Pai Gow (tiles) optimal strategy when not banking

JB created a fairly concise optimal strategy for pai gow when not banking. This is not to be confused with the long list of hands he previously published.

I don't think many people are dedicated enough to learn this strategy, but the staff here at the Wizard web sites believes in achieving new highs when it comes to game analysis. We welcome all comments.

Phwoor. I'll see if I can't have this memorized by the time I can afford to play pai gow.

I have been pouring over the long list of tiles and absolutely love this page.
It has cut drastically into my time on wizard of Vegas and news websites!
I am surprised by some of the splits in the very low valued hands...(zero/high five!)
I wonder if I will have the nerve to play the optimal strategy instead of playing for a push on occasion.
There are definitely some interesting deviations from "house way" or traditional play.
I am fairly certain I have seen most of these hands,
and play fairly close to optimal on the positive expectations,
but I know I have not been an optimal player on the lower half of the hands...

Just a note, there is some transpositions of tiles i have noticed,
Mostly between the look tile and the sam(gee joon).
It is somewhat widespread. Also some between tit and chit.

I will now memorize this new page and add it to my favorites,
Thanks again,JB (and Wizard) for all the hard work and obsessive dedication to solving this game!

Another note: Trump Plaza has pretty much stopped offering this game,
but I was told they will open the table on advance request for four or more players or for black chip action.

Quote: WongBo

Just a note, there is some transpositions of tiles i have noticed,
Mostly between the look tile and the sam(gee joon).
It is somewhat widespread. Also some between tit and chit.

Can you elaborate? Is this on the page linked to above, or on the big pages with all of the tile combinations?

It is on the large pages with the 3620 possible tile combinations.
I have noticed the problem most specifically on the "dealer banker" page
but have started seeing it on the other two.

Look at this example...
Gee, L2, H6, Gee
8/Pair
0.861612

The tile image shows gee joon split.
I will happily inform you of other specific examples as I see them, (by PM if you prefer)
There are quite a few, usually with the look/gee, chong/gee or tit/chit.

A few others...
L7, H2, H7, L7
9/Pair
0.767492

L6, H2, H6, L6
8/Pair
0.739893

Quote: WongBo

Gee, L2, H6, Gee
8/Pair
0.861612

L7, H2, H7, L7
9/Pair
0.767492

L6, H2, H6, L6
8/Pair
0.739893

All three pages are now fixed.

As a challenge, can you figure out what the correct play and the play which was shown have in common? Once you do, you might be able to figure out the mistake I made in the programming which produced those pages.

I'm curious how this compares to the "Wizard's Simple Strategy" (WSS), and JB's "Easier to Use Than the Wizard's Simple Strategy Strategy"(E2U). Is the percentage reduction in the HA compared to "WSS" or "E2U" worth the investment in time and brain cells to commit "Optimal When Not Banking" to memory?

The optimal strategy's house edge is about 0.22% lower than the simple pai gow strategy.

Quote: JB

As a challenge, can you figure out what the correct play and the play which was shown have in common?
Once you do, you might be able to figure out the mistake I made in the programming which produced those pages.

They all seemed to involve a teen/day and a pair and another tile of the same numerical value as the pair.
It would seem the program was randomly assigning the like valued tiles,
Recognizing like valued tiles as a pair, regardless of ranking,
and having no effect on the low hand....
Sometimes it came out right and sometimes it got transposed.

Quote: WongBo

They all seemed to involve a teen/day and a pair and another tile of the same numerical value as the pair.

Basically correct. What it was doing was going through the 6 two-tile hands, and all it was doing to identify the correct split (for display purposes) was checking to see if that particular 2-tile hand had the same rank as the low hand of the correct split. (What it wasn't doing that it needed to also do, was check to see if the opposite two-tile hand formed the rank of the high hand of the correct split.) So with paired Gee Joon, low 6, teen/day, the 8-point low hand formed by splitting is the same 8-point low hand formed by not splitting, and with that 4-tile combination, the pair-splitting way happened to be checked first and therefore incorrectly matched as the correct way to play.

With the three combinations you listed, the low or high hand of what was shown was the same rank of the low hand of the correct way to play.

Well, I am glad that you corrected it, glad to help in some small way.
I absolutely love this page.
it has already saved me $100, last night at Mohegan Sun..
I believe it went like this...
Dealer: 6/7: ping/ chong; foo/look
Me: 5/7: ping/ng; mooy/chit
PUSH!
I almost played the higher five, but remembered the optimal split
as I have been memorizing the high ten/ low ten hands this week.
JB, I owe you one! (hundred)

Quote: WongBo

Dealer: 6/7: ping/ chong; foo/look
Me: 5/7: ping/ng; mooy/chit
PUSH!

I'm glad it's working out for somebody. All of the strategy advice went horribly wrong for the Wizard the last time we played.