Thanks - but I need their *stake* as well to be included in the same diagram.

Anyway - I've chatted with CfB and he is happy for me to "drop a bombshell".

So get ready...

Try writing your idea in math or in a simulator rather than just trying to ask people to "refute" it.

Okay - a bit more than "slightly" in the 90/10 case.

Let's not focus on the 90/10 case for now (the other cases work much better in the simulator) but sure I grant you that the actual streaks could well be much *larger* that what I've showed for the worst case (I just want people to realise that long winning streaks are very much *possible*).

I am more interested in the 50/50 cases at this stage (if there is any "bug" in my code causing the skew as the percentages get higher then it won't matter if we just focus on those cases for now).

Now someone had suggested we don't let the winner be the same as the last winner. Let's modify our last example to do that:

blocks = 1440
a: 10
b: 10
c: 10
d: 10
e: 10
f: 50
fdfacfedafcfdafafebfedcfdfcecfbdefecfcfdfefafefefdfdbdfcfebfbfdafdfcafadabefcfa ecfbdfdfafcdfdfafcfedfcfafbfefefefbfedfdfcfadfcbfcfec
fcbcafbcfdfcfebefefdfafcebafcdefebfebdefecfbdfbfcebafcafeacbdefefdbfefafafaefbe dfcfececfbfcfbcfefebcbcfbafbafcbfecefcfefefcdafdfabdf
dfdfeafdfcfbfedfdfefacfdafcbfcfedefcafbfdcacefefecfbefbfbefbfeadbcedfedfdfdfbfe bfcecbecfbfafefefdfedfabafafefbcfefbfefadfcfcdafedfec
fdfefbefcecedefcfefdfcdafdfcfcecefebdfcacfefefdfaefdafcfbfcfbfcbfebabfdfefdfecf dfbadfefbfbfcbefcfcfadafdfefdfcfaecfebfeafedbacfbdbfc
bfcfacfefdafbebdfabafcfafdbfdfefafdcdbfbefbfcfefadfdacfbcdbdefefdcfcebafdfaefbf cdfafdefdfcebdaebaeabdfdefcfdfbfdbfefcebcfafcfdfefefb
dfefcdfdebfdfcdfdafdfbdfeafdafbefbcbfbfdafbfcaefedfbfbfbfafdfcbfbfdbebfcaefdefe fcebefdfcbeafeafdfcefefbfefcdadcadfdfdfbcfdefefeacfdf
cbfefefbafbfdfdfefcbfdfecfefafdfdfcdfbdfdafbdfcbfefcefdbfefcfcdafcdfcfbfdfefefd febfdefefdfcfefdecbcdacafdbafecfecfafdbfefefefefcfcfd
efdfdafdafedfbfcaecfeafdfefbdcfafebcfdbdfbefbfdfabfafdfabfdfefcfdfcfbfaefebfdcd fbfefcfbfefdebafebfadafcfbfefcfcfcadbfdfcfefcfcfbfdaf
abfcfafbfefdfdfafcfdfadfefdfecfbdfcfefdfefcbfdecbfcafeafcefedfbefcefcfbefefcdfe fcbfefbafcfafefefefcbcafefcbfbfefadfedfadfefdfdefafdf
dfbafceabfefdfcfdfafcafabfbefeadbfcfafbafcfdfceaecfefdadfcfdcefcfefefbfefcfedfb fbcfcfbafbfdefbfcbecfdfefdefefcfbfefefdfefdabafbcfefc
efcdfdcfacdeadefdbacfabfdbdfdefcfcdcafaedfefefdfdfbfdcefdfadfdfbeafbfcfcbfdfcfa fbfebfbfdcfdabeabdfbfcecacdacfceafcfcfcfd
wins( a ) = 138
wins( b ) = 168
wins( c ) = 190
wins( d ) = 203
wins( e ) = 220
wins( f ) = 521
best_streak( a ) = 1
best_streak( b ) = 1
best_streak( c ) = 1
best_streak( d ) = 1
best_streak( e ) = 1
best_streak( f ) = 1
best_combined_streak = 12

Well our best combined streak is 12 - so I don't think that the limit a streak to 1 is going to help us either.

