Snowie Backgammon Software

Snowie - Analyzing Backgammon

Snowie is a very sophisticated computer program for playing and analyzing backgammon. There is more information about it and Jellyfish and GNUBG, other computer programs, on the backgammon software page on this site.

Snowie Backgammon Interface

There is another backgammon program called GNUBG. I am not that familiar with it, but from what I know it:

a) Is as strong as Snowie and has as many features to analyze your backgammon game
b) Is not quite so user-friendly
c) Is free

Item (c) is not to be dismissed lightly. If you have not already bought Snowie, I'd suggest downloading GNUBG. GNUBG did not become available until long after Snowie. I'm sure that if it had been available in 1997, when Snowie first came out, Snowie would never have been invented. Although the remainder of this page focuses on Snowie, the same concepts are relevant to GNUBG.

The professional edition of Snowie permits you to import an entire match and analyze it, move by move, cube decision by cube decision. This has two important uses:

	It permits you to look at each play and see what you did right - or wrong.
	It lets you compare the skill of two players independent of the luck of the dice.

On this page, I'm going to discuss two topics:

	A detailed discussion of what the Snowie analysis means and how to interpret it.
	Instructions on how to save matches on the Zone and analyze them in Snowie. (Of course you need the Snowie program, or to know someone who has it. There is also a link for a program that will convert matches played on the Zone to a format compatible with Snowie

Snowie Analysis

When Snowie analyzes a match, basically it does the following:

At many points in the game, it estimates the equity of the position. Equity is the "fair value" of the game. In a very simple case, if you winning chances are 60% and your opponent's chances are 40%, and no gammons are possible, your equity is .200. It makes these estimates based on it's review of the position and the likelihood of each side winning a single game, a gammon, and a backgammon. In a match, it adjusts the evaluations based on how important it is to win a gammon at each match score.
Each time a player rolls, it finds the best move. If the player fails to make the best move, it will score him with an error by the amount of equity he gave up. If the best move would give you an equity of .275, and the move you chose gives you an equity of .240, your error rate for that move would be .035.
It also calculates a luck factor. If your equity before you roll the dice is -.500, and after you roll, if you play the roll to best advantage, your equity is -.400, you would get a luck factor for that roll of +.100, and your opponent would get a luck factor of -.100.
It also evaluates your cube actions, downgrading your evaluation every time you double when you shouldn't, take or drop when that's the wrong decision, or fail to double when you should. The actual mathematical impact of these decisions is not really clear.
It then takes the total of your skill for a game and a match and evaluates you in one of seven categories - Novice, Beginner, Intermediate, Advanced, Expert, World-Class, Extra-terrestrial. By Zone standards, Advanced is pretty good. I would expect a player who consistently rated Advanced to be rated about 2000.

Reading a Match Analyzed in Snowie

When you load a match analyzed in Snowie, you will see four windows. The top left lets you navigate from game to game. The bottom left is a list of all the moves in the current game. The top right is the header showing the players' names, and the big window shows all the moves.

Mostly, you want to browse through a give game, move by move. Let me take an illustrative game from a match posted on this site and explain what everything means. This is Game 1 of the match between Nack Ballard and Jerry Grandell.

Move 1 - Ballard, Green, rolls 4-3 and plays 24-21 13-9. If you are familiar with backgammon notation you know what this move means; if you are not, then you can look at the board diagram.

Snowie lists the 5 best plays here. These are all analyzed in 3-Ply. This is Snowie's highest level of analysis. There is a higher level called a "rollout." This is where Snowie plays the game out against itself many times. This takes a very long time to do though. For now, ignore the first play shown. There's a problem in the file. Look at the second play.

The best play, according to Snowie, was 24-20 13-10. This would result in Ballard winning a backgammon 0.4% of the time, a gammon or backgammon 12.4% of the time, and the game 50.3% of the time. He would lose 49.7% of the time, lose a gammon or backgammon 12.4% of the time, and lose a backgammon 0.4% of the time. If you weight all those out, you find that he wins on average 0.005 points per game. That is the "equity."

