Gambling with More Money Means Better Chances of Winning
If you're a good blackjack player, you can win 55% of the time. You ought to be able to make some serious money in the long run, but you could still go into the casino and lose all your money. The reason is that wins and losses can come in streaks -- they don't have to, but they occur naturally in a long sequence of coin tosses (or blackjack plays). A streak of losses could take away all the money you're playing with, and in that case you have no money to play with and you have to go home.
One solution, as gamblers have observed, is to bring massive sums of money to the casino. It's still possible that a long losing streak could take you out. But the bigger your pile of money, the less likely you are to hit a big losing streak that takes you out. Then, if you're able to stay in the game, you can play on and your slight edge in winning (that 55%) can manifest in money.
Playing with more money increases your chances of winning.
(More technically, that 55% is a statistical average based on a large number of games. For that 55% to end up being the case, you have to be able to play a lot of games. The imaginary mathematician who's calculating that 55% is imagining that you have an infinite amount of money to play with.)
Investing with More Money Means Better Chances of Winning
Consider that this means for another type of gamble, the business venture. Playing a bit fast and loose with the analogy, we can think of the venture as something that has an unknown outcome, which won't necessarily work, but which has a good idea and "should" work given a good chance (that's the 55%), an opportunity to try different things, a little tweaking, a little luck, and so forth.
For the worthy but uncertain venture in question, investing MORE can make the venture more valuable (better chance that it won't run out of money and that it will succeed).
Corollary: size of investment affects valuation in a fashion that is not merely additive.
Corollary: from a risk and payoff perspective, the proper size of an investment isn't how much money the startup "needs" or how much the company is worth from a discounted cash flow perspective. The proper size of investment is the amount of money that will make sure that the startup isn't left at the blackjack table with no money.
Corollary: these considerations make one big round of investment much more valuable than a few smaller rounds, even if they add up to the same dollar amount.
Corollary: these financing questions don't view whether a startup runs out of money as a particularly good indicator of the quality of the idea or of the execution. Although naturally your likelihood of running out of money at the table depends on the quality of your edge (5% or whatever), it also depends on the number of hands you play and the size of the stakes of an individual hand relative to your total financing (and these factors more depend on your type of business, industry, etc).