, I have posted a number of math analyses in this forum (including one on the first page of this thread) that no one has commented on.
TwoFeathers, you are among the many people in this forum that I do like and respect. You are also the only fellow southeastern-er I am aware of who posts with any regularity on this forum!
Shackelford is industrious, intellectually curious, bright and pays attention to quality in his work. He has achieved a lot and I respect him greatly.
Babs is smart and grounded, she impresses me as a decent human being - sort of a warden amongst the forum's misfits and weirdos.
I am fascinated and very impressed with Romes and Miplet especially. Also, there are a couple of dozen people who only post occasionally in the forum who I wish would post more often - I would love to learn from them.
However, I have posted a number of math analyses in this forum (including one on the first page of this thread) that no one has commented on, and my disappointment in that has probably soured my attitude towards the in-forum math geeks..
Most of all, I admit to having philosophical differences with PaigowDan and (especially) MathExtremist. They seem to have some good qualities but I have become weary of the parochialism, arrogance and condescension that they have directed at me (and others) in their posts. I am unaccustomed to condescension and, as a result, I'm pushing back at Dan with my own condescension. It is what it is.
The dealer (or player) will be dealt a 7-card Ace-High Pai-Gow with a frequency of 9.4%. Here is what I calculate for a range of ace-high pai-gow hands with a composition-dependent model that I have.
Hand Win Push Lose EV A-KQ-J743 0.1446 0.3753 0.4811 -0.340 A-KT-9732 0.1206 0.3177 0.5614 -0.447 A-QJ-T732 0.0911 0.2621 0.6486 -0.562 A-JT-9732 0.0426 0.2053 0.7527 -0.712 A-87-6432 0.000 0.1116 0.8887 -0.889
With an AKQxxxx hand, you are able to put a KQ in front, but your EV is still -0.34. When your Ace-high pai-gow is AQJTxxx, your hand up front drops to a QJ and your EV plummets to about -0.56. And if your 2nd card is a Jack or lower, then God help you.
So, allowing the dealer's hand to automatically push when its an ace-high pai-gow is worth something like 5 - 5.5% in EV. That's an enormous advantage for the dealer that the player needs to overcome by being able to see the dealer's hand and setting his hand optimally.
Getting this thread back on topic ;-), the above indicates that the frequency of the Ace High Pai Gow hand occurs for the dealer just under 10%. I think a less noticed mechanism is in the 6-8% range...players notice a bad event one in 10-11 hands. Once in 14 or so hands, while seeming a small difference, is important in "feel" of a mechanism.
Gordonm888, could I ask you to calc how often a player would benefit from pushing on the Ace High Dealer Pai Gow because otherwise they would lose?
I would have a tendency to just muck my cards if I couldn't beat the dealer...as I think about that, the game could incorporate that rule (e.g. the player shall muck their loser hands immediately) in an effort to speed up the game...that type of time and motion savings may provide some room in HE necessary to maintain profitability. If the dealer didn't have to reveal and check 50% of the player's hands because they were mucked as losers, that would be a positive for game speed.
By the way, house way for two pairs smaller than 6's is to ALWAYS play two pair behind, regardless of low hand. For example, 73/55442.
Thank you for asking! Here is my calculation::
On 1.04% of hands, the dealer will have an Ace-High Pai Gow (which is defined to include either a natural ace or a joker as the high card), and the player would have a hand that would normally lose to the dealers hand. (A dealer will be dealt an ace-high pai-gow with a frequency of 9.79%, I slightly misquoted that number in an earlier post.