rod03801: But is there a specific reason to NOT consider odds?

The main reason is that doing so wouldn't add any new information. A position evaluation already includes the odds. In fact it includes the odds, and outcomes, of everything that could possibly happen from that position until each end of the game. All of that exploration into future possibilities is condensed into how much it'll win and how much it'll lose, on average, from that position.

How a bot learns is by playing a million or trillion or gazillion games through to the end and, for each position along the way, it records the outcome. If that position already has a value from one or more outcomes then the latest outcome is merged into the value. Many positions occur again and again and so the value for each of these positions becomes more and more accurate. Positions that occur more rarely will accumulate fewer outcomes and be less accurate. Also, the closer a position is to the start of the game the less accurate it'll be because a smaller percentage of the myriad possible paths will be travelled by the set of games that are explored.

However, that's an as if kind of explanation. No database can store each and every position; that would be impossible given the sheer number of possible positions. (Although it is possible with hypergammon because, with only 6 checkers rather than 30, there are many fewer positions). The neural network method that the bots use is very clever. During the explorations mentioned above, when adding in the outcome for a given position, what they do is record and merge the value for the position with that of positions that are like the given position. By recording "positions that look like <this>" instead of actual positions, the storage requirements are greatly reduced, although this is at the expense of some degree less accuracy for a given position.

In a well designed neural network those "positions that look like <this>" will be fine-grained enough to capture the subtleties of positions that are fairly similar visually but different backgammonly, such as one with a blot that can be hit directly using a 6 and a matching position where the blot is just one pip further away and needs both dice in order to hit it.

Apart from the ability to store all that information with a practically sized database, the other, and huge, advantage of the neural network method is the ability to generalise. Because it doesn't store actual positions you can give it a position that it's never seen before and it can always find a similar position whose values can be used. The mathematical "distance" from the position to the similar position will vary but often it's not so far that the accuracy suffers too much. Thus the computer can respond as if it knows the position, even having never seen it.