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Thread: Unique rule value?

  1. #1


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    Unique rule value?

    What's value to player when BJ always pays- even when dealer also has BJ?

  2. #2


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    Quote Originally Posted by cottage cheese View Post
    What's value to player when BJ always pays- even when dealer also has BJ?
    cottage cheese,

    The answer depends on the number of decks. I'll show how to calculate it for 6D.

    We have to determine the probability of simultaneous BJ's. For 6D, we get the prob. as

    P(2 BJ) = [2*24*96/(312*311)]*[2*23*95/(310*309)] = 0.0021665...

    which is roughly 1 in 461.6 rounds.

    Now, with normal BS this would be a push, because with BS you don't take "even money". However, with your Unique Rule, this is instead a win of 1.5 units... assuming BJ pays 3:2, of course.

    Therefore, the player gains 1.5*0.0021665 = 0.003250..., or +0.325%, which is a pretty good improvement.

    Hope this helps!

    Dog Hand

  3. #3


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    Quote Originally Posted by Dog Hand View Post
    cottage cheese,

    The answer depends on the number of decks. I'll show how to calculate it for 6D.

    We have to determine the probability of simultaneous BJ's. For 6D, we get the prob. as

    P(2 BJ) = [2*24*96/(312*311)]*[2*23*95/(310*309)] = 0.0021665...

    which is roughly 1 in 461.6 rounds.

    Now, with normal BS this would be a push, because with BS you don't take "even money". However, with your Unique Rule, this is instead a win of 1.5 units... assuming BJ pays 3:2, of course.

    Therefore, the player gains 1.5*0.0021665 = 0.003250..., or +0.325%, which is a pretty good improvement.

    Hope this helps!

    Dog Hand
    goodness, i could not follow that math, but .325% is a nice improvement. I forgot to mention it is an 8-deck game that indeed does pay 3:2. Even if the advantage is slightly less, still very helpful to know approx value. thanks dog hand!

  4. #4


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    Quote Originally Posted by cottage cheese View Post
    goodness, i could not follow that math, but .325% is a nice improvement. I forgot to mention it is an 8-deck game that indeed does pay 3:2. Even if the advantage is slightly less, still very helpful to know approx value. thanks dog hand!
    cottage cheese,

    For 8D, the improvement is this:

    1.5*[2*32*128/(416*415)]*[2*31*127/(414*413)] = 0.0032778..., or +0.328%.

    The improvement increases as the number of decks increases, since more decks gives a lower effect of removal.

    Hope this helps!

    Dog Hand

  5. #5


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    Using my own simulator I found an improvement of +0.323% for 6D and +0.324% for 8D which is aligned with the numbers of Dog Hand.

  6. #6


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    cottage cheese,

    By the way, I should indicate that this "BJ wins vs. Dealer BJ" rule is worth a lot more to a card counter than the +0.325% (for 6D BS) shown above in this thread, because both the probability of simultaneous BJ's and the counter's wagers increase with increasing count. The actual improvement in EV depends on a number of factors, chiefly the penetration and the bet schedule, and so is most easily found through simulation.

    As an example, consider a 6D, H17, DAS game with 5/6 penetration played heads-up by a HiLo counter spreading 1-15 as follows:

    <=+1, 1
    +2, 2
    +3, 4
    +4, 10
    >=+5, 15

    This is the canned 1-15 spread in CVData.

    Without the bonus, his EV is +1.120%, but with the bonus, it's +1.568%: an improvement of +0.448%.

    I analyzed the CVData output and found that only 3.80% of the rounds had a TC of +5 or more, but the player received 5.22% of his BJ's in these "+5-or-better" rounds.

    Hope this helps!

    Dog Hand

  7. #7


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    Outstanding stuff! Now just to find the rule in the wild.

  8. #8


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    Quote Originally Posted by refinery View Post
    Outstanding stuff! Now just to find the rule in the wild.
    refinery,

    You can always ask cottage cheese! ;-)

    Dog Hand

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