Nabla

Ok, I'm back on-line. It seems that my brain still was able to function at least a bit even when deprived of sleep. The issue brought up by JPS is important, and his solution looks like a good one. Treeburst155: I think the solution should be coded into the scoring program. It is better to keep the original scores in the result file intact. I'll send a message here when I've implemented the changes (perhaps next week or so).

It's the middle of the night over here so my thinking is not at its best, but the problem is real and the solution sounds good to me. I'll return to the issue tomorrow after I've slept a bit

There seems to be some litter here, but the original issue is still valid. Persistent little buggers, aren't we Bump.

Bump.

Had to bump myself since noone has even noticed this.

As was suspected, the original algorithm is not optimal when the number of players is large. For eight players the new version of the program (which optimizes over all possible side changes) is able to find a schedule for which #3=0 and #4=4, so the comparisons are done evenly. The solution provided by the original algorithm has #3=4 and #4=2. The optimal solution is ================================ # Scenario_1 PlayerA PlayerB PlayerC PlayerH PlayerD PlayerG PlayerE PlayerF # Scenario_2 PlayerC PlayerA PlayerB PlayerD PlayerE PlayerH PlayerG PlayerF # Scenario_3 PlayerA PlayerD PlayerE PlayerC PlayerB PlayerF PlayerH PlayerG # Scenario_4 PlayerE PlayerA PlayerF PlayerD PlayerC PlayerG PlayerH PlayerB # Scenario_5 PlayerA PlayerF PlayerG PlayerE PlayerH PlayerD PlayerC PlayerB # Scenario_6 PlayerG PlayerA PlayerH PlayerF PlayerE PlayerB PlayerD PlayerC # Scenario_7 PlayerA PlayerH PlayerG PlayerB PlayerF PlayerC PlayerE PlayerD ================================ My friend working with combinatorial problems has provided me with a book which writes about these balanced schedules. It seems that our problem is related to a construction called balanced Room squares. I'll let you know if the book is of any use.

<blockquote>quote:</font><hr>Originally posted by vskalex: Little clarification needed: When will it start? Are we on go, or still waiting for Nablas update? <hr></blockquote> The schedule is optimal for six players, so no changes are coming. The planned launch date is the 11th of November. We are still aiming for that. However, because of the schedule thing (which took some time) we (at least I) have to work hard until that.

We have proved on the blackboard that the six player schedule we have is indeed optimal. So the search for the better schedule is over (assuming that we made no mistakes ). I'm also examining other possibilities for the scoring function. The flatness of the current function with large values when R is around 20 is somewhat disturbing. We have a good candidate. I'll get back to you on this once I have some pictures. ("You" probably being Treeeburst155 since we seem to be the only ones reading this now. )

<blockquote>quote:</font><hr>Originally posted by Treeburst155: I think November 8th may be a bit optimistic for a start date, although I'm not sure. <hr></blockquote> In the opening message we announced November 11th as the D-day. We're still aiming for that (although the recent schedule optimality investigation did put us on a tight schedule).

Hello again! It seems (once again) that you probably can't get everything in life . So for now we'll stick with the original schedule. See this page for an explanation. (I try to keep discussions concerning the tournament system in the same thread so that people can read the whole story there.) [ 11-06-2001: Message edited by: Nabla ]</p>

