work only in very long run which doesn't make sense coz currency where stakeholders don't spend coins will die much earlier.

Can you please repeat your calculations with 20% but not 0,1% or just say that there is no lie in my words.

[Dervish]

The equation for difference is
d=P/p=P/(P-P²/4)=4/(4-P)

for 1% (1 million) d = 4/3,99 = 1,0025 difference 0,025% CFB have rounded it to 0,03%
for 5% (5 millions) d = 4/3,95 = 1,01265 difference 1,265% I have rounded it to 1,27%
for 20% (20 millions) d = 4/3,8 = 1,05263 difference 5,26%

Do you assume the total coins join forging is 100 millions?

Sorry mistake. It should be read

for 0,1% (1 million) d = 4/3,99 = 1,0025 difference 0,025% CFB have rounded it to 0,03%
for 5% (50 millions) d = 4/3,95 = 1,01265 difference 1,265% I have rounded it to 1,27%
for 20% (200 millions) d = 4/3,8 = 1,05263 difference 5,26%

Here I wrote correct numbers:

So if we has 1000 persons with 200 000 NXT each, when they unite to the pool they increase their income by a half!
But here we look in to very big pool. If pool power will bee 50 000 000 NXT. It will increase income of member with 50 000 NXT about 12%

[BitThink]

It means:

Yes I have lost coefficient calculation.
Benefit somewhat less than I expected.
For 1 million in a single splitting the difference is 0.03% (and here I quoted Come-from-Beyond)
For 50 millions in a single splitting the difference is 1.27%

And now I say that for 200 millions (20%) in a single splitting the difference is 5.26% (20%/19%)

Where is the lie?

Alice owns N, Bob owns N/2 + N/2 (==N).

Let's assess Bob's chance to hit target assuming that base target is such that Alice hits it within 1 minute (say, 0.001 probability):

Every of the accounts has 0.0005 chance to hit the target (0.001 * N/2 / N)
Chance that none of the accounts does it == (1 - 0.0005) * (1 - 0.0005) = 0.9995 * 0.9995 = 0.99900025
Chance that any of the accounts does it == 1 - 0.99900025 = 0.00099975

Thus the combined stake does have advantage which proves Dervish point of view. Let's calculate this advantage:

Alice / Bob = 0.001 / 0.00099975 = 1.000250062515629

Thus Alice quotient of advantage = 1.000250062515629 - 1 = 0.0003 = 0.03%

Max value of advantage quotient can be reached if Bob splits all his coins among very big number of accounts. It will be close to 0.05% in this case.

PS: 0.05% advantage is compensated by dispersion and can work only in very long run which doesn't make sense coz currency where stakeholders don't spend coins will die much earlier.

Can you please repeat your calculations with 20% but not 0,1% or just say that there is no lie in my words.

I will try for CFB


Alice owns N, Bob owns N/2 + N/2 (==N).

Let's assess Bob's chance to hit target assuming that base target is such that Alice hits it within 1 minute (say, 0.2 probability):

Every of the accounts has 0.0005 chance to hit the target (0.2 * N/2 / N)
Chance that none of the accounts does it == (1 - 0.1) * (1 - 0.1) = 0.9 * 0.9 = 0.81
Chance that any of the accounts does it == 1 - 0.81 = 0.19

Thus the combined stake does have advantage which proves Dervish point of view. Let's calculate this advantage:

Alice / Bob = 0.2 / 0.19 = 1.0526

Thus Alice quotient of advantage = 1.0526 - 1 = 0.0526 = 5.26%


I also find out the reason why split reduces the chance. It's because these two accounts do not exchange information so they cannot avoid duplicate work.

[Come-from-Beyond]

Can you please repeat your calculations with 20% but not 0,1% or just say that there is no lie in my words.

Ok. Let's do it step by step.


Imagine we have 5 people only. Each of them owns 200M. Total forging power is 200+200+200+200+200. Agree?

Edit: Maybe u don't lie but just confused. I don't state that u spread incorrect information intentionally.

[Come-from-Beyond]

Alice owns N, Bob owns N/2 + N/2 (==N).

Let's assess Bob's chance to hit target assuming that base target is such that Alice hits it within 1 minute (say, 0.2 probability):

Every of the accounts has 0.0005 chance to hit the target (0.2 * N/2 / N)
Chance that none of the accounts does it == (1 - 0.1) * (1 - 0.1) = 0.9 * 0.9 = 0.81
Chance that any of the accounts does it == 1 - 0.81 = 0.19

Thus the combined stake does have advantage which proves Dervish point of view. Let's calculate this advantage:

Alice / Bob = 0.2 / 0.19 = 1.0526

Thus Alice quotient of advantage = 1.0526 - 1 = 0.0526 = 5.26%

I marked incorrect assumption with red.

