How is the next forger decided in Nxt? I've read both the Nxt whitepaper and many other resources on the wiki but I still can't seem to understand how exactly the forging process works. From what I understand, there are a bunch of online users with their account "unlocked" (so they can sign the next block if they win). I don't understand how the winner (or the next forger) is decided. Is it random, or is it based on how many nxt coins one has?

For example let's imagine there are three users online with their accounts "unlocked": Alice (has 40 nxt), Bob (has 55 nxt) and Fred (has 13 nxt). The wiki says:


  Your probability of forging a block depends on your share of the total
  number of coins that are active on the network.


If that's true, wouldn't Bob (who has more coins than Alice and Fred) win the block generation every time? But then how is it possible that even accounts with little coins are still able to win at forging? Does it have something to do with the fact that the winning forger has to wait 1440 blocks before they can forge again? Is this what gives a "chance" to the less-rich users to win sometimes?

Also, if Bob is winning every time, couldn't he just go back the last 10 blocks or so and replace them with different blocks?
Which account is entitled to forge the next block depends on several things.

The last block added to the blockchain includes a 32-byte "generation signature" (actually a hash). This signature is concatenated with the public key of each account attempting to forge the next block, then sha256 hashed to produce a new generation signature to be included in the next block, the block currently being forged. The 8 most significant bytes of the new signature are combined into a 64-bit integer in reverse order (little endian) to determine the "hit" value of each account.

These hit values are effectively random and can't be known before the latest block is added to the blockchain, but after that they are known throughout the network. Any account receiving a newly forged block from the network can verify that the generating (forging) account is eligible to forge, because it knows the last block's generation signature and the public key of the forger, both of which are included in the new block, and thus can compute the hit value for any account.

Because the hit value is effectively random, every account with a non-zero EffectiveBalance has a chance to forge. A low hit value is desirable, because then even an account with a low balance can get a hit. The formula for getting a hit is

hit &lt; BaseTarget * EffectiveBalance * TimeSinceLastBlock

The BaseTarget is dynamically adjusted with each new block so that a hit occurs somewhere on the network about once per minute. A hit will eventually occur even if the hit value is by chance very high, because it becomes easier to get a hit with each passing second because of the TimeSinceLastBlock (in seconds) term.