Gialmere
Joined: Nov 26, 2018
• Posts: 1075
Thanks for this post from:
September 5th, 2019 at 5:34:42 PM permalink
Pai Gow Riddle

Since coming to the wizard sites I've been slowly learning the game of Pai Gow. I've finally reached a level where I've memorized all the tile names and ranks and can set a hand in the traditional way in 10 seconds or less. So it's time to learn the Wizard Way and complete my masters in what I call "casino game skills for recreational players".

While I found the WOO PG pages to be invaluable once reaching an intermediate level of understanding, I found even them to be intimidating at first. I ended up at PaiGow.com which is a nice site for players who need to be taken by the hand and slow walked through the game from the beginning. (It also has a good practice area that helps you memorize things although you have to pay to get its advanced startegy.)

Anyways, there's a fun facts section still under construction that presents the following riddle: Which of these two hands would you rather be dealt? Here are the hands...

Hand #1 is the obvious, knee-jerk choice but is it the correct one? I've pondered on this, moving the available remaining tiles around in my mind, but have decided to present it here cold. Are there any PG masters here that can elucidate? (I confess my brain is stuck in "uhhhhh" mode.) I should note that the site does not specify if you're banking, nor if you're playing to win or not to lose. It does, however say that all you assets are on the line. Also, since the section is under construction, the answer hasn't been posted yet.
Have you tried 22 tonight? I said 22.
charliepatrick
Joined: Jun 17, 2011
• Posts: 1854
Thanks for this post from:
September 5th, 2019 at 10:31:58 PM permalink
I was surprised when I worked it out but you would prefer to have hand #2! I suspect part of the logic is you have one of the tiles that could create a higher pair for the dealer.
Hand #1 - chances of winning 96.601% - chances of losing 0.015% - EV = .917560
Hand #2 - chances of winning 96.918% - chances of losing 0.181% - EV = .918916
Gialmere
Joined: Nov 26, 2018
• Posts: 1075
September 6th, 2019 at 5:16:11 PM permalink
Thank you CP. The math is certainly nonintuitive to say the least. I think you're right about the banker high hand getting choked off. It's still weird though.

For the first deal you're offered paired Yun and Gor. Only paired Gee Joon, Teen and Day can beat that and the bank would need two of those three to win. How could a hand with a mere (by this riddle's standards) Gong possibly improve things?

For the second offering you still have a paired Gor now with said Gong. The Gong, however, contains Teen and Yun tiles which eliminate two of the four pairs above the paired Gor leaving the bank only two pairs (Gee Joon and Day) to beat it. The Gong is obviously more vulnerable. The bank could tie it with the other Teen and a Chop Bot. A Wong could be made from either the remaining Teen tile or by using a Day Tile (although using a Day would mean only a paired Gee Joon would be left to beat the paired Gor). There are also, of course, a dozen pairs still available above the Gong.

But the math doesn't lie. Hand #2 is superior due to some freak mathematical wizardry for this special case. The riddle really does boggle the mind.
Have you tried 22 tonight? I said 22.
Gialmere
Joined: Nov 26, 2018
• Posts: 1075
Thanks for this post from:
October 23rd, 2019 at 7:39:53 AM permalink
Dice Riddle
A dealer slams a shaker containing two dice down on the table, peeks under the lid and tells you that one of the dice is showing a 1. You then place a \$1 bet that snake eyes has been rolled. The dealer opens the shaker lid and reveals two 1s. Assuming true odds, how much money should you be paid?

Have you tried 22 tonight? I said 22.
charliepatrick
Joined: Jun 17, 2011
• Posts: 1854
Thanks for this post from:
October 23rd, 2019 at 8:52:31 AM permalink
This one, albeit in a different guise, was asked on another thread a few years ago.
Think one die is red and the other is green.
Essentially there are 11 ways out of 36 of throwing at least one "1", think 1-1 1-2 1-3 1-4 1-5 1-6 2-1 3-1 4-1 5-1 6-1. Thus true odds would be 10/1.
unJon
Joined: Jul 1, 2018
• Posts: 1409
Thanks for this post from:
October 23rd, 2019 at 1:48:50 PM permalink
Quote: Gialmere

Dice Riddle
A dealer slams a shaker containing two dice down on the table, peeks under the lid and tells you that one of the dice is showing a 1. You then place a \$1 bet that snake eyes has been rolled. The dealer opens the shaker lid and reveals two 1s. Assuming true odds, how much money should you be paid?

Does “one of the dice is showing a 1” really mean “AT LEAST one of the dice is showing a 1”?

Also need to know if the dealer would always say the same sentence if at least one dice showed a 1. Otherwise no way to get to true odds, because you don’t have an the conditional probability to run a Bayesian.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
charliepatrick
Joined: Jun 17, 2011
• Posts: 1854
October 23rd, 2019 at 3:25:20 PM permalink
Quote: unJon

...Does “one of the dice is showing a 1” really mean “AT LEAST one of the dice is showing a 1”?...

I think that's a reasonable assumption - at least one of the dice has a "1".
Gialmere
Joined: Nov 26, 2018
• Posts: 1075
October 29th, 2019 at 9:18:39 AM permalink
Quick Logic (easy)
At a casino, Andrew is closely watching Susan while Susan is closely watching David. Andrew works for the casino but David does not. Is a casino employee closely watching a non casino employee?

Yes?
No?
Insufficient data?
Have you tried 22 tonight? I said 22.
unJon
Joined: Jul 1, 2018
• Posts: 1409
Thanks for this post from:
October 29th, 2019 at 9:47:09 AM permalink
Quote: Gialmere

Quick Logic (easy)
At a casino, Andrew is closely watching Susan while Susan is closely watching David. Andrew works for the casino but David does not. Is a casino employee closely watching a non casino employee?

Yes?
No?
Insufficient data?

Nice one.

Yes. If Susan is a casino employee, then her watching David makes the question a yes. If Susan is not a casino employee, then Andrew watching her makes it a yes.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
Wizard
Joined: Oct 14, 2009
• Posts: 21007
Thanks for this post from:
October 29th, 2019 at 9:53:54 AM permalink
Quote: Gialmere

Dice Riddle
A dealer slams a shaker containing two dice down on the table, peeks under the lid and tells you that one of the dice is showing a 1. You then place a \$1 bet that snake eyes has been rolled. The dealer opens the shaker lid and reveals two 1s. Assuming true odds, how much money should you be paid?

If I may reword the question as "A dealer will slam a shaker containing two dice down on the table, peek under the lid until at least one of the dice is showing a 1. You then place a \$1 bet that snake eyes has been rolled. The dealer opens the shaker lid and reveals two 1s. Assuming true odds, how much money should you be paid?

Given that wording my answer is

\$10 + your original \$1 wager

As was noted, the same problem was debated here for months already. It is still a sore subject with me.
It's not whether you win or lose; it's whether or not you had a good bet.