Looking down to his actual play, you find that he wins 0.5% backgammon, 12.7% gammons or backgammons, and wins the game exactly 50% of the time. Overall he wins 0.003 points per game, or 0.002 points less than perfect play. If he made every play 0.002 worse than the best choice, he would have an overall error rate of 2, which would be superb.

Move 1 for while - Grandell, white, rolls 5-3. Snowie first analyzes each move on 1-ply. Then it discards moves that are very bad and analyses the rest on 2Ply. In the case of this move, by the time it got done with 2-ply it was sure that it knew what the best move was - so it didn't take the time to go to 3-ply. Grandell's move of 24-16* was best - the * means that he hit an opposing checker.

One thing you will notice is that if you multiply out the probabilities of the outcomes, you find that Grandell averages 0.099 points per game. So why does it say +.140? This has to do with the doubling cube. Snowie realizes that you don't have to go all the way to winning the game when you can double. If the game had to be played to completion, Grandell would win about a tenth of a point, but given that he can double, and is in the lead, he will get more use out of the doubling cube than Ballard will.

This "equity" also accounts for the match score. Of course, at 0-0 to 25, both players can "use" every point. But suppose the score were 24-23? Now, gammons for the player leading would not mean anything, so a gammon would count as only 1 point in Snowie's calculations. Also, even at other match scores, not every point is worth the same. Snowie is very precise as to the value of each point toward your goal of winning the match. Yes, these calculations are detailed and somewhat complex. But the ability to reflect all these factors is part of what makes players like Ballard and Grandell super-experts.

Let's skip down now to just after move 7, where Snowie says that Grandell made a "Correct decision not to double." The "money equity" it shows are the probabilities if the game is played to completion. It says that Grandell will win 0.353 points per game on that basis. If he doesn't double now, it estimates that he will win 0.528 points, but that if he doubles and Ballard takes - doubling the value of the game, but giving his opponent control of the doubling cube - he will win 0.485 points, or 0.042 less (it looks like 0.043, but there's some rounding). Of course if Ballard drops, Grandell will win a full point. So Grandell should not double, and if he does, Ballard should take. The "8%" figure means that Grandell should double if he thinks Ballard will drop as much as 8% of the time. Of course, Ballard is a fine enough player that he would not drop.

Now go down another move, to where Grandell actually doubles. Snowie concludes that his money equity is 0.521. This is right about in the doubling range, depending on the position. When you have a money equity of 0.500, if you take a double you lose one point on average, and if you drop a double you lose one point (of course). But when your opponent owns the cube, that is worth something to him. So your opponent would take at exactly 0.500. How much above .500 depends on the value of the cube.

In this case, Snowie concludes that Grandell wins 0.875 points if he doubles and 0.873 if he holds the cube. A razor-thin non-double - certainly not an error to double. Ballard drops, costing himself an average of .125 points by doing so. That is quite a large error.

Understanding Snowie Evaluations

Most players who invest the $380 in Snowie Professional Edition are relatively familiar with backgammon concepts. But a lot of people coming to this web page are not, and I'm offering to do some Snowie analyses for players on the Zone. So here are some very basic notes on what the information means.

Checker plays are evaluated as follows. Snowie estimates the likelihood that if the game were played to completion, of each side winning a backgammon, gammon, and a single game. Those are the six figures that you see for each play that is considered.

Snowie uses "gammon prices." This is a fairly complex concept, but basically what it means is that a gammon is not always "worth" twice as much as a single game. In some situations, depending on the match score, a gammon may be worth more than twice as much as a single game, or less than twice as much, or maybe even nothing at all.

So what it does is estimate the outcome based on each move, weight them by the importance of winning 1, 2, and 3 times the value of the cube, and rate the moves.