Call it what you like - the problem is what are the implications if a forger "hides their blocks" in order to track and create a better fork and what should TF do in order to minimise the risk of damage.

So here I've gone back to the 1st simulation configuration but now added a new "combined best streak" which combines all the accounts apart from the last one:

blocks = 1440
a: 10
b: 10
c: 10
d: 10
e: 10
f: 50
ebfcefffcefffcafffcfedafffcfbaacaaaffffffeabafdfcdfffeffcfcfffaffdfbaffbeafeafe fbfdfbffbfdaffdcafceffcbafeffadafffafedffaccdecfabafe
fefcbafafcfeffffdadcfbffbbafbfaeeffbffbefacffafeddfbafeafdfbfebfefcfffebfcadffc ffffafeafbebbefffabcfeffefbdfefcadaafedbfffafafcffeff
dfecfafbdfbfcfbdfffffdfffadbfffbfbafffedadaebafffafbfffafccaefbcabfcaffaffffcff fdfffffaafcfbfcfdcafcfaefcedcfffbfffcfafdcddaacfacdde
fafabffccfeffafdbfdfcbfaccffebcefefffeadacfbecedfdbbffeccbbfacbefffbffffffefcff fffdaffcebffbbfdcbefafffecfffaffaffffffbffedfdcffbfaf
fffbfffffebdadeffffaffbbfcfdfcffaaffffcaffeffeefffaffcecfcffdfffffbfaffffdbdaff eccfffffbfefeadffffeedefcffcdbfbfffefffafadffddbdfcef
cbbddccbffbffcceaadfbcffffdfebeaebfedeffcfbfaddcbaabccfffffaadfffffadeffffdcffffaccfffcbfdbffffcddaeeafdebfcfffcdcddffeafafbeffbfffa
fffaffcbfcffefcaafeafffffcebafadbffefebfdfcffefffcfefcfdfafeffbbfaffbfdffafffda cffcfffcfcfbfcbfdeafffaddeffcdfbeffeceaebbfffafdfabff
adffcfdfdaffadbfcffbdcffaffbfdcaaaffefddfffffdfdbefaefcffecfaeecdcddcfedbfcbfdf dfffeafcdffeebfafffbbfacbcfffbbfefffdbfeffafffbfbaffa
ffbffbfbfffaaecdfbfcffffbfcfffbfcafeefdffdfbfafdffceffffdffafdffdfdbffbbfbfaafe edffdfffffaaecdfffffcdfbfbcdcafeeacfeffffefffffdddfdc
cfebfffbfeecdcffcfaaabbbdfbfcbbedfdfbddfffffbfddaffefedfdeffffefbcfecfcefdbfafa efafddabffbeedadffffafffffffcbdbbcffeabadcbefdffbecaf
ffdfdafcfdfbfcffdebdffabffbdaaefefffffdefacdefacfffcafecefabfdcfbffdffefeffffbb ecaaabbffffdbfeefefcbfffafffbfccfcacbffef
wins( a ) = 165
wins( b ) = 156
wins( c ) = 150
wins( d ) = 147
wins( e ) = 146
wins( f ) = 676
best_streak( a ) = 3
best_streak( b ) = 3
best_streak( c ) = 2
best_streak( d ) = 3
best_streak( e ) = 2
best_streak( f ) = 7
best_combined_streak = 10

I've again "bolded" the longest streak which now happens to be our combined one (that hurt my eyes to find).

Running it a few times shows that sometimes the best combined streak is better and at other times worse so I'd say on average it's going to be the same (i.e. "splitting up accounts in to smaller accounts" won't help).

Good - as security of the network and blockchain are the "most important things" (I think we can all agree that if either the network or blockchain are damaged badly it would not bode well for Nxt).

We need to also model the possibility of getting an effective "winning streak" by having multiple smaller accounts to know whether or not the situation changes (I am not sure yet so once again will need to "see it through simulation").

The figures skew as the larger stake holder gets bigger due to the way the math is done (you can see when I publish it) but in any case if anything it might be showing slightly "better" results that the reality (certainly not worse).

I'm leaving out a slight detail about the "math" which is relevant to the numbers becoming more skewed as the largest stake holder has a higher % (will get to that later).


