The Analysis Tree (AT) spreadsheet provides for collecting and organizing analyses that have been posted by various analysts and displaying them (if desired) in a Tree format. It also calculates analysis statistics on a move-by-move basis and provides several capabilities to allow finding specific analyses.

To use the AT spreadsheet you need a Microsoft Excel 2003-compatible spreadsheet that will properly execute Excel macros. Both OpenOffice for Linux and NeoOffice for Mac OS X should work and are downloadable for free, but I haven't tested the AT spreadsheet on either of them, although I've been told that it works fine (including the macros) using NeoOffice.

You will also need to set your macro security to Medium (requires your approval to proceed) or Low (doesn't require your approval to proceed) since the AT spreadsheet is not digitally signed (I don't know how to do that yet, maybe some day).

The AT spreadsheet is made up of several tabs:

a. <Notes Tab>. This tab, containing both this summary and detailed information on the contents of the other tabs.

b. <Changes Tab>. Tab summarizing the changes from version to version of the AT spreadsheet, including added capabilities and bug fixes.

c. <Summary Tab>. Tab summarizing the average evaluations for each of the analyzed (both by engine and humans) next moves by either side, engines used for the analyses, and the Average Move Evaluation Calculator (AMEC). See below

d. <Game Score Tab>. Tab listing the moves to date and the FEN string defining the position after that move, the current position, and the change over time in the average evaluation of the position after each move (by both sides) for the Principal Variations (PV) for each move.

e. <Move Tabs>. Tabs containing the analyses that are still applicable prior to that move. The tab named 'W02' lists the analyses applicable for White's 2nd move, the tab named 'B04' lists the analyses applicable for Black's 4th move, etc.

The current (next) move is highlighted in dark blue and lists the analyses that are applicable for the next move. Earlier moves that contain analyses that are no longer applicable are highlighted in light blue and the moves within those tabs are highlighted in gray italics. Move tabs corresponding to moves still in the future have no analyses listed and are not highlighted.

Moves within a move tab can be displayed in either <Full> or <Tree> display formats. In Full format all the moves are shown. In Tree format the moves that are the same as the previous analysis (the row just above it) are hidden, so for each analysis you only see the moves that deviate from the previous analysis, as is usual in a Tree display format.

Often there are many analyses applicable for a move and it's easy to lose track of which analyses you're interested in. You can make it easier to find these analyses in one of 3 ways:

a. <Highlighting>. You can specify 2 different moves (H-Moves) to be highlighted, and whenever either one of those moves appear in one of the analyses in that move tab the moves are highlighted in either yellow (first H-Move) or orange (second H-Move).

b. <Focusing>. Even though the analyses containing the moves that you are interested in have those moves highlighted, it may still be difficult to follow all the analyses you're interested in because if there are many analyses in that move tab then much vertical scrolling may be necessary. So you can specify that only those analyses that contain the highlighted moves be displayed.

c. <Filtering>. The move tabs contain the name of the Analyst that made the analysis, the date and page where the analysis was posted, the engine (if any) used for the analysis, the depth reached by the engine, and the PV that the analysis represents. You can select which of these you are interested in and specify that only those analyses be displayed.

The AT spreadsheet calculates some simple statistics in the 'Summary' tab. For each next candidate move it counts the number of analyses involving that move, the average engine and human evaluation of that move, and for engines including both all analyses or those with PV=1 only. This latter is significant because the PV (or PV=1) represents the of the resulting position given best play by both sides. And averaging the evaluations is a simple way to try to eliminate any evaluation biases by one specific engine.

Finally, the AMEC provides a way to calculate the average engine evaluation for any move in any specific move tab, and can do this average calculation using the evaluation of any or all PVs.

I'm thinking about the idea of running a Benoni Taimanov Attack Challenge game here on chessgames.com. There was considerable debate over this in the last big Team Game against Akobian. This attack was the main reason people seem to fear the Benoni. Especially with the move order where White plays Nc3 early.

I have been analyzing the line with Rybka and comparing these lines with the chessgames database and there are significant errors for Black in the games where Black lost.