The Snowie evaluations are based on parameters selected by the user, depending on how he wants the analysis done. I use Level 3, which is the highest level of analysis, and tell it to be very liberal in how many different moves it looks at. There is, however, a higher level, called a "rollout." That means actually having the computer play against itself many times and seeing how it comes out. The usual procedure is to do it in groups of 1296, so that it can rotate the first roll for each side through all 36 possibilities. Sometimes the next roll isn't all that critical, sometimes it can make a huge difference - this minimizes the luck factor. Rollouts sometimes show the original analysis was very accurate, sometimes if finds flaws. Usually the flaws aren't huge, though. I often use the option to do a rollout anytime Snowie finds a checker play blunder. I usually do 2592 rollouts, sometimes more if I'm running the match analysis overnight.

Snowie can also do rollouts with or without considering the doubling cube. Usually there's not a huge difference between the best play allowing for the cube, and not considering it. "Cubeful" rollouts are also not all that meaningful if the actual players won't turn the cube at the accurate point, or take or drop correctly. Cubeful rollouts also take longer. But if done properly, they are more accurate.

When doing a cubeful rollout, Snowie evaluates the match in terms of match-winning chances (mwc). For example, suppose you're in a given position and the score is 4-3 (match to 7) and the trailing player might double. If the other player drops, naturally the match-winning chances will be 50%, since the score will be tied. Snowie will play the game out assuming both that the player doesn't double (which it will call Ce, for cube in the Center) and assuming the cube is on 2 and given to the Opponent (called Op). It plays the game out, determining for each game what the result is, and then weights this by the likelihood of the player on roll winning from that match score. So if, for example, it shows match-winning chances of .48 for no double, .49 for double/take, and .50 for double/pass, it means that it is a good double (you increased your match-winning chances by 1%) but also a good take (the opponent increased his match-winning chances by 1% by taking). If those figures were instead, say, 53%, 57%, and 50%, it would mean that you were too strong to double. By doubling you decreased your chances from 53% to 50% if your opponent correctly dropped, but increased them to 57% if he incorrectly took. In general it is not a good idea to double hoping to induce a big error. If those percentage were, say, 53%, 57%, and 52.8%, it might be worth risking the 0.2% you would lose to gain 4% - it means your opponent needs to take only 1 time in 20 to show a profit.

Checker Plays

Snowie's evaluations of checker play are quite accurate and valid. At the level of true backgammon experts, it is not unusual for players to suspect that Snowie has made an error in evaluation and to test it with a rollout (having the program play the game out against itself thousands of times) and find the initial evaluation was wrong. However, taken as a whole, the estimates are pretty good. If Snowie says you made a serious error, you definitely made a serious error.

There is very little scope in backgammon for making inferior plays based on psychology. Occasionally I may choose a slightly inferior play because I know my opponent will not find the right counterplay to it, but those are rare. If you always make the technically correct move, you will do extremely well. If one player, over time, has a lower error rate in checker play than another, the it would be just a feeble excuse by the weaker player that he "knows" what he's doing when he makes the wrong play. It doesn't wash.

Snowie categorizes checker misplays into "errors" and "blunders." Errors are those with an equity more than .020 worse than the best play, blunders are those more than .080 worse than the best play. A true expert can hope to keep his errors to close to 1 a game, and his blunders to 1 a match. Most blunders result from having the entirely wrong idea about a position - for example, failing to hit when you should, running instead of staying on an anchor, that sort of thing.

Cube Decisions

Snowie's evaluation of cube decisions is tougher to interpret. Snowie assumes that you are playing an opponent of equal ability to you, who will always make the right cube decision. Consider, though, a couple of possibilities:

You are playing a much stronger player. The score is 1-1 in a match to 9, and you hold the cube on 4. Your opponent has one checker left on his 1-point, you have 3 left on your 1-point. It is your roll. Normally, it would be foolish to double. You have a 1/6 chance of winning the game, so if you double (and put the match on the line) you will have a 1/6 chance of winning the match. Against an equal player, even trailing 5-1 you would have about a 25% chance, so you would be trading chances of 75% 1/6 of the time (you're leading 5-1 when you roll doubles) and 25% 5/6 of the time, for a net of 33%, for a 1/6 chance of winning the match.

