Here's the critical sentence from your cite:

"It was valued at 12,500 korona, and defined as 3,800 to one kilogram of fine gold – which meant that the pengő was pegged to the gold standard, but without exchange obligation."

Which means it can be inflated at will. The US did the same thing, pegging the dollar to gold, then inflating the paper money. The result was fiscal collapse leading to the Great Depression. The fix was to make it illegal to exchange dollars for gold, making the "gold standard" a complete fiction.

I think you are conflating a few things. What you have to remember with the gold standard is that the supply (or probably more correct, holdings) of gold determine the money supply when a gold standard is in place, as does the price of gold (the conversion rate). A reduction in the money supply (fear of deflation, leading to bank runs) and a massive withholding of production are generally the two key events cited as causes of the Great Depression. The later being the reason for the massive public works programs of the time were started.

The inflation of the US currency happened much later. Roosevelt banned private holdings of monetary gold and gold certificates, incentivized gold imports and gold production which lead to the inflation. That was nearly 5 years into the depression though.

> supply (or probably more correct, holdings) of gold determine the money supply when a gold standard is in place

It does not when the money is not convertible to gold. Such is a fictitious gold standard.

The bank runs in the Depression were caused by inflation devaluing the value of a dollar by about half since 1914, yet was still convertible to gold. People suddenly realized they could DOUBLE THEIR MONEY by converting their paper money to gold. So they ran to the banks to do this. Of course, there wasn't enough gold to support that, and the banks collapsed. The runs did not stop until FDR made it illegal to exchange dollars for gold.

> The inflation of the US currency happened much later

Check the historical inflation figures. The dollar lost half its value 1914-29.

According to the wikipedia article, the pengő was very stable while it was pinned to the gold standard.

The hyperinflation for them took off after all the coins had been hoarded eventually during the more gradual devaluations beforehand.

Regardless of being officially pegged to gold this is where they went wild printing all new notes for which there was no physical backing.

Leaving their precious metal reserves more valuable to other countries than their own. They probably continued to hoard them anyway.

>Economies are complicated dynamical systems, I think we can all agree that there are many possible variables in the inflation equation.

No doubt about it, there's simultaneous equations for which solutions are not well-known, obvious, or forthcoming.

> In one of the last acts of World War II, the Szálasi government took control of banknote printing and issued notes without any cover

In this example, the only important variable was M, as expected.