[Dervish]

Thank you for your attention to my math. I agree that my words may be confusing, but they correct. And I also agree that in small amounts phenomenon is negligible.

And I want to remember that when I first point out that paradox I even has no idea to make a pool. I just study NXT forging algorithm. And then you answer:

Этo знaчит, чтo фopжить oднoй бoльшoй кyчeй выгoднee, чeм нecкoлькими мaлeнькими.

Дyмaeшь нaдo дeлaть пyл? B пpинципe, eгo вce paвнo нaдo дeлaть, пoтoмy чтo тe, y кoгo мaлo мoнeт cфopжaт блoк тoлькo чepeз тыcячy лeт. Ecли ктo-тo пpидyмaeт бeзoпacный cпocoб этo cдeлaть (чepeз мyльтиcигнaтypы или eщe кaк-тo), тo я бы взялcя зa peaлизaцию.

Do you think it is necessary to do a pool? you said.
And I think. Hm... He is right! And start to make pool. Spent about ten days for it on winter holidays. And now make final steps with codding.

[BitThink]

Alice owns N, Bob owns N/2 + N/2 (==N).

Let's assess Bob's chance to hit target assuming that base target is such that Alice hits it within 1 minute (say, 0.2 probability):

Every of the accounts has 0.0005 chance to hit the target (0.2 * N/2 / N)
Chance that none of the accounts does it == (1 - 0.1) * (1 - 0.1) = 0.9 * 0.9 = 0.81
Chance that any of the accounts does it == 1 - 0.81 = 0.19

Thus the combined stake does have advantage which proves Dervish point of view. Let's calculate this advantage:

Alice / Bob = 0.2 / 0.19 = 1.0526

Thus Alice quotient of advantage = 1.0526 - 1 = 0.0526 = 5.26%

I marked incorrect assumption with red.

Why?

The probability is 0.2 if he has 20% of Nxt, right?

[BitThink]

Can you please repeat your calculations with 20% but not 0,1% or just say that there is no lie in my words.

Ok. Let's do it step by step.


Imagine we have 5 people only. Each of them owns 200M. Total forging power is 200+200+200+200+200. Agree?

Edit: Maybe u don't lie but just confused. I don't state that u spread incorrect information intentionally.

Now I think, if one of them split it to (100, 100), all other four actually may have a little bit more probability due to that one's loss. That only makes the difference larger.

I believe that actually the large holder does have a considerable advantage in forging, although it may be not that important anyway. As I always think the forging profit is negligible.

[Come-from-Beyond]

Alice owns N, Bob owns N/2 + N/2 (==N).

Let's assess Bob's chance to hit target assuming that base target is such that Alice hits it within 1 minute (say, 0.2 probability):

Every of the accounts has 0.0005 chance to hit the target (0.2 * N/2 / N)
Chance that none of the accounts does it == (1 - 0.1) * (1 - 0.1) = 0.9 * 0.9 = 0.81
Chance that any of the accounts does it == 1 - 0.81 = 0.19

Thus the combined stake does have advantage which proves Dervish point of view. Let's calculate this advantage:

Alice / Bob = 0.2 / 0.19 = 1.0526

Thus Alice quotient of advantage = 1.0526 - 1 = 0.0526 = 5.26%

I marked incorrect assumption with red.

Why?

The probability is 0.2 if he has 20% of Nxt, right?

No, the point is that if base target == 100%, then guy with 200M can hit the target within 1 minute only with 0.1 probability. If someone starts playing with probabilities the system will just raise difficulty lowering advantage of combined stake.

[Come-from-Beyond]

Can you please repeat your calculations with 20% but not 0,1% or just say that there is no lie in my words.

Ok. Let's do it step by step.


Imagine we have 5 people only. Each of them owns 200M. Total forging power is 200+200+200+200+200. Agree?

Edit: Maybe u don't lie but just confused. I don't state that u spread incorrect information intentionally.

Now I think, if one of them split it to (100, 100), all other four actually may have a little bit more probability due to that one's loss. That only makes the difference larger.

I believe that actually the large holder does have a considerable advantage in forging, although it may be not that important anyway. As I always think the forging profit is negligible.

Let's discuss situation when 2 guys combine 200 and 200 into 400. What total forging power will be in this case?

[Dervish]

Imagine we have 5 people only. Each of them owns 200M. Total forging power is 200+200+200+200+200. Agree?

What do you mean when saying "Total forging power"?

Why don't we imaging 3 people with each of them owns 333,333333M?
I have already solve that task.