But maybe you have virtually no chance of coming back from down 5-1, if you're much weaker. Maybe you should double and put the whole match on this one roll. It might be right, but Snowie would tell you that you made a horrible cube mistake.

You are playing a much weaker player. You reach a position where you can double, or play on for a gammon, knowing that no matter what happens you can probably double next turn even if your position gets weaker and your opponent will still have to drop. Let's assume the following are reasonable:

	You don't double: You will keep playing until you win a gammon or can double and get a drop. Net 95% wins and 5% gammon wins, net gain per game 1.05 points.
	You double, he drops: Net gain 1 point.
	You double, he takes. You expect to win 5% gammons, 80% single games, and lose 15% single games. Net gain per game, 1.50 points with cube on 2.

If your opponent is good, you are .05 better off not doubling. But if he would take the double as much as one time in 10, you are better off doubling.

In both cases, a seemingly poor cube decision can in fact be correct, but Snowie will still downgrade your rating. However, it is important to not use this to just dismiss Snowie's insights. If you are the weaker player and you are constantly missing doubles, you are in fact making more serious errors than Snowie indicates, not less.

Luck Factor

Everyone complains about luck in backgammon. Honestly, it's nice sometimes to get killed in a match when you think you played well, put the match into Snowie, and then see with your own eyes how unlucky you were!

The luck factors are reasonable. They suffer from some defects, but in general, the luckier player will have a positive luck factor.

Here is one way to make some use of the luck factor. First, multiply the luck factor by the number of total dice rolls. You won't see that, but Snowie will tell you the number of unforced moves you have, so increase that number somewhat (since when you are on the bar and can't enter, or in some other situations, you may have only forced moves). Divide this by 100. This is the number of games that your luck gave you or cost you. For example, assume your luck factor in a match is +.80 and you had 110 unforced moves. Raise the 110 to (say) 125. Multiply by .80, getting 100. Divide this by 100, getting 1.00. This means that you were lucky by 1 full game, and your opponent unlucky by 1 game.

However, there are some important qualifications to the luck factors!

They do not account for the position of the cube. A slightly luck roll with the cube on 4 is much more important than a much luckier one with the cube on 1.
They do not account for "overage" in cube decisions. Let's say you are on roll in a race, trailing 52-40, and the cube has not been turned. Roughly speaking, if you roll a 9 or higher the position is no double, a 9 exactly is a double/take, and an 8 or lower is double/drop. So it doesn't matter if you roll a 2-1 or a 6-1. 2-1 might be unluckier by .15 or so in equity, but it has no bearing on the outcome of the game, you still lose one point.
They must be adjusted in thinking of numbers of games. You don't need to win a full game to win a game. Let's say that after a few rolls, both sides have played perfectly but your equity is +.600 (i.e. if there are no gammons your winning chances are 80%). Your net luck is "only" +.60, yet you have in effect won a full game by doubling. So if you win a match by 2 points and your total luck is 2 games, it doesn't follow that the skill level was even. A total luck factor of 2 games should win you more than 2 points - more like 3 or 4 or maybe even more, depending on the cube position.

The final item needing explanation is "jokers." A joker is a roll which results in an equity increase or decrease of more than .300. A joker can be a very good roll for you, or a very bad one for your opponent. I don't know of any particular significant to joker count, other than just for interest.

Analysing the Luck Factor

In reviewing a fairly large number of matches run on Snowie, I have noticed something interesting. The player with the higher luck factor almost always wins. So does that mean that backgammon is really a game of luck? It’s easy to come to that conclusion.

Kit Woolsey once wrote that he expected to win only 55% of his games. I don’t know what level of player he was suggesting he was playing against for the 55%. It’s also true that on average, a good player will win more points when he wins, and lose fewer points when he loses, due to skill with the doubling cube and in playing effectively for gammons. But still, 55% advantage to the better player is hardly overwhelming. Is backgammon a game of skill?

First, let me point out that in backgammon, you do not need to win the game. You need to reach a position where you can make a strong double – in other words, where you have about a 75% chance of winning. Reaching that point and turning the cube is as good as winning.

