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Originally Posted by
UNCBear4SJ
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
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