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I'm going to explain a bit about backgammon programs for those who know nothing or have only recently come across them.
The best backgammon programs these days play at World Class level - in other words they will beat the highest level of player as much as they will lose against them - equal skill + equal luck = equal wins and losses (over time).
They work by playing a huge number of games against themselves and amassing statistical data. The mechanism inside is called a neural net because it resembles (in an incredibly simplified way) a network of neurons. I say incredibly simplified because while our brains have billions of neurons and up to tens of thousands of connections from each, current neural nets in use today number in the hundreds or low thousands and are interconnected much more simply. Nevertheless, these nets do gain real expertise.
The best backgammon programs can select all the possible moves for a given position and dice roll and state (very accurately) what order the moves should be ranked in and (less accurately) what the winning/gammon/backgammon chances are. Ditto for cube decisions. The programs have no intellectual understanding of why a move is the best, it's simply the result from the neural net's statistical weightings. This is akin to intuition in humans - many experts know what they are doing but would find it a real challenge to explain with precision the input and copnsiderations that have made up their decisions. People, of course, have self reflection and can examine their intuitions and generate reasons for them - rationalising - but this process is usually after the fact and, while sounding plausible, is prone to error.
There are two well known backgammon programs - Snowy and Jellyfish - that play at World class level. These are commercial programs and cost $$$. They are much in use by the top level players and have radically changed the game at that level by overturning beliefs previously held dear. There is also a free program, GnuBg, that has already been mentioned on this board. It is on a par with the others strengthwise but has a lower ease of use. But, hey, it's free!
You can play against these programs and they will tell you when you are making a bad move, or they can give the list of moves for a given dice roll with the winning chances calculated for each. Choosing the top move gives the best chance of success at that point.
I use GnuBg. I was taught backgammon in my teens by an Arab who lived next door but had no-one to play with; I got reasonably good as far as I remember. When he moved, I then had nobody myself and left the game alone for many years. I picked it up again about a year ago and played against the robot players at VogClub. Then I discovered GnuBg and started analysing my games and using the program to help me make my moves.
To say that it helped me is an understatement. Initially the program judged my games to be "Awful!" and "Beginner", occasionally "Intermediate". In the last year I have come to play many games at "Advanced" and "Expert" level, and even some games (I guess what you might call standard games) at World Class level. This is something that any of the top 50(?) players here is capable of. I still have much to learn and certain game types will find me making blunders that get me classed as Beginner again. I thoroughly recommend using GnuBg if you are serious about learning the game, if it suits your style of learning, and, probably most importantly, have the time for it. I'm unemployed and have had the luxury of being able to spend 100's of hours examining moves and games and asking what the backgammon programs cannot answer - "Why is this move the best?" In other words my prowess results from the use of a good tool coupled with sheer hard work.
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Cheating
The opportunity to cheat is immediately obvious - you only need enter the current position and dice roll and ask for the moves. A successful cheat would not play an entire game according to what the machine said but would only use it to advise in tricky situations. In other situations it would be possible to pick the 2nd or 3rd moves, even 7th, etc, if they were not desperately worse than the best. This makes it somewhat difficult to detect a cheat.
In practice, however, if you examine the games of the top players at most sites, you will find that even the best will make bad moves and even huge blunders - as judged by the program. These programs are very exacting judges. The player will sometimes be able to argue why their move is good but more often it will be recognised that the move was indeed a poor one. This makes it somewhat easier, then, to detect a clumsy cheat. [That's in general, though. For Fencer to detect backgammon programs would be impossible as he would have to analyse everything. It takes several minutes per game and that's computer power which is not available - nor, if it were, would it be very productive use of his servers.]
Using a computer when playing against a robot is hardly cheating but when playing against other people it certainly is - unless there is disclosure and acceptance beforehand.
What about using the computer to analyse a move after it has been made? A main reason to do this is to maximise learning while that move is pertinent in the mind. The aim is to improve your play in future games by recognising the type of position and/or knowing how to act given a particular dice roll - building one's intuition or heuristics. But is it cheating, even if not as obvious as examining a move beforehand?
Well, it will have no effect on the game in some situations but in others it will. If you are attempting to trap a piece behind a prime and have been concentrating on adding a block at the front, but the bg analyser marks your move down because it reckons that you should have been trying to close the rear end first, then your next moves will be influenced as you change your plan. The computer's analysis has suggested a tactic in an ongoing situation - and therefore been of benefit even though used in retrospect.
On the other hand there are very many situations, especially at the start of the game where the volatility of the position means that tactics must be kept very fluid and every position examined as if the game were starting from there. In those situations the use of the computer would not be of much benefit in the current game.
(do skréše) Vlitni do špilo v to rano! Při vepoštěni taho si aj se sópeřem namontojte "táhnót a pobét toť" a furt dokola oževojte léstek bóchánim do klávese F5! (TeamBundy) (okázat šecke vechetávke)