Now, let me suggest a different kind of game. It is a coin tossing game. Sam Strong wins when the total number of heads minus the total number of tails tossed equals 5, and Wally Weak wins when tails exceed heads by 5. Clearly this is a game of luck, not skill.

Well, suppose we change the game so that Wally needs to get 7 more tails. Now, when we tally up the results for each game, it will still show that the winner was the luckier player. But Sam will win more games. Every so often Wally will get to an advantage of 5 or 6, and then the game will turn around. If all you do is count the “luck factor” – over time it will come out even, same number of heads and tails. But by being able to win with less luck in his favor, Sam wins more games. This is the equivalent of knowing when to make a proper cube turn. If a weak player fails to double at the proper time, he is giving his strong opponent more chances to win – even if it only involves turning the luck around.

Now let’s introduce a “skill” component. Suppose that each player needs only an advantage of 5 to win the game. However, on each toss, Sam has a 10% chance to use his “skill” to temporarily blind Wally after the coin lands so that it can be re-tossed – in effect to negate the toss if it comes up tails. So what we’ll do is, we’ll “score” a toss like that as plus luck for Wally and plus skill for Sam.

Clearly there is a strong “skill” component in this game. Sam has the chance to use his skill to negate some of his opponent’s luck. Notice that in this game, by taking one tails toss in 10 and changing it to a non-toss, we get only about 52.6% heads and 47.4% tails – not an overwhelming advantage.

I wrote a program to simulate this game 100,000 times and here’s what I found:

	In the first game, where the difference is due to needing to reach a smaller advantage, Sam will win 58.4% of the games. Of course, in none of these games will his “luck factor” be greater than Wally’s.
	In the second game, where each player needs to reach 5 but Sam has a skill advantage, Sam will win 62.9% of the games. Of these, he will have the greater luck factor in 61.5% and a smaller luck factor in only 1.4%.

My conclusion, then, as follows. In an individual game of backgammon, it is rare for the skill component to predominate over luck. You still have to be luckier than your opponent to win most of the time. However, the more skillful player is able to end the games in which he is luckier before the dice have a chance to favor his opponent, and is able to prolong games in which a weaker opponent would have already lost.

It does follow from these that when the stronger player wins, he will usually win with a smaller luck advantage than the weaker player will have when he wins.

Getting a Match Analyzed

In order to analyze a match in Snowie, you must do three things: Save the match, convert it to a format Snowie can read, and then run it through Snowie. Let me discuss those three things.

Saving the match file. To save the log of dice and moves in a Zone match, do the following:

	On the game board, click on "Game/Settings/Display/Display Move Notation Pane." This will open up a separate window.
	The new window has a "Save" button at the bottom. After the match ends, you want to click on this, then follow standard Windows protocol to save it to a file. If you don't know how to save and Email files, well, that kind of information is not what this site focuses on.
	The game log will disappear as soon as one player leaves the game. Therefore you must save the game before either player leaves the table. What I do is this - I go through the steps to save the file except for the final "Save" click. Then as soon as the match ends and I see the "Match Over" screen, I save it. It helps to ask your opponent to wait a moment until you have it saved, but I can usually save it quickly enough even if I don't ask. Practice a little, you'll get the hang of it.

There is another way - much better - involving use of a program called CaptureLog. This is on the same page at www.wingflyer.com referenced in the next paragraph. If you run this program while you are playing a Zone match, and click on "auto capture" it will save the match while you're playing, and the match will still be available even after you leave the table. I don't know how Jim wrote this program, but he did a great job.

Converting the file. Jim Borror and I wrote a program called Bunny's Zone Converter, that will convert these files to the same format used by the computer program Jellyfish. This program is available on some releases of the Snowie disk itself, or you can download it from http://www.wingflyer.com/. If you don't own Snowie and are sending the file to someone else to run for you, they probably can convert it also.
Analyzing the match. Now you import the match into Snowie Professional edition - or get someone else who owns the program to do it for you. The rest of the instructions are in Snowie.

If you want to purchase Snowie you will need to go to the Snowie site and purchase it here