The rules for Tikal includes two versions of the game. In the basic version each player simply picks the next tile from the prepared stack. In the auction variant one tile is revealed for each player, and these are auctioned off to the players, who bid using victory points.
I am not quite content with either of these methods. In the basic version the luck of the draw is somewhat too significant, which is the reason why the auction variant is included. However, the latter takes away much of the flavour of the game, as the auctions feel like a metagame that has nothing to do with exploring and digging.
My variant is something of an an intermediate solution, preserving the thematic feel of the basic rules, while while offering the players more choices and reducing the luck factor.
The first player reveals two tiles, and selects one to play, using the normal ten action points. A marker is placed on the remaining tile.
Subsequent players reveal one more tile, and selects either this or the one passed by the previous player. A marker is again placed on the other tile.
Except for the special case of the first tile, players get nine action points plus one more for each marker on the tile, if any.
If a volcano tile with markers is selected, the bonus action points are not spent on the scoring round, but in the following non-scoring round.
The last player has to select the single remaining tile.
Note that luck is not reduced only by giving the players a choice
between two tiles, but also by increasing the value of bad
tiles
until they are worth enough to be picked.
The fact that the number of action points vary slightly will also
tend to reduce time spent by players prone to analysis paralysis
counting exactly how far each other player will be able to move on their
subsequent turns.