How did card distributions for Battle Road tournaments work?

The values for these examples you gave purely indicate how desirable they are. Japanese collectors are crazy about rarity. Show them an XYZ Ash’s Greninja Promo and a store buylists it for $3k even though it shares the same art with a $5 promo without the stamp. But even then, the Rainbow Energy are still selling for the price you quoted even on Mercari Japan, a place frequented by Japanese collectors. That only shows low desirability.

Values work in tandem with the market. If its desirable, people would pay more, if not, then no one would think twice for an extra stamp. Look at error collectors, a wrong number listed at the bottom right of a Dark Dragonite skyrockets the price by 20 times or a missing damage on a Ninetales commands a super thick premium on it even when they share the same artwork on cheaper alternatives.

I am aware that I am directly in conflict with my question to you above by saying that so I guess the better answer to your original question is that the prices are the way they are because of desirability. Yes, sometimes it is as linear as rarity but yet again, we are all in a market with people paying more than 20cents for a Pokemon card, what is rational anymore?

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