In the movie
21, the main character, Ben, participates in "counting cards" in the game of blackjack. This is a simple system which allowed him and his teammates to know which dealers were favorable; in other words, a higher (although slim) probability of winning.
I won't go over the details of how to count cards, but basically they used a -1, 0, 1 system. 2, 3, 4, 5, 6 were given the number -1; 7, 8, 9 were given 0, and 10, Jack, Queen, King, Ace were given +1. The premise of the system is that every time a card was revealed (it doesn't have to be your own), you would add or subtract accordingly. By doing so, we get a "value"; this value tells us whether or not the current deck is favorable to bet on.
Basically, a high value meant it was not favorable (since to get a high value, you exhaust the 10s and Aces, which are the easiest way to win), and a low value meant it was favorable (using the opposite reasoning, by exhausting the low numbers, there is a higher probability of getting those 10s and Aces).
An example to cement the point before I move on:
We add the appropriate numbers as they appear from left to right:
1-1+0+0-1-1-1-1+1+1 = -2
We end up with a final "value" of -2. This tells us that more low numbers have been used, and therefore we have a higher probability of getting 10s and Aces.
Before I go to the main point of this post, I'll mention that Casinos use multiple decks, I think 6 is the number, when playing Blackjack. However, they do not shuffle the cards back in every game; this is what makes the counting system possible.
In this post, I propose the usage of card counting while playing Mahjong. Although the nature is different, the motive is the same; to predict probability during a game.
The simplest way (And perhaps the only practical way) to do so is if you are looking for one particular suit, so you are trying to form either a half flush or a full flush. For example, I am going for a half flush of Pin; we will denote the suit of interest with a value of +1.
For the other suits (AKA the ones we are not interested in), we denote one of them +100, and -100. For our example, we will denote Man +100, and Sou -100.
Finally, any honour tiles will be denoted 0, since these tiles are essentially "floaters", tiles that take up space that most of the time no one wants.
It may seem preposterous to "count" tiles, but I propose that it is in fact practical. Once again, this is best shown with example.
Due to the nature of Mahjong, and how we discard tiles (As opposed to Blackjack, where we can only add cards, not get rid of them), it would be redundant to count tiles in the hand for two reasons:
1. It will result in double counting of your own hand (You count once in the hand, and again when you discard; we are only interested in the discarded ones)
2. You can't see your opponent's hand. If they decide to steal a tile from the discard, then we in fact do include those in the count (only the new tiles revealed by the player declaring Pon, Chi, Kan though).
As such, we will only count discarded tiles, and those revealed when taking from the pool.
I start by discarding 3 Man, and the computer players follow by discarding honour tiles. So the total count so far is +101 (The +1 comes from the Dora indicator, which we also include when counting, as it is "in the pool" per se). As an aside, I pick Man to be +100 because it is easily memorable (In the sense that Man tiles are essentially large numbers, and you obtain large numbers by adding).
We continue in this fashion:
We start with my second discard, 1 Pin, then South player's (Player on the right) second discard.
-1000+0+
0+0+0 = +1
Not shown in the picture is that I declared Pon on West player's South tile, hence the triple bolded +0. I now begin again, starting with my third discard, South player's Third discard, then West player's second discard, and North player's second discard. Then we count accordingly:
-100+0-100+0 = -201
+100+1+0+0 = -102
-100+1+0-100 = -303
+100+1-100+1 = -305
+0+1-100-100 = -506
+0-100+100+0 =
-506
So the final count (Before I declare Ron) is
-506. I know what you're thinking. "-201 + 100 + 1 isn't -102, it's -101". This is true, but it saves work on unnecessary math. The point is to keep track, not to add. So we essentially have two values we keep track: the +100 -100 series (The uninterested tiles) and the +1 series (The tiles of interest). In that sense, only the first digit (And the second digit should the count go to four digit numbers) are subjected to the negative sign.
But what does this number -505 tell us. It lets us infer a few things.
1. As of this point in the game, more Sou tiles have been
dealt than Man tiles (This is the only conclusion we can ascertain).
2. There are, at most, 30 Pin tiles left in the game (At most is the best case scenario, as the final 14 tiles are never revealed unless someone gets a Kan. Even so, that leaves 5 Reverse Dora tiles that are not revealed during the game.)
3. The proportion of Sou tiles to the rest of the tiles is
less favorable (This is inferred by comparing the first number, in this case 5, with our last number, which is 6. Since the last number is greater than the first number, we infer that it is less probable of drawing a Sou than anything else). This last inference is very sketchy, as the suit of interest only encompasses 25% of all tiles, while the other 75% is encompassed by the other suits and the honour tiles. If there was at least 3 deviations away from that value (So -18 or +18), then it would be a stronger inference that it would be
more probable to draw the suit of interest.
It's not hard to keep track of two numbers in your head; with practice it'll help you up your game.
PS: That hand was a half-flush with one triplet honour/wind. The way the hand is constructed, it sums up to 30 fu, 3 fan, which amasses 5800 points, all to be paid by North player (The one who dealt the winning tile). I'll do a post on the point system eventually...