I am actually mulling over a few ideas at the moment and also which to discuss this with CfB and indirectly with BCNext so let's not rush into that for now.

A good point - and understand that I am not "advocating to do anything" at this stage - just presenting some statistical analysis (something that this project needs to have done before making "claims" about percentages and "safety").

The simulator figures are correct and unedited - I will release the source code later so you can play with it yourself.

The actual outcome of any 1 run is of course "random" (as it can be using "srand" and "rand").

Of *stake* (% of entire balance of NXT).

Of course that can be done but is irrelevant (what matters is stake proportion here).

I will be releasing the source code to my simulator so you will be able to play with it yourself if you are interested.

I am presenting some statistical modelling in a way I hope the community might follow (rather than in math) so that we can work out the best solution for TF.

So let's run two more simulations over 100 years with the 1st giving the major stakeholder 80% and the second 90%:

blocks = 52560000
a: 10
b: 10
c: 80
wins( a ) = 9245377
wins( b ) = 9225484
wins( c ) = 34089139
best_streak( a ) = 10
best_streak( b ) = 9
best_streak( c ) = 38

blocks = 52560000
a: 10
b: 90
wins( a ) = 13480613
wins( b ) = 39079387
best_streak( a ) = 13
best_streak( b ) = 53

As we can see our 90% stake holder achieved a "lucky streak" of over 50 blocks - so clearly even 50 confirmations potentially isn't going to protect us from a 90% "attack".

Without penalty or some other approach the forger who gets a long streak can "undo that many confirmations" by building a "secret" chain.

But what if I increased the largest holding to say 60% (by removing "f" and giving his balance to "e")?

Again over 100 years:

blocks = 52560000
a: 10
b: 10
c: 10
d: 10
e: 60
wins( a ) = 5945713
wins( b ) = 5937915
wins( c ) = 5931002
wins( d ) = 5923375
wins( e ) = 28821995
best_streak( a ) = 7
best_streak( b ) = 7
best_streak( c ) = 7
best_streak( d ) = 8
best_streak( e ) = 27

So "e" has one of 50% of the times (as expected) and had a slightly better "lucky streak" (27 vs 26) - still seems to look good for 30 confirmations right?

Well now I run it again removing "e" and transferring the balance to "d" and we get the following:

blocks = 52560000
a: 10
b: 10
c: 10
d: 70
wins( a ) = 7159269
wins( b ) = 7143871
wins( c ) = 7136512
wins( d ) = 31120348
best_streak( a ) = 8
best_streak( b ) = 8
best_streak( c ) = 8
best_streak( d ) = 33

So 30 confirmations isn't looking so good when one player has 70% of the stake.

Just to get an even clearer picture lets try a 100 year simulation:

blocks = 52560000
a: 10
b: 10
c: 10
d: 10
e: 10
f: 50
wins( a ) = 5189498
wins( b ) = 5182029
wins( c ) = 5175688
wins( d ) = 5171205
wins( e ) = 5166631
wins( f ) = 26674949
best_streak( a ) = 7
best_streak( b ) = 7
best_streak( c ) = 7
best_streak( d ) = 8
best_streak( e ) = 8
best_streak( f ) = 26

Once again "f" has won roughly 50% of the blocks and his largest winning streak is longer but again not that much longer (when you consider how long he's been at it).

So although we need proper math to get the exact % it starting to look as though with "no penalty" this system would appear to be quite safe if you waited for 30 confirmations (or is it?)...

So let's now extend our sample from 1 year to 10 years and see what we get:

blocks = 5256000
a: 10
b: 10
c: 10
d: 10
e: 10
f: 50
wins( a ) = 519010
wins( b ) = 517408
wins( c ) = 518301
wins( d ) = 517377
wins( e ) = 517117
wins( f ) = 2666787
best_streak( a ) = 6
best_streak( b ) = 5
best_streak( c ) = 6
best_streak( d ) = 7
best_streak( e ) = 8
best_streak( f ) = 22

Again "f" has around 50% of the blocks and he has improved on his longest "winning streak" but only by 2 more.

So it's starting to look as though without any sort of change (be it penalty or other) we would really want to have a few more than 22 confirmations to be comfortably "safe" from such an attack.