I want to illustrate several points with this post. The cube actions I give are going to be from Snowie because I believe they represent Hugh's database. I don't have a database loaded with my copy of GNU. Someone may find some errors in the values I am listing. That shouldn't change the points I am trying to make. I believe they are valid whether or not the illustrative positions are valued correctly.
The following position represents minimum wastage for both sides, to the extent my data is correct. The pip differential is 5 and the gold standard table tells us that the proper cube action is double / pass. Using N57 with a one pip adjustment also tells us this is double / pass. The Snowie database tells us that white wins 22.6% and the proper cube action is double / take.
The score (after 0 games) is: GNU_bg 0, user 0
Move number 3: user on roll, cube decision?
| GNU_bg | 43 |
|---|---|
| |
| user | 38 |
Position ID: 6B4AANAeAAAAAA Match ID: cAkAAAAAAAAA | |
If a new minimal wastage table was constructed using ideal bearoff positions such as these, the table would show us that we have a take when we are within 5 pips and the leader has a count of 38. Let's call this Table #1.
Now let's look at how a position with distributional features works using Table #1. Here the pip differential is 2. The Snowie database shows us that the proper action is double / take and that white wins 23.3% of the time. For a player to use the table with this position, he or she must be able to evaluate white's position as needing 3 additional pips due to distribution. With this adjustment in hand, the table works. It correctly tells you that with an adjusted pip differential of 5 you are at the point of last take.
The score (after 0 games) is: GNU_bg 0, user 0
Move number 4: user on roll, cube decision?
| GNU_bg | 40 |
|---|---|
| |
| user | 38 |
Position ID: uW0AAEB7AAAAAA Match ID: cAkAAAAAAAAA | |
Now let's walk through the same steps only assume we will build our table off with a distribution that is more level. Call it Table #2. In the position below, the database shows White winning 25.2% of the time with the proper action being double / take. Adding a pip to white's count results in a proper pass. So, our table would record the point of last take as 4 pips, consistent with the GST. So far, this does not create any problems.
The score (after 0 games) is: GNU_bg 0, user 0
Move number 5: user on roll, cube decision?
| GNU_bg | 42 |
|---|---|
| |
| user | 38 |
Position ID: bDsAAGjbAAAAAA Match ID: cAkAAAAAAAAA | |
Finally, let's go back to the second position above which I will repeat again for reference. We can correctly evaluate this position on Table #2 as long as we can look at the position and evaluate it as requiring an extra TWO pips for white. White has two additional pips from distribution as compared to the basis of the table.
This is my entire point. Using Table #1, you must reach a distribution adjustment of 3 pips to get the correct result. Using Table #2, you must reach a distribution adjustment of 2 pips to get the correct result. Either table will work as long as you make the right adjustment. The same holds true for the GST. It will work as long as you make the right adjustment.
The score (after 0 games) is: GNU_bg 0, user 0
Move number 4: user on roll, cube decision?
| GNU_bg | 40 |
|---|---|
| |
| user | 38 |
Position ID: uW0AAEB7AAAAAA Match ID: cAkAAAAAAAAA | |
Therefore, the basis for the table that will work best is the basis that allows us to best estimate the distributional adjustments needed in practical positions. If players can do that best working from an ideal such as is seen in position #1, than that is what should be used. If they can do that best working from position #3, then Table #2 will work best. The same can be said for the GST or any other alternatives that we might consider. But, in all cases, to acheive precision, it is essential that the player understand the basis used and be able to quantify the differences in distribution compared to that table.
Note that the GST or Table #2 can work correctly in evaluating the first position listed in this post too. All that it takes is an ability to see that you need to adjust the white checkers for distribution by -1. I have found it easier to start with the ideal and adjust from there. That's why I favor a minimal wastage table.