I also ran the base position last night and got this:

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Analysis by Rybka 2.3.2a mp 32-bit :21 ply

1. = (0.12): 3...Qh4+ 4.g3 Nxg3 5.hxg3 Qxh1 6.Be3 Qg2 7.Qf3 Qxf3 8.Nxf3 fxe6 9.dxe6 a6 10.exd7+

2. = (0.17): 3...Bxc3+ 4.bxc3 Qh4+ 5.g3 Nxg3 6.hxg3 Qxh1 7.Be3 a6 8.exd7+ Bxd7 9.Bf1 Qe4 10.Qf3

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1. = (0.12): 11...Qh4+ 12.g3 Nxg3 13.hxg3 Qxh1 14.Be3 Qg2 15.Qf3 Qxf3 16.Nxf3 fxe6 17.dxe6 a6 18.exd7+

2. = (0.17): 11...Bxc3+ 12.bxc3 Qh4+ 13.g3 Nxg3 14.hxg3 Qxh1 15.Be3 a6 16.exd7+ Bxd7 17.Bf1 Qe4 18.Qf3

In your line 1. after 18...Bxd7 19.Bxd7+ Kxd7 20.Bxc5 (which may not be White's best move but it seems reasonable) the issue is whether Black's R+P can stand up to White's N+N.

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Starting from this position Rybka 4.1 evaluates the resulting position at d=25 as a draw by repetition as best play after: 20...Kc6 21.Be3 Rhe8 22.Kf2 b5 23.Nd4+ Bxd4 24.Bxd4 Rad8 25.Be3 Rd3 26.Rc1 Kb7 27.Re1 Rd6 28.a3 h5 29.Rc1 Rd3 30.Re1 Rd6 31.Rc1 Rd3 32.Re1 Rd6 33.Rc1 Rd3 etc. And other continuations by Black do not yield more than a [+0.07] eval for White in Rybka's top 5 variations.

Palliser gives 14...Qg2 a ?! saying that after 14...Qg2 15.exd7+ Bxd7 16.Bxd7+ Kxd7 14.Qa4+ that "followed by some timely checks and 0-0-0 practice has shown that he [Black] faces problems" but that's as far as he goes. I wish he had mentioned what "practice" referred to. So maybe White should not exchange queens by 15.Qf3 as Rybka 2.3.2 suggested.

Instead Palliser suggests 14...Bxc3+! and cites the game R.Starke-H.Daurelle, Corr. 2008 which continued 15.Bxc3 a6 16.exd7+ Bxd7 17.Bxd7+ Kxd7 18.Qb3 b5 19.0-0-0 Rhe8! 20.Bxc5 and only now 20...Qg2 claiming this to be a key improvement over 20...Rac8 as played in I Sokolov vs Topalov, 1996 which ended 1-0. The correspondence game ended in a draw and Palliser claims that White didn't have anything better.

In line your 2. 17.Bf1 seems like a curious move. 17.Bxd7+ Kxd7 would have transposed into the Starke-Daurelle game. After 17...Qe4 18.Qf3 Qxf3 19.Nxf3 Rc8 (which may not be Black's best move) it's again a question of whether Black's R+2P can stand up to White's B+N.

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Yet starting from this position Rybka 4.1 evaluates the resulting position at [+1.75], d=25 after: 20.Rb1 b5 21.a4 Bf5 22.Ra1 Be4 23.Ne5 f6 24.Ng4 Bf5 25.Nxf6+ Kf7 26.g4 Kxf6 27.gxf5 Kxf5 28.d6 Rce8 29.Kd2 Re5 30.axb5 axb5 31.Bxb5 Rd5+ 32.Kc2 Rd8 33.d7 R5xd7 34.Bxd7+ Rxd7 35.Rf1+

And other White continuations are almost as advantageous. So apparently in these positions White does much better in the B+N vs. R+2P endgame than in the materially less advantageous N+N vs. R+P endgame of your line 1. So apparently having the bishop(s) in these endgames more than compensates for Black having the extra pawn (although I question many of the moves by Black)!

Regardless of the final outcome, the line has not, IMO, been sufficiently explored to reach a definitive conclusion. There are a lot of opportunities for both sides.

Note that my lines above were not as deep as they need to be. I just wanted to get an unbiased view of the opening using Rybka.

I will take a closer look at your lines as well. If any of these lines look losing for Black even with best play then the line of course should be abandoned.

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Analysis by Rybka 2.3.2a mp 32-bit :25 ply

1. = (0.00): 1.Bd4 Qxg3 2.c4 Qxb3 3.axb3 bxc4 4.bxc4 Rac8 5.c5 Rxc5+ 6.Bxc5 Rc8 7.Kb2 Rxc5

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3 pawns all connected for the piece.

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And no other lines held much promise for White.

