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Hi, mushin
I think this is one of the many areas of probability that is NOT easily understood. I suspect tons of people have the same 'intuition' you had. In case you're still looking for some way to get your head around why the seat position doesn't have an advantage, maybe this will help...
You wrote the following, which I think is very relevant: "Assuming that high counts spit out high cards sooner than later."
Assume you're playing a shoe game. If the TC is +3, that means there are more high cards remaining than would 'normally' be expected in a truly random shuffle/deal at this point. The problem is that you don't know WHERE those 'extra' high cards reside in the remaining cards. They MIGHT be the very next cards to come out of the shoe, or they MIGHT be about to come out after 5 cards are dealt or they MIGHT come out in a mostly haphazard way (without any apparent clumping at all) or they MIGHT even be behind the cut card (and thus may NEVER come out in this shoe).
Counting does not tell you WHEN those 'extra' high cards will come out or even IF THEY WILL COME OUT AT ALL - only that they are there in the remaining cards. Sitting in 1st base is no more of an advantage than any other seat if you don't know WHEN the 'good' cards will come out. All you know as a counter is that the remaining cards INCLUDING THE CARDS BEHIND THE CUT CARD are weighted to favor high cards. OVER THE LONG RUN (and this is a VERY long time), this will give you an advantage because your chance of getting a 'good' hand (and/or a dealer bust) is generally better (probability-wise) in this scenario. But, again, you just don't know WHEN or even IF they will come out of THIS shoe. (When they don't come out, you can get big losses as you ramp up your bet and lose big. Welcome to variance!)
You could easily see EVERYONE at the table get a high card for their first card and this would not be surprising at all. (I bet you've seen that happen several times at a high TC and you were relieved to see that someone to your right did NOT get "your" card, right? But, this is not correct thinking. You just don't know WHEN those 'good' cards will come out of the shoe.)
I don't know if that helps at all. It's how I got my head around the idea you're working on.
Best of luck!
SiMi
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