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Subject: Strategies for Latin American Dominoes rss

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Francisco Alcala
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The following strategies apply to the Latin American game of dominoes. The rules for this variant appear in another post on the rules forum, and I strongly suggest reading that thread before reading these strategies, since they apply to this game variant only.

I must say that Dominoes is not a luck-driven game, even when it appears to be so. Yes, there is some luck at the tiles each player takes, but from that point instinct, experience, and knowledge will define the winner. The fact that experienced players can wipe out casual players with ease confirm that Dominoes is a game of skill.

For experienced players, many of these strategies might appear as very basic or even misleading. Please take into account that these strategies were written considering inexperienced players as the target audience.

FOR A START, SOME NUMBERS

A complete set of double six dominoes has 168 points in total. This number gives us some interesting and useful information:

- Are you in a situation where you can block a game, and not sure if it is convenient? Do a quick count of the points on the played tiles, add the points of your tiles, and subtract this figure from 168. The result is the total remaining points on the other players’ tiles. Divide this number by 3, and that’s the average number of points each player has in their remaining tiles. Is this number lower than your own remaining points? Then there is a high chance of losing the round. On the other hand, if you have fewer points than this average, then your team has good odds of winning the blocked game.

- If you divide 168 by 28, you get 6. That’s the average number of points for a single tile. Note that it is not 7 (as anybody might think because 7 is the most probable roll when throwing two dice), because dominoes have combinations with a 0.

- Furthermore, dividing 168 by 4, you get 42. This is the average point count for the initial hand of 7 tiles. At the beginning of the round, count the points of your hand. Is a lot more than 42? Then you have a high hand, and points will be an issue during the round. Is far less than 42? Then you have a low hand, and good possibilities of winning a blocked game. Actually, a hand will oscillate between 15 (the lowest possible hand) and 69 (the highest possible hand).

- An additional numeric curiosity: on a blocked game, the sum of the remaining points is always an even number. So, both teams may have an even number of points, or both may have an odd number of points. If the sum of the remaining points for both teams is an odd number, then there is an error in the count, a tile was illegally placed, or one of the players is cheating (!).

BASIC CONCEPTS

There are seven tiles of each number
In a double-six domino set, there are seven tiles of each number. For example, there are seven tiles with a 3 on them: 3-0, 3-1, 3-2, 3-3, 3-4, 3-5, and 3-6. This is one of the most important concepts when playing dominoes: you should always pay attention at how many tiles of a certain number have been played (it is obvious by looking the played tiles); this way, you can guess if a player has tiles of a certain number or not. For example, if there are four tiles of 5 in play, and you have one more, then there are only two other tiles with the number 5 in the hands of the other players. Even more, by looking at the tiles in play and the one you have, you can easily find out exactly which other tiles remain.

An example of a practical application: it’s your turn, and you have the opportunity to play a tile in order to leave both ends of the game at 3. You look at the table, and find the 3-0, 3-1, 3-3, and 3-5 already played. You have 3-6 as the tile you pretend to play over a 6. You are trying to make the next player to pass and miss his/her turn by leaving only a choice of 3 for his/her to play. You can see that the remaining tiles of 3 are the 3-2 and the 3-4. Now, you have remembered that the next player passed previously at 4, so you can be sure that he/she doesn’t have the 3-4 in his/her hand. The only tile he/she might have is 3-2, so there is a high possibility for making him/her to miss a turn.

The firm
This leads us to another vital concept: the FIRM. This is the name assigned to the last tile of a certain number, when the other six tiles are at play. A double cannot be a firm. Suppose that there are six tiles of number 2 at play, including the double. This is only possible if one of the ends of the game have a 2; since there is only one remaining tile of 2, that tile is the firm. The player that has the firm can control the game to a certain point, because:
- That player cannot be forced to pass. However, he/she can be forced to play the firm tile.
- The other players are forced to play at the other end of the game, since nobody has another tile to play at the 2.
The player that has a firm must be careful. Other players are restricted to one of the ends of the line for playing, INCLUDING HIS/HER PARTNER. A player always has to evaluate the convenience of keeping a firm, against the possibility of affecting his/her partner.

The miss
Another important concept is the MISS. The miss refers as how many numbers you are lacking. At a certain moment, you must look at your tiles and find out which numbers are missing. If you do not have tiles for the numbers 2, 3, and 5, then you have 3 misses in your hand.

A good way of evaluating if you have a good or a bad hand is to look at how many misses you have. A hand with one miss is a good hand; one with 3 or 4 misses is a bad hand. A hand with no misses is not necessarily good, because it will usually have too much variety in numbers, impeding the owner to form a strategy.

Players always try to avoid passing, because this reduce the possibility of dominating the round. So it is important to keep the misses in our hand to a minimum. If you are in a situation where you have two options for playing a tile (and these options are apparently equal), then analyze if one of the tiles will leave you with an additional miss. If so, play the other one (this is assuming that there is no other evident advantage on playing one of the tiles, like getting a firm or forcing a pass of the next player).

Finding the other players’ misses is also important. The most evident way of noticing a miss is when a player passes, showing one or even two misses in his/her hand (if a player passes when there is a 4 and a 6 in the ends of the line, then it is assured that he/she have both misses at 4 and 6). Other, more subtle ways of finding a miss, can occur when a player plays a firm (the player may have a miss at the number of the other end of the line) or covers a number that tried to keep open previously.