So I think that the lines with 8...Nbd7 are playable as well as the lines with 8...Nfd7. But I don't know if Black has anything better than a draw. And while this may be moral victory I suspect that there are a lot less nerve-wracking ways to achieve a half-point.

But with the computers we have now the same could be said for any Black opening.

So what would it take to win? One possibility is to luck into finding a winning variation that's not only beyond most engines' horizon but that's somewhat forced so that once the "gotcha" move becomes visible to the engines being used it's too late to do anything about it. The chances of that happening are slim. Another possibility is to get into a position where the engines are just not that good (yet), for example a closed position that requires extensive maneuvering beyond the capabilities of most engines, and probably aided by human inspiration. But, as you said, convincing the team to adopt a line suggested by a mere human and not backed up by engine analysis will be difficult.

The minimax algorithm is used, as far as I know, in all chess engines that create and search a tree of possible moves. There are many enhancements to the minimax algorithm used in chess engines to reduce the number of branches in the search tree that must be searched, most notably alpha-beta pruning and its enhancements but the idea of the minimax algorithm is simple and central to chess playing engines.

Possibly first applied to chess playing by Claude Shannon in his 1949 groundbreaking paper entitled "Programming a Computer for Playing Chess", it describes how a machine or computer could be made to play a reasonable game of chess. His process for having the computer decide on which move to make was a minimax procedure for a 2-player game, based on an evaluation function of a given chess position, and an assumption that each player will make the best move possible.

The concept is reasonably simple. If you want to find the best sequence of moves from a given position, first evaluate the position after each of the opponent's legal moves (in practice this is not done since the number of positions evaluated is restricted but the basic idea is the same). This is the first ply. Then, for each of those positions, evaluate the position resulting after each of your legal moves. This is the second ply. Repeat the process at successively deeper plies until you run out of time, patience, or both. The highest ply reached is the search depth.

Now comes the minimax part. Remember that you want to find the best move for yourself so at each ply you want to select the move that results in the position with the highest (maximum) evaluation. Likewise, your opponent wants to find the best move for him/her/it ("it" to cover computers)-self so he/she/it wants to select the move that results in the position with the lowest (minimum) evaluation. So, if the search depth is N, then for each ply you want to select the move with the maximum evaluation. At the previous ply, search depth N-1, your opponent wants to select the move with the minimum evaluation. So, working backwards to the initial move, the minimax algorithm then involves selecting the moves that alternate between the maximum (when it's your turn to move) and minimum (when it's your opponent's turn to move) evaluations of the position. The sequence of moves that results from selecting the alternating maximum and minimum evaluations of the position at each ply is referred to as the <Principal Variation>, PV for short, and represents the best sequence of moves for each side.

The biggest problem with the minimax algorithm is that, in its basic form, the size of the search tree grows geometrically. So, if the average number of legal moves at every ply is 5, the number of positions to be evaluated at ply = 1 is 5, at ply = 2 is 25, at ply =3 is 125, etc. At ply = 20 (not that deep as analyses typically go), the number of legal moves is over 95,000,000,000,000. That's a lot of calculation!

To put it another way, in my 4-core, 32-bit, 2.66 GHz computer Houdini reports that it calculates on the average about 3,715,000 positions (nodes) per second. So, if it evaluated every legal move at every ply and the average number of legal moves/ply = 5, it would take over 7,000 hours to reach search depth = 20. And I don't know about you but I would have run out of patience long before that.

The Principal Variation (PV) is the sequence of moves that represents the best play by both sides. It refers to the particular variation that is the most advantageous for the player whose turn it is to move, assuming that the other player will respond with the move that best improves their own position. The PV is determined by the minimax algorithm; see AylerKupp chessforum.

Many engines are capable of listing not only the PV but the variations which correspond to second best play by the player whose turn it is to move, third best play, etc. according to the number of variations that you have requested. This is typically referred to as "Multi-PV" analysis but it's really a misnomer; there is only one PV and all other variations are, by definition, not "principal". But we're probably stuck with the terminology, so the variations are usually listed as PV=1, PV=2, etc.

Multi-PV analyses have the following characteristics, although I've seen some exceptions that I can't account for:

1. If the same search level is reached for all listed variations, the PV will be listed first and will have either the highest evaluation (if it is White's move) or the lowest evaluation (if it's Black's move). This is the consequence of the minimax algorithm which selects the minimum or maximum evaluations at alternating search levels, representing either Black's or White's best move. The remaining variations will be listed in either monotonically decreasing order (if it is White's move) or monotonically increasing order (if it is Black's move). This is logical since, for example, the evaluation for White's 2nd best move should be lower than the evaluation for White's best move, and the evaluation for White's 3rd best move should be lower than the evaluation for White's 2nd best move, etc. The reverse applies to Black.

