You can check your work by comparing the following:  the option pool is 10% of the total shares, Jill owns 55% of the remaining shares, Jack owns 45% of the remaining shares. In this manner, the issue of the option pool has flowed smoothly through the calculations because you have focused it on a finite number of shares.

Second, if the option pool is not awarded in its entirety, then it typically reverts to the founders.
Third, if in the future you should want to increase the size of the option pool it is perfectly fair to expect the new investors to share in that dilution.

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