Tau Ngau (鬥牛) is a game that depends almost entirely on luck and the player just has to make no mistakes. It is translated as Bull Fight, and may be thus confused with Ding Niu, which is also translated the same way.
Basic rules
The game is played with a set of 32 tiles.
Players, including the banker, receive five tiles each.
From these five, the player must choose three that add up to a number that is divisible by ten without a remainder. He puts these three tiles aside (these tiles are called “bull”). The player adds the dots on the two remaining tiles and takes the remainder from dividing by ten (zero counts as ten). If the player fails to put the bull away, he is awarded zero points (actually zero, not ten, as in the “with bull” version). The banker does the same manipulations. After that, all players compare their hand with the banker’s hand.
As in most Chinese games, the [4:2] and [2:1] tiles can count as three or six, depending on the player’s preference.
Settlement
In the first version of the settlement, the rates are fixed and are the same for everyone. If the player failed to find a Bull, he pays the banker four bets. If the player was able to find a Bull, then if his hand is higher, he will receive the bet from the banker multiplied by the difference between his hand and the banker’s hand. And if his hand is smaller, then vice versa – he pays the banker. If the hand is the same, no one pays.
For example, the player’s hand is [6:5][4:1] which is worth six points (6+5+4+1 = 16, ten is taken away). If the banker failed to find a Bull, then the player receives six bets (6-0 = 6), if the banker found a Bull and his hand is [6:6][4:4], i.e. 10 points (6+6+4+ 4 = 20, tens are taken away, zero remains, which counts as ten), then the player pays him four bets (10-6 = 4). If the banker has [1:3][1:1] in his hands, i.e. also six, then he and the player do not pay each other. If the banker’s hand is[5:4][2:2], i.e. 3 points (5+4+2+2 = 13, we take away the ten), then he pays the player three bets (6-3=3).
Paradoxically, in this game, the player can pay the banker more if he set the Bull aside than if he hasn’t done it. For example, if the player folds the Bull and gets one point ([5:4][1:1]) and the banker gets ten, then he pays the banker nine bets. If he decides not to fold the Bull, then he will pay the banker only four bets.
In this case, whether the banker places his Bull before or after the players plays a big role, but the rules are silent on this. Another strange thing in these rules is that a player without a bull pays the banker in any case, even if the banker also does not have a bull.
These rules are taken from the book “Jogos, brinquedos e outras diversoes populares de Macau”, the author of which, unfortunately, described the rules a bit sluggishly, so there could be a mistake.
Settlement version 2
In the description of Tau Ngau on Pagat website, it is believed that zero is always considered zero, and bets are not multiplied and are independently chosen by each player. Players compare their hands to the banker’s hand. Whoever has a bigger hand wins. If both failed to put down the Bull, or if they have the same hand, then it is a draw and no one loses money, neither the player nor the banker. It is clear that if someone was able to put off the Bull, and the other could not, then the first is considered the winner.
This is a much more balanced calculation than the previous one, but contains less element of excitement.
Also, in this version, the role of the banker goes around the circle if the banker was able to put down the bull. Otherwise, the banker does not change.
Analysis
There is almost no strategy in the game, the main thing is simply to find three tiles that add up to 10, 20 or 30. Where a player can go wrong is to accidentally put down a wild tile ([4:2] or [2:1]) if there is an option not to do it and if this wild card can be used to improve value of the remaining two tiles. If the time to search for such a combination is limited, then the player may not have time. Because if the player finds such a combination without error (and such a combination does not always exist), then the casino does not have any advantage, as in the version from the Pagat website, and even an advantage is on the player’s side, if you believe the rules from the Portuguese book.
Chinese Dominoes GuPai 