To give concrete numbers to pgs statement:
Pick 2 hypothetical startups: A and B. A will go on to be a 10 billion dollar company and B will be a 100 million dollar company. Now, valuations at round B series vary from say $40 million to $400 million (as pg said 10x). Note: they arent yet worth what they will be worth later. Now, say you take a 20% equity cut for the round and there is no dilution between this and when they go public (just a simplifying assumption). At the end, the 20% equity is worth either 200 million dollars for A or 20 million for B. The difference in profit is 180 million dollars; much more than any additional amount you would have paid to get in on a higher valuation. Therefore, if you believe the company to be of the A type, you will pay that 20% of a higher valuation.
> pay whatever the price happens to be.
This is what pg means: the difference in profit between A and B was 180 million dollars which far exceeds the difference in cost in investing in the two. This makes the investors rather price insensitive IF they think that you are in the A category. The reason that investors have the mental model of assigning to categories rather than guessing the percent chance of success is that they know often they guess wrong. There are simply too many variables to create any sort of accurate chance of success.
That's the problem I have with this line of thinking. An investor doesn't "believe" it to be type A. An investor gambles that it's going to be type A. Reasoning after the fact that you should have been willing to spend more on the winner, without accounting for probabilities, is flawed reasoning. If anyone could see five years ago that the company was certainly going to be worth $10b today, then it would have been worth $10b five years ago (after adjusting for inflation). If no one else could see it but you, and yet you were somehow certain, then sure, but that's not typically the situation.
[Before continuing, let me point out that you flubbed the math: 20% of $10b is $2b, not $200m. The difference between A and B equity is $1.98b, not $180m. This wasn't particularly important to your point, but since I am continuing this example I thought it might avoid confusion to note the error.]
Since most people generally prefer frequentist reasoning, here's another try. Suppose you invested in 100 companies, one of which was company A and the other 99 of which failed. If you invested at 20% in all 100 companies valued at $40m each, then you've spent $800m and have $2b in equity. If you invested in those same companies at $400m valuation each, then you spent $8b for that same equity of $2b.
> without accounting for probabilities, is flawed reasoning.
This is the problem. It is rather illogical to believe that one can come up with an accurate probability of success for a given company given the multitude of variables both known and unknown. For example, AirBnB was thought to be not only bad, but a terrible idea initially yet it is one of the biggest winners in all of the YC batches. What probability of success did investors give it? Think of it from the point of view of an investor who passed up on AirBnB. How much do you think that these probabilities that you come up with mean when you know how bad you are at deciding whether to invest at all.
Moreover, whatever money you make on any startups that do not make $BIGNUM is rounding error by comparison.
If you'd reword that as "the basic rules of expected value are difficult to apply to startups", there'd be some chance it was true :).
And yet, difficult as it may be to apply, expected value is the framework to rationally make a decision about low probability / high payoff investments. Of course, if YCombinator is already invested at an early stage (note: when the valuation is quite low), I can understand why pg wouldn't care too much about the later stage valuations. If you look at what's best for YC, it's first and foremost that companies get the money they need to succeed (an incentive aligned with the founders and any investors) but probably also that the valuations (after their own investment) be as high as possible so that more of the pie remains for later investments. This latter incentive is clearly not aligned with investors and as an investor I'd take the advice to disregard valuation with a big grain of salt.
Excerpt: "To a first approximation, a VC portfolio will only make money if your best company investment ends up being worth more than your whole fund." This is the big hit, and VC's are trying to optimize their chances of getting one of these. That's different from trying to precisely calculate expected return. As long as you've found it, it won't matter if you paid a bit too much.
I actually think he's more likely to simply care a lot about making life better for founders, though. He may care about investors too, but I warrant it's less.