What is considered a decisive evaluation of a board in chess? Following on from this question, it was suggested in answer and a discussion in the comments that an evaluation of a board of +1.5 is 'decisive' in the sense of allowing an estimation of which side would win with reasonable certainty.

However, this was debated as to whether it would hold at a professional or amateur level as a rule of thumb. Thus, my question:

What evaluation at the amateur and professional level is sufficient to make a reasonable determination of the outcome of the game, barring highly anomalous moves by either party?
You need to realise that any number given as answer (including the 1.5) is just a rough estimate which depends on many factors. Professional players were  mentioned because their play will be close to that of computers so that blunders/mistakes do not affect the statement. An evaluation around 1-1.5 in the midgame often means that the player can make use of his advantage further improving the evaluation. On the other hand in an endgame with few pieces on the board a similar evaluation can be a lot more drawish because there are few options to improve.

And there are many other reasons why you can't really give absolute numbers.

If you want to discuss the situation for amateur players it gets really vague as you need to make assumptions about the blunder rate. Perhaps the following is useful....

When analyzing a game in lichess, the engine knows three levels of error: blunder, mistake, inaccuracy corresponding to a change in evaluation of 3, 1, 0.5 respectively. So for instance if you start from an advantage of 5, you can make a blunder and still have a won position.