The neural networks of Snowie
have been completely renewed. The structure is different and some input
features have been added or changed. That means, that Snowie had to learn
everything from scratch again. Again, Snowie only knew the rules of
backgammon and played many games against itself to learn by the time,
which features of a backgammon position are important and in what degree.
The standard learning algorithm for neural networks applied to Backgammon
is the so-called TD-Lambda algorithm. This was used for the net in Snowie
1-3 (they had exactly the same neural network). We succeeded in advancing
this TD-Lambda algorithm and additionally applied a new learning
technique. As a result a significantly stronger brain was born.
Before explaining specific advancements in Snowie's Backgammon skill,
here are the test results of Snowie 4 against Snowie 3 for money games:
1-ply cubeful, 268410
games with variance reduction:
Snowie 4 wins 3.9 points in 100 games.
medium, 125360 games with variance reduction:
Snowie 4 wins 4.8 points in 100 games.
3-ply cubeful, 20%,
medium, 75400 games with variance reduction:
Snowie 4 wins 3.3 points in 100 games.
These numbers show a significant
improvement, considered that Snowie 3 played already better or at least as
good as the top experts.
One thing that has been asked many times is: "Does Snowie 4 slot
with opening aces?". This question results from the old controversy
between former world class players who preached the opening slot with 2-1,
4-1 and 5-1 and the new generation of computer programs (Jelly Fish and
Snowie) who condemned them. The answer to this question is: "YES,
Snowie 4 slots with a 2-1, but not with 4-1 and 5-1".
This answer has a much deeper value than just settling the controversy. If
a computer program suddenly slots with 2-1, this is a consequence of a
much better understanding of the whole game. Slotting in the opening
results in positions with more men back, more complex middle game
positions, more priming games, more "backgames", more positions with hits in
the bearoff etc. Especially "backgames" were a big weakness of all existing
computer programs and they all try to avoid to have many checkers back.
Snowie 4 is much better at evaluating positions with hit checkers in the
bearoff and also in containing these checkers. Therefore:
As you can see, there is a long
tail of improvements leading to the 2-1 slot.
The biggest differences can be noticed in backgames and outfield prime
games. In backgame positions that Snowie 3 considers as a pass, Snowie 4
beavers now! The opposite happens with outfield primes: Snowie 3 couldn't
recognize outfield primes and beavered when it had one checker behind a
6-prime, if this prime was far away from the home board. Snowie 4 would
routinely pass all these kinds of positions. About these two extreme
subjects I will write another detailed article in the future.
This concept is widely used in
backgammon and poker, and protects
players from losing more than they can afford. In these money games you
do NOT have unlimited stacks of points available. You play a certain
amount per point and each player has a limited stack of money at the
In a single game you cannot lose or win more than the lowest of
the two players table stakes.
For example you are playing £5 per point and you have £25 at the table.
If you lose 8 points in the next game you only lose your £25. However, if
you win 8 points you can only win £25. This makes it fair; if you have a
lot of money at the table or only little, there is no advantage either
Logically, if you have £25 at the table and your opponent has only £10,
both players can only win or lose £10 in the next game. Always the lower
amount of money counts for that.
The concept 'Table Stakes' introduces a match characteristic into money
games. If one player's table stakes is relatively low to the cube value,
the doubling window as well as the correct checker play may differ from
the normal money game strategies. In extreme cases the gammon price can be
0.0 (if a gammon doesn't gain any extra money) and the doubling cube can
become dead (if a re-cube cannot be applied because of the lack of money).
Snowie 4 is capable to analyze all these situations correctly. It is
possible to import the Table Stakes money game sessions and analyze them with respect to the money that the players
have in front of them.
Snowie 4 comes with a new
3D-board. It is possible to edit the complete board,
the colours, textures, angle of view, light position, etc. Build your own
3-D board and use it at your favourite Backgammon server + in Snowie!
Additionally the complete graphical style of Snowie changed. It looks more
modern and fresh.
The registration process of your
copy is now fully automated over the Internet. Some users had trouble with
it before, sending wrong numbers or typing the code incorrectly into
Snowie. Now you just click one button and your local Snowie tries to
connect to our server to exchange the personal numbers and the
Also the menu structure has been modified. For inexperienced users there
were too many options and they got confused or uncertain what to do. Now
the menus are clearer and easier, better predefined settings are chosen
and the more advanced options moved to the background.