In my logic, triple check not possible. Because I assume there is a move with two pieces at once needed. The only move I know is castling. The King can not give a check. So is triple check impossible?
Triple check is possible in xiangqi, aka chinese chess. There is even the possibility for quadruple check.
Unique to xiangqi is a triple check, which arises in three combinations. In the first case of a cannon, a chariot or soldier, and a horse, the horse moves to give check, uncovering a double check from the chariot and the cannon. In the second, rarer case of a chariot or soldier and two horses, the chariot moves to give check, uncovering a double check from the two horses. In the third case of two cannons and two horses, one cannon may uncover a double check from the horses and act as a screen for the other cannon. Quadruple check is also possible, arising with two horses, a chariot, and a cannon. Triple and quadruple check cannot be blocked.
To look at this systematically, let's say white is attempting to triple-check black.
At the start of white's move, black's king is not in check. So we have to go from zero checks to three checks.
When a piece moves:
- the previous square it occupied becomes vacant (possibly creating a discovered check)
- the target square becomes occupied (possibly creating a check from this new position).
These discoveries are possible:
- Pawn, knight or king moves: discovery by bishop, rook or queen.
- Bishop moves: discovery by rook or queen.
- Rook moves: discovery by bishop or queen.
That only leads to two checks. (One unoccupied square can't cause two discovered checks because there is only one rank/column/diagonal between the king and that square).
What other options exist? Do any of the special-case moves support a third check?
This causes two squares to become vacant, so two discoveries are theoretically possible. Could this work? Let's say white plays gxf6. For this to be a triple-check, and hence attacked by the pawn, black's king must be on g7 or e7. Assuming g7 (since it creates a possible discovery) we have a position like this:
8/6k1/8/4RpP1/4BRQ1/8/8/5K2 w - - 0 1
When the pawn captures, it opens up a discovered check along the g file. You can see that the removal of the black pawn cannot create a discovered check, as it is positioned a knight's move from the king, neither on a file, rank or diagonal.
So, en passant can achieve:
- two discovered checks
- one discovered check, plus one regular check by the pawn
- but not two discovered checks plus a regular check by the pawn
Castling causes two pieces to move at once, which sounds promising. But one of those pieces is a king, which can never give check, so it doesn't help. And since the rook starts from A1 or H1, it can never give a discovered check in the process, either.
So, at best, castling yields one check.
Pawn promotion sounds superficially interesting, but it's essentially like a normal queen move: a square is vacated, a square is occupied. Two checks are possible.
Double pawn move
The ability of a pawn to move two squares doesn't help: it's still vacating one square and occupying one other.
Triple check is possible in the chess variant known as Cylinder Chess. In this position, 1.Ra8 discovers check from the queen and bishop, so it's triple or maybe quadruple check, depending on whether you count one or two checks from the rook, which is attacking the black king from two directions.
[FEN "4k3/8/8/8/R3K3/8/8/3Q1B2 w - - 0 1"] 1. Ra8+
Even if you could like take a pawn en passant and open up two lanes in 1 move, only 1 lane will be mathematically relevant to checking the king.
See, you can attack the king from a ton of directions, but all checking moves can mathematically only make 1 or 2 lanes/diagonal opened and thus relevant for delivering a check.
Chess notation for diagrams use + for a single check and ++ for a double check, but I've never seen a +++ character for a triple check. They simply don't exist.
The check itself defined as a player's king is under threat of capture by attacking piece(s) on next opponent's turn. According to standard chess rule, the pieces which can be counted as checking the king are pieces which able to move directly to the king's square.
These conditions counted as double check instead of triple check, assumed the pieces are attacking in one move:
1) Rook battery with queen/bishop/knight/pawn (second rook at the same file/rank not counted).
2) Queen-bishop battery with rook/knight/pawn (whoever supporting piece at the same diagonal not counted).
These conditions counted as single check instead of double:
1) Queen-rook battery (or two rook battery).
2) Queen-bishop battery.
Also, triple check is impossible in standard chess due to multiple checks must be executed in only one move, which allows maximum of 2 pieces capable to attack the opponent's king directly at the same time (attacking pieces are neither subject to be captured nor interposed by other opponent's pieces).