A choice of 3 forgers does not really improve things because all it does is take a big number and divide by 3.
Not divide. Suppose each forger has a small chance
e of failing to forge (whether by d/c or some other reason. Assume this
e is the same for all forgers to keep things simple). Then the chance of all 3 not forging is
e^3, which is much smaller than
e. Consequently the chance that the block gets generated on time is 1-
e^3, this is much more reliable than 1-
e, which is if there were only one candidate to generate the next block.
I'm guessing actual TF would choose more than 3 candidates, coz if you end up with only 2 candidates, no one can check against the other. With more candidates, idea then is that the chance of too many candidates dropping out from a pool is still much lower than that of any one specific candidate dropping out (math is no longer as simple as the above). And you can scale up the number of candidates as network connectivity and speed increases.
So if you keep [the number of accounts] low, you are hoping that some few specific accounts are all online and ready to forge.
That's not how Nxt works. The account that forges the next block is selected from only online accounts with an effective stake, not from all existing accounts.
Yeah it's tough to understand, even if you manage to read through all of this, and related threads! Helps if you can clear away existing assumptions from previous crypto experience, Nxt is designed from scratch. The wiki (link in my sig) may also help.