Pai Gow Tile Pairs
September 8th, 2016 at 12:43:21 PM
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Are the ranks of Pai Gow Tile pairs arbitrary, or am I missing a pattern?
September 8th, 2016 at 1:20:58 PM
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Of the 32 tiles, 22 are 11 pairs of matching tiles; of the other 10, eight are 4 pairs where the number is the same (9-9, 8-8, 7-7, 5-5), and the remaining pair (1/2, 2/4) are tiles that can each count as 3 or 6.
September 8th, 2016 at 1:25:14 PM
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I don't know if there is any pattern intended, but there is a pattern that I found. This is the way I remember the order.
The highest ranking tiles are a group of special tiles, and you just have to remember them. From best to worst, these are gee-joon, 12, 2, 4+4=8, and 1+3=4. The 12, 2, 8 and 4 tiles represent heaven, earth, man and goose. I'm not sure if this is particularly relevant, but it may help me to remember them so I figured I'd mention it. Gee joon, 12, and 2 have special properties, so they're pretty easy to remember.
The next highest tiles are tiles which I identify as identical and symmetrical. That is, the two tiles in the pair are identical to each other, and the top and bottom of each tile contains the same number/pattern of pips. These tiles are ordered in descending order based on the total number of pips. These tiles are 5+5=10, 3+3=6, and 2+2=4.
Next come the identical, asymmetrical tiles. The two tiles in the pair are still identical to each other, but now the top and bottom of each tile contains a different number/pattern of pips. Again, these tiles are ordered based on descending total. 6+5=11, 6+4=10, 5+1=6, 4+1=5.
The lowest pairs are the mixed pairs. In mixed pairs, the two tiles do not contain the same pattern. Again, these pairs are ordered based on descending total: Mixed 9 (5+4. 6+3). mixed 8 (5+3. 6+2), mixed 7 (5+2, 4+3), and finally mixed 5 (4+1, 3+2).
So, in summary: pull out and arrange the top 5 pairs, which you simply have to remember. Then split the tiles into identical symmetric, identical non-symmetric, and non-identical. Within each group, arrange from largest total to smallest. Done!
The highest ranking tiles are a group of special tiles, and you just have to remember them. From best to worst, these are gee-joon, 12, 2, 4+4=8, and 1+3=4. The 12, 2, 8 and 4 tiles represent heaven, earth, man and goose. I'm not sure if this is particularly relevant, but it may help me to remember them so I figured I'd mention it. Gee joon, 12, and 2 have special properties, so they're pretty easy to remember.
The next highest tiles are tiles which I identify as identical and symmetrical. That is, the two tiles in the pair are identical to each other, and the top and bottom of each tile contains the same number/pattern of pips. These tiles are ordered in descending order based on the total number of pips. These tiles are 5+5=10, 3+3=6, and 2+2=4.
Next come the identical, asymmetrical tiles. The two tiles in the pair are still identical to each other, but now the top and bottom of each tile contains a different number/pattern of pips. Again, these tiles are ordered based on descending total. 6+5=11, 6+4=10, 5+1=6, 4+1=5.
The lowest pairs are the mixed pairs. In mixed pairs, the two tiles do not contain the same pattern. Again, these pairs are ordered based on descending total: Mixed 9 (5+4. 6+3). mixed 8 (5+3. 6+2), mixed 7 (5+2, 4+3), and finally mixed 5 (4+1, 3+2).
So, in summary: pull out and arrange the top 5 pairs, which you simply have to remember. Then split the tiles into identical symmetric, identical non-symmetric, and non-identical. Within each group, arrange from largest total to smallest. Done!
