I'm quite fond of his version:
"We know that all these rather crude expectations of uniformity are liable to be misleading. The man who has fed the chicken every day throughout its life at last wrings its neck instead, showing that more refined views as to the uniformity of nature would have been useful to the chicken."
Notably, Russell does not abandon induction in that work, he seems to retreat to a probabilistic, almost Bayesian conception of it (along with a resignation that it seems the best we can do, but a passionate closing defense that it's good enough).
I'm very comfortable with that same probabilistic confidence approach here. (Hence the "bet" language.)
Humanity has frequently abandoned scarce resources upon discovering superior substitutes, while seldom abandoning them through exhaustion. Theories of economics and measures of human progress, while not being ironclad rules, provide rough explanations as to why this keeps happening.
So, sure, happy to concede it is not a foregone conclusion that humanity will always outgrow scarce resources. Nothing is ever 100% certain. But our certainty should generally increase with our observations of a trend, so it seems highly probable for any particular case.
It remains generally unwise to bet against all well established trends, the mere possibility of wrung necks notwithstanding.
Or, as Russell closed the work:
"That some risk of error remains must be admitted, since human beings are fallible. Philosophy may claim justly that it diminishes the risk of error, and that in some cases it renders the risk so small as to be practically negligible. To do more than this is not possible in a world where mistakes must occur; and more than this no prudent advocate of philosophy would claim to have performed. "
Ever heard of the inductivist turkey?
"This turkey found that, on his first morning at the turkey farm, he was fed at 9 a.m.
However, being a good inductivist, he did not jump to conclusions. He waited until he had collected a large number of observations of the fact that he was fed at 9 a.m., and he made these observations under a wide variety of circumstances, on Wednesdays and Thursdays, on warm days and cold days, on rainy days and dry days.
Each day, he added another observation statement to his list. Finally, his inductivist conscience was satisfied and he carried out an inductive inference to conclude, “I am always fed at 9 a.m.”.
Alas, this conclusion was shown to be false in no uncertain manner when, on Christmas eve, instead of being fed, he had his throat cut. An inductive inference with true premises has led to a false conclusion". (Bertrand Russel)
(I though there's also a Black Swan NSS theme in this, but on a second thought the eventual exhaustion of limited resources is hardly an unforeseeable Black Swan -- whether people have bet on them being exhausted and lost a billion times in the past or not).