Killing a double
Doubles cannot be firm tiles. Why? If you have a double, let’s say 4-4, and the other six tiles with 4 are already on play, then your double is unplayable. It is dead.

This is a “feature” of the doubles. They can be killed. If there are five tiles of a certain number in play, and the double is still in somebody’s hand, then a player can play the sixth tile covering the number, killing the double.

The player that has the killed double cannot dominate. The tile is also dead weight, so the options for play are reduced. It is indeed a bad thing. Even worse if the killed double is a heavy one (the 5-5 or 6-6).

If you have the opportunity to kill a double, you must consider that the double could be owned by your partner. Some players usually do a self sacrifice, killing their own doubles, in order to give an advantage to their partner (giving them a firm, for example).

A double that is the only tile of that number in your hand is susceptible to be killed (if you have the 5-5, and none of your remaining tiles have a 5, there is danger of getting the 5-5 killed). Those doubles should be played at the first opportunity (unless the situation gives you a better choice).

SHOWING THE PATH

Dominoes is a game of imperfect information. You cannot know which tiles other players have. You also cannot talk with your partner. So how do you tell your partner about which numbers to play?

There are some ways to do it. A direct approach is to leave the same number on both ends of the line at the first opportunity. Other way is to play a couple of tiles that leave the same number in one of the ends of the line. The starting player can easily show the path with the starting tile (even more if the player starts with a double).

Covering numbers can tell your partner about the numbers you don’t like. Suppose that, at a certain moment, there is a 1 in one end. You have only two tiles with 1s, so you play one of them fast and with decision, covering it. Your partner then may deduce that you are not interested in having a 1 at the end of the line (and it’s true; it could cause you a miss and even a pass later). It could also be interpreted by your partner as that you are interested in the number you played (if, for example, you covered the 1 with the 1-5, your partner could think that you want to play for 5s). These ambiguities are the sort of thing that makes this game interesting.

GETTING ALL TOGETHER – SOME EXAMPLES

You are the starting player (A). You have the 3-1, 3-3, 3-5, and 3-6 in your hand (among other three tiles). Starting with the 3-3 is a good decision:
- It tells your partner (C) that you have a strong hand of 3s.
- There are only three tiles with 3 remaining: 3-0, 3-2, and 3-4. As an average, each of the other players should have only one tile with a 3. So, the starting tile can force a pass for player B.

Suppose that B plays 3-2. C then should play a 2, leaving a 3 at one of the ends of the line (following the game marked by A). If C plays 3-0, for example, you could deduce that C has a miss at 2 (there is no good reason for blocking the start of a partner earlier in the round; if C covers the 3 when having tiles with 2 available, then C is trying to make his/her game or didn’t care about his/her partner starting tile; in any case, this shows that C is a deficient player).

OK. C is a good player, so he/she plays a 2: 2-4. Now, there are two tiles with 3 somewhere, 3-0 and 3-4. If D has 3-4, he/she could play it at the 4, leaving 3 at both ends. If this happens, A could deduce that D also has the 3-0 tile (leaving the game with the same number at both ends when you have a miss on that number is not a very smart choice). Even if D has the 3-0, playing the 3-4 at the 4 is a risky choice, but valid: D is trying to force A to play all the tiles with 3 and destroy A’s strategy; however, trying that so early in the round is very risky: D doesn’t know yet where the other 3s are, so it is possible that D could be forced to play his/her last 3 and leave A with a firm early in the round (with disastrous consequences).

So, if D has both tiles (3-4 and 3-0), a better option is to play 3-0, covering the 3. Playing the 3-4 at the 3 is also risky: it is too early in the round, and since C played 2-4, it is possible that C has more 4 tiles. 3-4 at the 3 is feasible if D has three or four tiles with 4, but it is also a very aggressive play that could affect B. D should not forget that he/she is the last player, so he/she is the one with lesser probabilities if dominating the round (at least so far). By playing 3-0, D is covering A’s start; this tile also does not allow A to bring another 3: there are a 0 and a 4 at the ends of the line, and D knows that A has neither 3-0 (already played) nor 3-4 (D has it).

Now you (A) have to play. You can play any tile with 0 or 4 (supposing you have one). You cannot play 3-4 because D has it (but there is no way of knowing it yet). No matter what your play is, C will figure out that you don’t have the 3-4 (since you didn’t play it), or that you have it and played in a conservative style, keeping the tile for a better occasion.

--------------

Well, that’s just the beginning. I hope these basic strategies could help some new players to get into the game faster, and to find that this game has choices that really matter during the game.
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Mattias Wikstrom
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Thanks for posting this! It was very illuminating.
 
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p55carroll
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A good, useful article. Thanks!

Just one little quibble:
Quote:
If you have a double, let’s say 4-4, and the other six tiles with 4 are already on play, then your double is unplayable. It is dead.

That's only true if the other 4s are all covered in the layout. If the other six tiles have been played, but there is a 4 at one end of the layout, then the double is not dead.
 
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Fabrizio Marcotulli
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Patrick Carroll wrote:
A good, useful article. Thanks!

Just one little quibble:
Quote:
If you have a double, let’s say 4-4, and the other six tiles with 4 are already on play, then your double is unplayable. It is dead.

That's only true if the other 4s are all covered in the layout. If the other six tiles have been played, but there is a 4 at one end of the layout, then the double is not dead.


Hi,

I just want to address that, for the case in question, either the remaining 4s are covered or there is a 4 on each end of the line, making it so the double blocks the game immediately.
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