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Thread: Progressive three of a kind bonus

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    Progressive three of a kind bonus

    This was observed on a regular, 6D blackjack table, not a Spanish 21 as was recently discussed and seemed similar.

    Bonus had two levels -- one for $1, one for $5. Both were based on poker hands. The top $5 bonus was in the low $40Ks, the $1 nearly $5K. Both 100% bonuses were payable on 3 Ace of diamonds (player hand and dealer up). 10% of the progressive for other suited trip aces. There were other lessor payouts based on poker hands of decreasing value.

    Since most of us use ace side counts, this seems eminently countable. I'm unsure, however, how to determine mathematically how ace-rich and at what progressive level this would become a positive expectation wager.

    Thoughts?

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    This one is called Lucky Aces. The Wizzard has analyzed it. Hit frequency ~27% and house edge ~16%. It seems to me this is easily countable.

  3. #3


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    Quote Originally Posted by UNCBear4SJ View Post
    This was observed on a regular, 6D blackjack table, not a Spanish 21 as was recently discussed and seemed similar.

    Bonus had two levels -- one for $1, one for $5. Both were based on poker hands. The top $5 bonus was in the low $40Ks, the $1 nearly $5K. Both 100% bonuses were payable on 3 Ace of diamonds (player hand and dealer up). 10% of the progressive for other suited trip aces. There were other lessor payouts based on poker hands of decreasing value.

    Since most of us use ace side counts, this seems eminently countable. I'm unsure, however, how to determine mathematically how ace-rich and at what progressive level this would become a positive expectation wager.

    Thoughts?
    UNCBear4SJ,

    If you're waiting for just the "3 suited aces" portion (3SAP) of the sidebet to be +EV, you're going to be waiting a long, LONG time.

    Let's consider the $5 bet, where the jackpot is $40K, or 8000 $5 units. Off the top of a 6D shoe, the 3SAP's EV is this:

    3 diamond aces prob = 6*5*4/(312*311*310) = 3.9893723121604E-6

    3 non-diamond suited aces prob = 18*5*4/(312*311*310) = 1.19681169364812E-5

    EV = 8000*3.9893723121604E-6 + 0.1*8000*1.19681169364812E-5 = 0.0414894720464682 units.

    Thus, the house edge is 1-0.0414894720464682 = 0.958510527953532, or roughly 96%.

    The good news is that at $40K the 3SAP becomes +EV if the shoe gets down to about 108 cards with no aces played.

    Alternatively, off-the-top it's +EV if the jackpot passes 8000/0.0414894720464682 = 192820 units, or $964,100.

    Hope this helps!

    Dog Hand
    Last edited by Norm; 01-17-2022 at 11:41 AM.

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    Quote Originally Posted by aceside View Post
    This one is called Lucky Aces.
    It is not. I looked up Lucky Aces on WoO and while it is similar, this one had a progressive payout for the top two (trip diamond aces 100% of progressive, any suited aces 10% of progressive) and the lower payout hands were based on poker hands, not frequency of aces in hand. (any trips, any straights, any flushes, etc.).
    Quote Originally Posted by aceside View Post
    It seems to me this is easily countable.
    I agree. But the question remains to the group (of forum participants who actually give correct advice): what is the math of how rich in aces the shoe should be and what dollar level the progressive should reach to make this a positive expectation wager?

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    You have to provide the pay table for people to evaluate. If it's something like Blazing 7s progressive side bet, it's not worth counting. If you replace the aces with 7s, are they the same?

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    An index for a side of Aces would probably change with the amount of jackpot. Higher jackpot, lower index. Then all the various little payoffs would add some padding to the EV and variance, helping to lower the index. If someone wanted to count just the Ace bet with a balanced count, it would probably be Ace of Diamonds = +12, other Aces +4, all other cards +1/2.


    Sent from my iPad using Tapatalk

    Edit: should be "all other cards -1/2", or the Aces could be tagged negative and the non-Aces positive.
    Last edited by bejammin075; 01-18-2022 at 03:58 AM.

