Is there a chess engine that makes the most common move in each position?

that would be very good for practicing gambits imo

1. You can create an opening book and have the program play from that book. Most chess GUIs handle the book part, if a book is configured, and an engine takes over only when there is no book move. This is how winboard/xboard, scid etc. work when you play an engine. In other words, it does not matter what engine you use as long as the position is within a book. So create a book with whatever you want - gambits book or sicilian book or just King's gambit book. Then use whatever engine you want to use.

2. Polyglot books (or for that matter, books in most formats) have a weight attached to each position depending on win/draw/loss statistics of that position. The GUI then chooses a move with probability determined by the weight on a position. One can control the weights while creating the book or one can edit the weights afterwards. For example, you can set a weight 0.45 on 1.e4, 0.4 on 1. d4, 0.1 on 1. Nf3, etc. And for each response to these moves, and so on.

3. Most common move can be chosen only up to a certain move, but very soon, like in 8-10 full moves you will arrive at a unique position. At lower levels much sooner, actually. So engine making the most common move will not work.

There is online bot listed in the bot section called lazy botjr that states it goes by pattern recognition and not calculation. It is a sub 2000 strength bot. Might give that a go.

You can try opening trainer in AimChess. It will randomly choose common moves in selected rating bands. It is quite good, I think. CONS it is a bit slower to open up the database.

Yes it’s VERY complicated .... you load up this thing called lichess and hit play.