Hello everyone! People in the Nordic CM tournament noticed that the scheduling program does not produce completely balanced schedules. In particular, it was noted that for six players the schedule that is created by the program makes one of the players play the allied side four times. Also the comparisons to other players are not equal. Here's an example. ========================================== # Scenario_1 PlayerA PlayerB PlayerC PlayerF PlayerD PlayerE # Scenario_2 PlayerC PlayerA PlayerB PlayerD PlayerF PlayerE # Scenario_3 PlayerA PlayerD PlayerE PlayerC PlayerF PlayerB # Scenario_4 PlayerE PlayerA PlayerD PlayerF PlayerC PlayerB # Scenario_5 PlayerA PlayerF PlayerB PlayerE PlayerC PlayerD ========================================== Note that C plays as allied four times out of five. Also note that C is compared against E and F only once. So there is some unevenness in the results. The question that naturally comes up is whether the result is optimal in the sense we would like it to be. First of all, let us define what we mean by optimal. We would like the schedule to fulfill the following criteria exactly. #1. every player plays each scenario exactly once #2. every player plays against every other player exactly once In addition, we would like the schedule to minimize the following criteria (definition first, translation afterwards ). The criteria are optimized in this lexicographic order (a schedule which has a smaller #3 value is better even if its #4 value is larger). #3. The absolute difference between maximum and minimum number of comparisons between different player pairs. The objective of this criterion is to have the players compared evenly against other players. (Using just tthe minimum number of comparisons might do here as well, but this is better.) #4. The absolute difference between maximum and minimum number of games played on the allied side for different players. The objective of this criterion is to have the players play both sides evenly. The example above fulfills #1 and #2. For #3 it scores a 2 (C is compared against B three times and against E just once), and for #4 the score is 2 (C plays allied four times, while D plays allied twice). I got the algorithm for the original program from a mathematician who's also a bridge player. The algorithm is used in bridge, but he did not have a formal proof of its optimality w.r.t. #3 and #4. In fact, after thinking about the problem for a while we suspected that the algorithm is in fact not optimal. (In particular, we suspected that the algorithm is further from optimal if you have a lot of players.) So I went on to write a program which tries to perform better. The improved portion of the program starts from the schedule created by the original program, and then performs a brute force optimization over all possible side changes to see how well it can do. For six players the result can be suboptimal, but for four players the result is guaranteed to be optimal. This is because for four players the pairings for each scenario are unique. If A plays B, then C has to play D, and you can examine all possible combinations just by changing sides. For six players the situation is more complicated. If A plays B, you still have to select whom C plays. So let's start with the four player example for which the solution is optimal for sure. For four players the original program gives the following results. ========================================== # Scenario_1 PlayerA PlayerB PlayerC PlayerD # Scenario_2 PlayerC PlayerA PlayerB PlayerD # Scenario_3 PlayerA PlayerD PlayerB PlayerC ========================================== The score for this schedule is #3=0, #4=2. The optimal solution is the same. Note that this means that all the criteria can not be achieved to the fullest when the number of players is four. One player - in this case D - plays all the time for the same side. Now let's move on to the case when we have six players. The original solution had #3=2, #4=2. In this case the (possibly sub)optimal solution obtained by all possible side changes is again the same. So for now, at least when the number of players is smaller than 8 we'll stick with the original results. As noted above the case of six players has not been proven in a bullet proof way. I'll try to work on it, perhaps together with tss who works at the same university, but in a lab which has all the tools - and education - to play around with logical and combinatorial problems. I'll post the new program (which has the optimality switch and computes #3 and #4 for the schedules) once I compile it for DOS (probably tomorrow). I'll post a message here when you can download the program. BTW, the running time of the brute force optimal version increases exponentially with the number of players. I'm running it now for eight persons and it takes at least hours (the case of six persons is computed in ten seconds). So it is unfeasible to run it for a large number of players. [ 11-06-2001: Message edited by: Nabla ]</p>

<blockquote>quote:</font><hr>Originally posted by Treeburst155: The schedule may change if Nabla can improve the program. The sections will remain the same however. <hr></blockquote> The improvement should be ready today, but at the latest it will be available tomorrow.

<blockquote>quote:</font><hr>Originally posted by Nabla: There's no problem with the program, the algorithm is implemented correctly, but I will examine again whether the algorithm is indeed optimal. I will get back to you on this.<hr></blockquote> Yes, there seems to be a problem with the algorithm. Back to the drawing board Forget the schedule for now, I'll get back to you once I've coded the correct solution.

<blockquote>quote:</font><hr>Originally posted by Treeburst155: The scheduling glitch is in the program. The goal of the program is to do the following: 1)no player sees any scenario more than once 2)every player plays every other player once 3)Allied/Axis duties are split evenly 4)Through the course of the five scenarios each player will find his scores compared to the others in his section two times each. We seem to have fallen short on #3 and #4. <hr></blockquote> To my knowledge the solution I have implemented now is optimal so that #1 and #2 are guaranteed and #3 and #4 should be fulfilled as well as possible. There's no problem with the program, the algorithm is implemented correctly, but I will examine again whether the algorithm is indeed optimal. I will get back to you on this. <blockquote>quote:</font><hr>Originally posted by Treeburst155: If there were only six people in the whole tournament this would be a definite problem. As it is with this tourney I can determine the median from 24 games if I include the Nordic Wannabee games. Being compared with the same players in your section several times is not nearly as significant when there are so many games to get the median from. Even 12 games is enough to minimize this.<hr></blockquote> This is a good thing.

