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"the deal is a good one if it makes the company worth more than"

Sure, if we assume that other deals are impossible. Which is a false assumption.

No. By saying it is a "good deal", the GP is just saying that your average outcome would be better than doing nothing. It is still theoretically possible for better deals to exist.

Edit: You aren't understanding my post; I just said that something can be a "good deal" compared to doing nothing regardless of what other options are available; i.e. YC offers a positive value proposition.

Yes, YC is a good deal in an alternative reality where YC is the only choice. However, I talked about doing YC in the real world, where other alternatives exist.

But the 1/(1-n) equation is still true no matter how many alternatives you have. The only change is if you have an alternative, say 10% for 1M from some VC, then you would ask yourself after I got 1M and the help VC, would the investment from YC still help my startup grow 6.4%?

I think you are missing my assumption in my OP "in the early stage of a startup". In fact at that stage of startup, even if you have a better deal than YC, you might still want to do YC (so you would take both two deals) because even after your take the better deal, YC can still gives your startup >6.4% growth.

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