At the 6,000' ASL evel, air density is about 20% less than at sea level hence combustion chamber pressures are that much lower (unless you have a turbocharger or super charger to compensate). Required octane level are much lower as a result. High octane petrol also doesn't evaporate as well so you may get worse fuel consumption with high octane especially if the air and engine temperatures are cold.

I used to live in Tahoe at about the 6,600' level. If I had high octane (for up there) gas in my old carburetted truck (required it as it was running nearly 11:1 compression) on cold mornings, I had to prime the carb, let the gas evaporate for about 10-20 seconds, then crank the starter otherwise the gas wouldn't evaporate and the engine wouldn't start.