And simple example to illustrate what we talking about:
1) We have wallet with 2/3 of billion NXT and other person have wallet with 1/3 of the billion
2) We have two wallets with 1/3 of billion NXT and other person have wallet with 1/3 of the billion

2) is obviously we have probabilty of succes 2/3
but in case 1) we have probabilty of succes 3/4


Here on horisontal axis value of opponent hit function and on vertical value of our hit function. Red space - we win. Blue space - opponent win.

P.S You may notice that for our last example [4] is not correct. The reason that P is very big and our assumption that 1 > (t_m * A * b₀) / N for each possible t_m is not true. It's became true for P<1/2.

[BitThink]

Alice owns N, Bob owns N/2 + N/2 (==N).

Let's assess Bob's chance to hit target assuming that base target is such that Alice hits it within 1 minute (say, 0.2 probability):

Every of the accounts has 0.0005 chance to hit the target (0.2 * N/2 / N)
Chance that none of the accounts does it == (1 - 0.1) * (1 - 0.1) = 0.9 * 0.9 = 0.81
Chance that any of the accounts does it == 1 - 0.81 = 0.19

Thus the combined stake does have advantage which proves Dervish point of view. Let's calculate this advantage:

Alice / Bob = 0.2 / 0.19 = 1.0526

Thus Alice quotient of advantage = 1.0526 - 1 = 0.0526 = 5.26%

I marked incorrect assumption with red.

Why?

The probability is 0.2 if he has 20% of Nxt, right?

No, the point is that if base target == 100%, then guy with 200M can hit the target within 1 minute only with 0.1 probability. If someone starts playing with probabilities the system will just raise difficulty lowering advantage of combined stake.

Ok, I got a little bit more.

In your example, 5 people have equally 200M, does the system adjust the difficulty so that the expected interval is 1 min. Therefore the probability of none of the 5 people to hit the target (P0) needs to be around 50%? (What's the value in your algorithm?). P0 = (1 - P) ^ 5. If P = 0.2, then P0 = 0.32, a little bit too high. If P = 0.1, then P0 = 0.59, almost. Seems P should be around 0.125.

Therefore, this is a WRONG argument:
"If I have p percent of the total Nxt, I have p percent of chance to hit the target in 1 min."
But this is true
"If A account has twice Nxt as B, A have twice as much chance to hit the target in 1 min."

In other words,
If we add up all the probability of hit the target in 1 min of all accounts, it is NOT 1.

[BitThink]

Imagine we have 5 people only. Each of them owns 200M. Total forging power is 200+200+200+200+200. Agree?

What do you mean when saying "Total forging power"?

Why don't we imaging 3 people with each of them owns 333,333333M?
I have already solve that task.

And simple example to illustrate what we talking about:
1) We have wallet with 2/3 of billion NXT and other person have wallet with 1/3 of the billion
2) We have two wallets with 1/3 of billion NXT and other person have wallet with 1/3 of the billion

2) is obviously we have probabilty of succes 2/3
but in case 1) we have probabilty of succes 3/4


Here on horisontal axis value of opponent hit function and on vertical value of our hit function. Red space - we win. Blue space - opponent win.

P.S You may notice that for our last example [4] is not correct. The reason that P is very big and our assumption that 1 > (t_m * A * b₀) / N for each possible t_m is not true. It's became true for P<1/2.

Yes, you are correct in this. You mistake is, as CFB has pointed out, assuming P(200M) = 0.2. This is wrong.
Make it simpler, suppose there's only one account, P(1000M) != 1. It should be around 0.5, so that the average interval is around 1 min. If the probability of hit target in 1 min is 1, then the average interval is definitely smaller than 1 min (maybe only 0.5 min depends on the distribution).

[notsoshifty]

Alice owns N, Bob owns N/2 + N/2 (==N).

Let's assess Bob's chance to hit target assuming that base target is such that Alice hits it within 1 minute (say, 0.2 probability):

Every of the accounts has 0.0005 chance to hit the target (0.2 * N/2 / N)
Chance that none of the accounts does it == (1 - 0.1) * (1 - 0.1) = 0.9 * 0.9 = 0.81
Chance that any of the accounts does it == 1 - 0.81 = 0.19

Thus the combined stake does have advantage which proves Dervish point of view. Let's calculate this advantage:

Alice / Bob = 0.2 / 0.19 = 1.0526

Thus Alice quotient of advantage = 1.0526 - 1 = 0.0526 = 5.26%

I marked incorrect assumption with red.

Isn't the part highlighted in blue also incorrect? "My first account forges" and "my second account forges" are not independent events.

[Come-from-Beyond]

Imagine we have 5 people only. Each of them owns 200M. Total forging power is 200+200+200+200+200. Agree?

What do you mean when saying "Total forging power"?

Each coin is like a mining rig. So we could use "forging power" to describe possibility to forge a block.