Recently I have started playing an online Japanese mahjong game called JanRyuMon. It is a really nice and graphically detailed game to play.
If you want to play this, you must first know the basics.

You must know what tiles you are dealing with. As for the wanzu series, it is easy to tell if you know Chinese well. If not, then you might need to look at how it arranges first before knowing what to do.
Basic Rules
Game can be in a normal 4-person Ariari mahjong, Nashinashi mahjong, or a 3-person Mahjong game. You will start with 13 tiles, and the objective of this game is to complete the hand with 1 pair and a set of sequences/triplets. (The exception will be the 7 pairs (七対子) hand.)
Drawing pile - This is where players will draw the tile. It goes clockwise.
Back tile - Where the dora indicator will be. The last 14 tiles are not usable.
Discard pile - Tiles that players discarded. If someone declares a riichi, the tile is placed horizontally instead.
Dora - You may notice that at the back tile, 1 upper tile is open. This is an indication that the tile 1 step higher than the indicator is the dora. It is a key in getting high scores. A maximum of 5 dora indicators are allowed at a single period of time.
To better understand what that means, look below
1-2-3-4-5-6-7-8-9-1 (For all 3 types)
E-S-W-N-E (Wind)
White-Green-Red-White (Dragon)
Lets say a 2-pin is the dora indicator. That means 3-pin is now a dora.
A special case is for 5-pin, 5-sou and 5-man. 1 in 4 of them will be coloured in red, and it is automatically a dora tile on its own.
Declaring a pon - (Meaning you want the triplet) can be called from any players. It must be open.
Declaring a chi - can only be called from the person on your left. In 3-mahjong game, calling a chi is not allowed. (In this case, you want a 3-sequence)
Declaring a kan - When you have a concealed triplet and have drawn the 4th tile, you can declare a closed kan. Even if there is a closed kan already revealed, your hand is still considered as fully closed provided you didn't do any pon/chi. If someone discards the 4th tile of the concealed triplet, you can declare an open kan and it is considered as open hand. If you have an open triplet and draw a 4th tile, you can declare a late kan. Taking the 4th tile discard to make a kan on the open triplet is not allowed. In all cases, declaring a kan will open a new dora indicator. More than 4 of it and the game will start over again. When declaring a kan, you need to take a tile from the back.
A special rule occurs when you declare an open kan (Meaning you take the 4th tile from someone's discard),. If you get a Rinshan Kaihou (Winning the hand from the dead wall after declaring kan), the person who discarded it will have to pay you in full based on the score you won instead of everyone dividing their chips to pay you. The special rule is known as, "The one responsible pays" but it is optional.
Declaring riichi - Only when your hand is fully closed, you can declare a riichi if your hand is ready to win. This costs 1000 chips to declare. Once you declare riichi, you cannot change your hand anymore.
Declaring tsumo - A tsumo is defined when your hand is ready to win and you have drawn a winning hand. If your hand is strictly closed and win by a tsumo, you'll get 1 han.
Declaring ron - A ron is defined when your hand is ready and someone discards the card that you want. It is possible for a double ron, even a triple ron! Make sure your hand have at least 1 han in order to win.
Furiten - This happens when your hand is ready, but you're waiting for the tile that you yourself have discarded. In this case, you cannot ron that tile from other players but can still win if you self-draw it. This is a bad situation which you need to look at your discards. Once discarded, it is a furiten tile for you.
You are also in furiten if you declare riichi but fail to get it on 1st opportunity.
When the game has no winners - Most commonly happens when players run out of drawable tiles. Remember that the last 14 tiles are not touchable.
Another situation is when someone declares a Kyuushukyuhai right from the start, that means that he has at least 8 tiles with terminals (1 or 9) and honors. This indicates that his hand is so bad that he wants to have a new hand. The starting hand can evolve into a Kokushi-Musou, but that would be a very easy giveaway as you will be discarding simple tiles at the beginning unless you are expert in making damaten hand. The condition is that there are no calls yet until his first turn.
Another situation is when everyone discards the same wind tile on their first discard. This may not look significant, but I find that you can actually do that to stop someone who made a Double Riichi. :P (Not applicable to 3-way mahjong)
And lastly, if more than 4 kans are declared or when more than 1 player declared 4 kans, (one player is allowed to have 4 kans, since SuuKanZi is a yakuman.) the game automatically ends and starts over. (Besides, too many doras = non-special yakuman hand spree. =.=)
Other situations can occur when all 4 players declare riichi, then the game ends automatically, or when 3 people take the very same tile that they need to win all at once. These 2 conditions are optional though.
Tenpai/No-ten - Only when the players run out of drawing tiles. A tenpai is when your hand is ready to win, and vice versa. In a rare case, a Naga-nashi-mangan (In case where the player discards nothing but terminals/honors, all tiles must not be called.) can be declared, and that player will win a mangan hand automatically.
Buttobi (A.K.A Bankrupted) - If any players do not have enough chips to continue playing (as in, getting negative points), the game may automatically end depending on the rules.
How to Play
The dealer will throw the dice, deciding on separating the draw pile and the back pile. Then, each player (dealer first) will take on a set of 4 3 times, then take 1 last tile. (For the dealer's case, it will take another one after that) During your turn, you'll draw a tile and discard one. How to move on is referred to the rules of the game.
I'll look into more detail in the keys of winning a decent hand.
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