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The Light section says

If the result is greater than 4, increase the number of dice for the next check. If the result on 3d6 is greater than 4, the light is extinguished.

“The result” being the total roll.

so don't start checking the total till the total dice is 3 or more? A lantern starts with 1d so 4 turns till I start checking? 

No, you’re looking at the total of each roll. So a lantern rolls 1d6. If that’s 4 or more, it moves to 2d6. If the total of 2d6 on the next roll is 4 or more, it moves to 3d6. If the total of 3d6 is 4 or more, it goes out.

OK got it