2. If the same search level is <not> reached for all listed variations, then it is possible that higher numbered (less good) variations will have a higher evaluation than the PV (if it is White's move) or a lower evaluation (if it is Black's move). This happens because the search at that level was not completed, and the evaluations at the lower search level have not yet been updated to reflect the evaluations at the higher search level. However, within the same search level, the same monotonically increasing or decreasing relationship between the evaluations will be observed.

It should also be noted that if an analyst posts a set of analyses where the indicated search depths of all the analysis differ by more than one, or if the analyses listed later have a higher search depth, then these analyses were likely <not> part of a Multi-PV analysis and each variation should be considered to be PV=1. Unless, of course, the analysis is sufficiently perverse to not list the PV at all. But I doubt that this happens, at least not on purpose. :-)

PVs greater than PV=1 can be valuable since they show other interesting approaches, lines which are not desirable to play, and, after all, our opponent may not play the objectively best move and we need to be prepared for any reasonable eventuality and avoid surprises whenever possible. But it would be rash to assume that our opponent won't play the objectively best move so in order to make the best decision as to which move to play we should really only look at analyses with PV=1

The AT spreadsheet can contain a lot of analyses, and it could be hard to find the analyses containing the moves you’re interested in. Three AT spreadsheet features can help, Move Highlighting, Focusing, and Filtering. Unfortunately some of this probably applies only to Windows-based spreadsheets, and I haven’t been able to test them in either Macs or Linux machines. If you don’t use a Windows computer, the information below may help, but you’ll have to try the equivalent commands and see if they work.

<Move Highlighting>. Each move tab in the AT spreadsheet contains two cells labeled H-Move1 (Highlighted Move 1) and H-Move2 (Highlighted Move 2). This allows you to highlight two moves in the move tab, in two different colors, making them easier to find.

The cell to the right of the “H-Move1” label is highlighted in dark yellow. If you enter a move (<without> a move number) in this cell will highlight all the cells in the move tab that contain that move in yellow, including, if you have the Display Type = “Tree”, those cells which are currently blank as a result of their contents being the same as the content of the cell just above it.

The same will happen if you enter a move in the cell to the right of the “H-Move2” label (highlighted in orange); all the cells in the move tab containing the move entered in the orange-highlighted cell will be highlighted in orange.

Note that <all> cells that contain the moves entered in either the H-Move1 or H-Move2 entry cells (those highlighted in yellow and orange) will be highlighted, regardless of whether it is a move by White or a move by Black. If you’re only interested in the move if it’s White’s move, you can indicate so by clicking on the cell to the right of the H-Move1 or H-Move2 entry cells. A down arrow will be displayed and, if you click on it, it will show a drop-down menu with a “White” and “Black” option. If you click on “White”, it will only highlight those cells containing the move you specified if it corresponds to a White move. Of course, if you click on “Black”, it will only highlight those cells containing the move you specified if it corresponds to a Black move.

<Focusing>. Highlighting the move(s) that you are interested in will help you find the analyses that contain that move. But there may still be many analyses, separated by many others, and that will require you to scroll up or down to see all the analyses containing those moves, making it difficult to compare them.

Instead of scrolling up and down, you can indicate that you want to <Focus> on the analyses containing the H-Move(s) you specified by holding down the <Ctrl> and <Shift> keys, and pressing F (for Focus), or <Ctrl><Shift>F. This will filter all the analyses NOT containing the H-Move(s) you specified, and will only display those analyses containing the H-Moves you specified. This should reduce the number of analyses displayed considerably, and you will be able to compare them more easily. And, if you have Display Type = Tree specified, you will be able to see where each of the highlighted analyses deviate from one another.

You can further focus on specific moves by specifying a logical relationship (OR, AND, NOT) between the H-Moves using a pull-down menu in the cell immediately to the left of H-Move 2 as follows:

OR: The analyses will be displayed if <either> H-Move1 <OR> H-Move2 are included in the analysis line.

AND: The analyses will be displayed only if <both> H-Move1 <AND> H-Move2 are included in the analysis line.

NOT: The analyses will be displayed only if H-Move1 <AND NOT> H-Move2 are included in the analysis line; that is, if H-Move1 is included in the analysis line and H-Move2 is not.