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Oh, wait, I’ve got it!
If the snoutling offering has a 67% chance (2/3) to come up in any slot, you would get a 3,7% chance that the dojo contains no snoutling offerings at all.
Each slot gives a 2/3 chance to come up with a snoutling offering.
To get one slot WITHOUT a snoutling offering is 1/3.
2 slots without a snoutling offering gives you 1/3*1/3=0,11=11% chance.
3 slots without a snoutling offering gives you 1/3*1/3*1/3=0,037=3,7% chance.
In that case the math works out for 100%, including the zero offerings you have seen.
On average you will get 3*(2/3) snoutling offerings on the initial visit, which adds up to 2. After that the rest applies normally as described in my earlier post and everything should average at 6 snoutling offerings.
I believe this nut is cracked.