Btw, this question itself can be answered without any of the game-theory math I did above:

Because the 1440 blocks out-of-the-game period is independent of the account's balance, it is obvious that the smaller the account you are using for the forging the better. If you have one big account, you're completely out of the block creation process for 1440 blocks, but if you have it distributed to many small ones, only one of them is disables so you still have most of your accounts taking part in the lottery.

So without further thinking it can be seen that this 1440 block disabling period is unfair towards big accounts and incentivises splitting them to small ones.

Edit: Ok, this may not be true... do I understand correctly that once an account created a block, it's effective balance is zeroed out for 1440 blocks? If not than what I wrote in _this_ post is incorrect, but doesn't change what I wrote above about using the second-best accounts for forging.

Alice owns 500M NXT (only 1 account), Bob owns 500M NXT (two account with 250M on each).

Let's assess chances to HIT a TARGET for both of them:

Let's take a base target that gives Alice 1/1000 chance to hit it within a short period of time after a previous block. Bob's chance will be 1/2000 for each of his accounts.

Alice's chance == 1/1000 = 0.001
Bob's chance == 1 - (1 - 1/2000) * (1 - 1/2000) = 1 - 0.9995 * 0.9995 = 1 - 0.99900025 = 0.00099975

Alice Bob = 0.001 0.00099975 = 1.000250062515629   =>   This contradicts to ur statement

What's wrong in my math?

@Come-From-Beyond: Any comment on my "Spam the network for 7.5% increase in block generation" approach?

I don't really understand your math here. Why would Bob's chance be lower than 0.001 ?

I think we can agree that after any given block there is a 50% chance of selecting Alice next, and 25% for each of Bob's account. It's easier to reason when it is presented this way.

Where Bob has an edge is that if one of his blocks is selected, he may check whether it is better for him to not publish his block. That happens when his other block is going to be the second best one, and makes the genSignature to select him after that too.

Yes I know that there are some mechanisms to punish accounts that are not publishing when it's their turn, but that doesn't matter if the accounts are small and many enough.

But user didn't konw that,  i didn't konw the time is used for broadcasting until i saw the code.
And the transaction will be broadcasted anyway.

Ah, I have to model this situation before I come to a conclusion.

You didn't understand vamdor's attack correctly, I think.
The question isn't about chances to forge a block, it's about choosing which block to forge in a way that increases your chances to forge the block AFTER that.
So it's similar to my "move alot of coins around to increase your chance"-attack, just without all the coin moving

Ok, so basically what you are saying is that Bob's accounts are at a disadvantage because they are competing against each other, and the loss is where both accounts hit the target at the same time. (as it doesn't give twice the winnings). But... this could be said of any two accounts regardless of who controls them. The question is what happens when two hits the target the same time? It seems to me that there is a kind of difficulty defined and the one with the higher difficulty wins. In that case we are back to:
Because the time when they hit their target doesn't matter.


I don't see why it would be incorrect. The only difference between the two approaches is that the second one disregards the timing of the events, and collapses the selection process into one step. Your approach can account for the lowered block-generation rate in the "gaming the lottery algorithm" I described, but because only the fees are given to the forger, it doesn't matter. (well, actually it just adds to the incentive to not publish the first winning ticket and use the second one, even when the second one isn't giving you the winning hash for the next block. So you can wait for a few more transactions and get the fees from those too. This makes gaming the system even more worthwhile than my original formula suggests)

Which bits are limited and why you think that is relevant?

Bob's accounts compete but still help each other. The net outcome is almost zero. If 2 hits r made simultaneously then next blocks determine who wins.



I think this is the problem. See my next reply...



When base target is very high large accounts hit the target within a few seconds with 100% probability while small ones need a hour to reach 100%. Forging becomes very unfair in this case.