[LittlePeter]

I don't understand where N-1.1111 comes from. Isn't it enough for all the shares to add up to less than N-1 for there to be a profitable bet?

If all no shares add up to S < N-1, then gross winnings will be N-1-S > 0, which when multiplied by 0.9 to get net winnings will still be positive.

[unholiness]

From the fees. 90% of a $1.1111 profit is $1.

Notably, you don't need to post $N to make this bet. PredictIt calculates your worst case scenario and holds only that money. A set of "No" shares worth N-1.12, if it existed, would be literally free to hold. Fees are included in that calculation, but also fees are based on the difference between that cost to hold and the return. So yes, profits mean different things in different parts of that calculation in this degenerate case.

A full set of Nos worth N-1 would be a guaranteed loss of $0.10 per share from fees. PredictIt would hold that 10¢ and you would never see it again.