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Originally Posted by aceside
It seems something is not right. For a 6-deck shoe, EV should be -17.6%. At TC +4, EV should be slight negative, I believe. For an 8-deck shoe, EV should be slightly positive.

If we use ASC, the critical TC should drop one when aces per deck drop one. Can you double check?
Look how quickly the EV changes with the count. Yes, Shackleford's analysis shows a -17.6 EV off the top for this pay table. The sim I show above at TC 0 shows -18.0%. Don't you recognize those as the same? TC = zero isn't a single point off the top of the deck, rather it is a whole bunch of simulated situations over a range of TC from -0.5 to +0.5. The EV changes by 6% for each 1 TC, and the small difference you pointed out is only 0.4%. The sim above would show an EV of -17.6 above at a TC of +0.07. What is the TC off the top with a single low card as the burn card? TC +0.17. So the difference you are focused on is a fraction of the difference of a single card.

Then look at TC +4. It's close to the break even point. Simulations depend on the simulated conditions, which I noted. If I changed things at all, like rounding the deck estimate instead of truncating, it is going to change the exact results around a break-even point. The simple idea is that the EV changes very quickly with the count. If you make this bet at +4, you might have a negative expectation if your deck estimation is off or if you determine true count differently than the simulated results. You are better off waiting until +5 to bet this one, to be sure about it.

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Originally Posted by bejammin075
The sim above would show an EV of -17.6 above at a TC of +0.07. What is the TC off the top with a single low card as the burn card? TC +0.17. So the difference you are focused on is a fraction of the difference of a single card.
Wonderful work! This is convincing. The rapid growth of EV with TC is easily understood. The density of 10s is roughly proportional to the TC, so the probability of two-10 hands is proportional to the square of TC. It quadratically increases. Is it possible to do an ASC on top of this?

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Don’t hold me to this, because I side count differently, but I think you could make a simple adjustment. Let’s say you’ve played four of six decks, and you’ve seen 20 aces played when you expected to see 16. You would want to count those four extra played aces as a non-ten valued card, so you would multiply that number of aces by 2 and add 8 to the running count. You would probably use the same index. More aces played means more tens remain, increasing the EV.

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