Haven't read all the posts so it may be mentioned before. Current PoS implementations use some sort of wallet weight as a way to handle competitions for blocks. Wallet weight is basically the amount of coins in the wallet. So if I have a big wallet with very small coin blocks (i.e. I transfer the coins in thousands of small transactions), I have the chance of staking a lot of new blocks continuously with the full weight of my wallet each time. That's the problem.
I have 1% of all stake in 1 wallet. My chance to generate a block is 1%
I have 1% of all stake in 1000 wallets. My chance to generate a block is 1%
I see no problem here. (Nxt)
edit: I guess what you meant is:
I have 1% of all stake in my wallet, and I transferred it there in 1000 small transactions.I still don't see a problem for PoS.
Yes.
Your chance of generating a block is 1%, next block again 1%, next again 1%. That's a problem. The high weight of your whole coins are used for each individual small stake, increasing your chance every single time which makes you a lot more likely to find consecutive blocks
at zero cost.
Ideally your chance shouldn't be 1%, the secure way is 0.001% since you transferred the money in 1000 small transactions. You should either have a big block of coins (1 big transaction), so you have a 1% chance ONCE, or you have 1000 small blocks, so you will have 1000 chances of 0.001%. You should not have a 1% chance, 1000 times.
Sorry, I don't get what you mean.
In PoS your stake matters, not your amount of transactions.