same colored bishops & 1 pawn up. Is it a draw?

Imagine an endgame where all remaining pawns are on the kingside, white has 3 adjacent pawns, black has 4 connected pawns, and both sides have a dark squared bishop. Is that position likely to result in a draw or is it a likely win for the side with the material advantage?

I'd probably give black a slight advantage on winning, but that's pretty drawish to my way of thinking.

Interesting, but I have always thought of it as more or less winning for Black, with same-colored Bishops. (Of course it always depends on the particular position.) Opposite-colored Bishops are much more drawish.

I just gave it a look... I programmed an example of that type of position into my computer, and the result was a draw. Perhaps I stand corrected.

I think it depends on who can get their king out to lead the pawns down.  Whoever gets the king out from has the advantage.  Material alone, not enough in this case (my opinion)

If all said pieces were on original squares, I think a draw would be very likely -- it would be too easy for the defender to set all their pawns on the opposite color, then as pawns trade down to 3 vs 2 and 2 vs 1 I would think a defense would be easy to find considering the bishop will sac itself for the last pawn.  The defender would just have to be careful not to give up too much space or let the enemy king get really active (which should be easy to prevent).

So I'm thinking something like this.  (Where if white puts a pawn on a dark square, black will tie defenders to it).

or this

If what I said was true, then the best bet would be to not trade any pawn and play it really cagey.  Don't play too many pawns moves and try to maximise your king and bishop's usefulness, aim for zugzwangs, and give the defender a chance to screw up.  As a defender, basically just set a pawn chain on the opposite color and shuffle your bishop back and forth lol.