In another thread, a question was asked about why the floating advantage happens and what the “mechanics” are behind it. The thread quickly devolved, without, I think, really helping the OP much. I’ve re-read the relevant sections of BJA3 and Griffin multiple times, and put a lot of thought into it, and I think I finally understand it myself, but I had to talk myself through it in a different, more explicit way than BJA3 or Griffin describe it. My explanation to myself may help others understand it as well.
Here goes:
First, I propose we define the Floating Advantage Theorem: “As the pack is depleted, the true count count indicating a given advantage decreases in the most common true counts.”
As to why this happens, here’s my best understanding:
- Average advantage is the same at all points in the pack; there is no inherent advantage change as the pack is depleted (some may want to read that again).
- True count is a tool to indicate and estimate advantage; it is not advantage unto itself.
- At very high and very low true counts, advantage *per true count* is lower than at moderate true counts (due to more pushes in very high true counts and poor double-down prospects in very low true counts)
- As the pack is depleted, very high and very low true counts become more common and the mean absolute value of the true count increases.
- As the pack depletes, very high and very low true counts become a larger fraction of all true counts. To maintain the same average advantage throughout the pack (refer to point #1 again), advantage per true count at more common true counts must rise to offset the lower advantage per true count at the now-more-common very high and very low true counts.
- Therefore, as the pack depletes, the true count *indicating* a given advantage must decrease at moderate true counts. These “moderate” true counts are approximately high-low -4 to +4 (by God!) as indicated in BJA3.
Throw out your corrections / improvements to what I’ve said, or, if it’s perfect as is, go ahead and inflate my ego. If I'm way off, enlighten me.
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