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    Quote Originally Posted by Dog Hand View Post
    If you're waiting for just the "3 suited aces" portion (3SAP) of the sidebet to be +EV, you're going to be waiting a long, LONG time.
    heh heh. That's why I asked.
    Quote Originally Posted by Dog Hand View Post
    Let's consider the $5 bet, where the jackpot is $40K, or 8000 $5 units. <some good math presented>
    Thank you, Dog Hand! this is they type of guidance I was looking for.

    Quote Originally Posted by Dog Hand View Post
    The good news is that at $40K the 3SAP becomes +EV if the shoe gets down to about 108 cards with no aces played.

    Alternatively, off-the-top it's +EV if the jackpot passes 8000/0.0414894720464682 = 192820 units, or $964,100.
    Very interesting stuff.

    This appears to be a localized rather than wide-area networked progressive (possibly casino rather than region based). I'd not seen this before this weekend and now I've seen it in two different casinos. In the one I was in today, the $5 bet progressive was up to a bit over $117K and the $1 bet progressive was just over $15K.

    Quote Originally Posted by Dog Hand View Post
    Hope this helps!
    Very much! Thank you!

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    Quote Originally Posted by bejammin075 View Post
    An index for a side of Aces would probably change with the amount of jackpot. Higher jackpot, lower index. Then all the various little payoffs would add some padding to the EV and variance, helping to lower the index. If someone wanted to count just the Ace bet with a balanced count, it would probably be Ace of Diamonds = +12, other Aces +4, all other cards +1/2.
    I hadn't really been planning a count just for this side bet since I already keep an ace side count and intended to find ways of utilizing that, but this is an intriguing option. Thanks, Bejammin075!
    I agree that the other, smaller payouts aren't really worth tracking, though they'd add a bit of EV padding as you mention.

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    Quote Originally Posted by UNCBear4SJ View Post
    I hadn't really been planning a count just for this side bet since I already keep an ace side count and intended to find ways of utilizing that, but this is an intriguing option. Thanks, Bejammin075!
    I agree that the other, smaller payouts aren't really worth tracking, though they'd add a bit of EV padding as you mention.
    I didn't say the small payouts are not worth tracking. I don't know what they are, or how many of them there are. Actually I think it would be important information to know. The Aces are trackable and some math could be developed to tell when the side bet is profitable. If you factor in the many small payouts, you will detect a +EV situation more often. If you already side count Aces, maybe you could modify your side count to pay special attention to the Ace of diamonds, there are only a few in each shoe.

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    Quote Originally Posted by Dog Hand View Post
    3 non-diamond suited aces prob = 18*5*4/(312*311*310) = 1.19681169364812E-5
    Dog Hand, could this part of the bet be calculated differently? My interpretation of UNCBear's description is that it would be any triple Aces that aren't 3 diamonds. So the first Ace could be any Ace, the second Ace could be any Ace (including diamonds) and the 3rd Ace must be non-diamond. Well the order doesn't matter, point is, only 1 Ace needs to be non-diamond, so instead of your numerator being 18*5*4, I think it would be 24*23*18. What do you think?

  11. #11


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    Quote Originally Posted by bejammin075 View Post
    I didn't say the small payouts are not worth tracking.
    Sorry for putting words in your fingers. The $5 ones are:
    Suited trips, non aces: $750
    Straight flush: $200
    non suited trips: $100
    Straight: $25
    Flush: $15

    $1 ones:
    Suited trips, non aces: $125
    Straight flush: $25
    non suited trips: $20
    Straight: $7
    Flush: $3

  12. #12


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    If I use my interpretation of the Aces side bet, using the probability (24*23*18)/(312*311*310), and substituting that in Dog Hand's equation, I get about 0.296 bet units won, or a 70.4% house edge. But if all the other payouts were included, that could change things a lot, depending on what they are.

  13. #13


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    Would a wrap-around King-Ace-Two count as a straight?

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