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Thread: Proving CA algorithms incorrect (or at least inexact)

  1. #157


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    Quote Originally Posted by iCountNTrack View Post
    Hi Cac,

    This is a great question, as it highlights one of the strengths of the “locally optimal” algorithm. Yes, the algorithm decided (albeit incorrectly) to resplit when facing SplitHand1: (10,10) and SplitHand2: (10). However, that’s not the only way resplitting can occur. It can also happen at SplitHand2, in one of two scenarios: SplitHand1: (10,7) and SplitHand2: (10,10), or SplitHand1: (10,10) and SplitHand2: (10,10). In both of those, the locally optimal method determined that EV of resplitting at SplitHand2 to be lower than standing on SplitHand2.

    A key advantage of both the locally optimal and globally optimal algorithms is that they continually re-evaluate strategies every time a card is drawn. The reason the locally optimal method yields a higher EV of 0.40 (which is in between no resplits at all with EV of 0.44 and resplit all the time with EV 0.38) is that it determined resplitting to be worse in certain states, whereas your algorithm (CDP, I believe) always opts to resplit whenever possible.
    Actually, I have several algorithms, though none of them are perfect. Some are still under review. The best one is OPN, followed by CDP. With both algorithms, the result obtained is 0.38. None of them are automatic; that is, I have to specify whether I want SPL1, SPL2, or SPL3. Nonetheless, the 0.40 still piques my curiosity.


    That's not quite what's happening. In the globally optimal approach, you explore all possibilities and compute the EV at the overall round level (that's why it's so slow). These possibilities include resplitting. So resplitting is explored and calculated but since it yields an overall lower round EVit's discarded. The 0.5271 value refers to the sub-scenario I mentioned earlier, where you calculate the EV specifically for resplitting when SplitHand1 is (10,10) and SplitHand2 is (10).
    Yes, it's clear now.

    Sincerely,
    Cac
    Luck is what happens when preparation meets opportunity.

  2. #158


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    Quote Originally Posted by Cacarulo View Post
    Actually, I have several algorithms, though none of them are perfect. Some are still under review. The best one is OPN, followed by CDP. With both algorithms, the result obtained is 0.38. None of them are automatic; that is, I have to specify whether I want SPL1, SPL2, or SPL3. Nonetheless, the 0.40 still piques my curiosity.
    SPL1, SPL2, and SPL3 are options offered by casinos. In both the locally and globally optimal algorithms, these options are evaluated and only used if they maximize EV; otherwise, they’re discarded. For SPL2, the globally optimal method found that resplitting always lowers EV, so it’s dropped, resulting in an EV of 0.44—essentially corresponding to SPL1 (no resplitting). I think this is one of the major differences between "split when you can" and "split if you can, determine if better otherwise discard"

    By contrast, the locally optimal method concluded (incorrectly, due to its methodology) that resplitting is better than standing for SplitHand1, but worse than standing for SplitHand2. So you are getting a mix of standing and resplitting. As a result, the final EV landed somewhere between always resplitting and never resplitting.
    Chance favors the prepared mind

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