<blockquote>quote:</font><hr>Originally posted by tero: Originally posted by Nabla: [qb]Think about a chess game. Now there are configurations which are trivial (patent solutions apply) and there are configurations which are highly challenging even for the best. Yes. But you can predict and project the opponents intentions and moves by the gambit he chooses. 1. unit placement is an important part of CM 2. it is possible to have fixed initial positions which alienate the player from the game ("I would never have placed the units this way") Where would the fun be in playing out Thermopylae or Cannae if you we restricted to the historical deployment and course of action ? [/QB]<hr></blockquote> Come on, relax First, I've been testing this particular scenario we are talking about and I can tell you that making decisisions in this game is just so painful. Second, since we are doing something new here, I've sent the scenario to both WBW and Treeburst155 and they will ultimately decide whether this particular scenario will be included in the tournament or not. Third, it is just one scenario we are talking about here. Luck and initial conditions have a role in CM, but the best players should stand out. The least that will happen is that you will experience feelings of joy and frustration We guarantee that gameplaying will not be reduced to mechanics. Quite the opposite, we design situations which require most painful decisions to be made. [ 11-04-2001: Message edited by: Nabla ]</p>

Currently it seems that if you exit a map during the battle it is either a good thing or a bad thing. 1. It is a good thing if you exit to an exit zone. You gain points. 2. It is a bad thing in every other case. Not only will it lower your morale if your units run out of the map in panic, but the morale also suffers if you order them to move off the map. This causes some problems for me, especially in designing some unbalanced scenarios. Now wouldn't it sometimes be wise to order your units out of the area? The classic example would be the FO with no rounds left. Also, if some of your units are trapped, wouldn't it in reality lower the morale more if you left them there to be killed. So I'm suggesting that there would be a battle parameter indicating that morale should be lowered only if troops exit the map by themselves - or perhaps even not lowered in any case (this should be really easy to implement). If you order them to exit, no harm done. This feature is very important for unbalanced battles and tournaments, and should be very easy to implement. What do you say? [ 11-08-2001: Message edited by: Nabla ]</p>

<blockquote>quote:</font><hr>Originally posted by tero: The terrain and the forces are the same for all in the side. The deployment zones are the same for all. What is the "random factor" that allows people to use other than patent solutions to the tactical problems facing that one side if the placement of units is fixed ? <hr></blockquote> Think about a chess game. Now there are configurations which are trivial (patent solutions apply) and there are configurations which are highly challenging even for the best. But it is true that 1. unit placement is an important part of CM 2. it is possible to have fixed initial positions which alienate the player from the game ("I would never have placed the units this way") I'll think about this. Nothing is carved on the stone yet. Would this correspond to a definite perhaps?

<blockquote>quote:</font><hr>Originally posted by tero:A question about the scenario set ups: I take it that since the scoring will be modelled after bridge the scenarios we will play will allow free placement of troops anywhere(within the players side of the map of course) without any restrictive deployment zones.<hr></blockquote> This is something I've had to think about quite a bit. Although I'm not sure how it is related to the scoring system... Anyway, the element of surprise - or, to be more accurate, the possibility of an element of surprise - is important in unbalanced scenarios. The way in which these elements are introduced is also important. To take an extreme example, if in a normal attack you and your opponent both know that you have the forces to crush him totally, he should just run away as fast as possible. However, if only you know that you have superiority (or suspect it), the situation is much more interesting. Therefore generally the element of surprise is hidden from at least one side. However, sometimes some of the elements of surprise can be present at the very beginning, and it is a whole lot easier to have them around at round 1. Let us think about the following hypothetical situation. Your task is to occupy a certain area, that is, move to the area and make sure that it's secure. As far as you know the area should be practically free of enemies. First, it would be pretty boring to have you perform the task up to the point where something happens. Your opponent would probably be bored to death. Second, although the (possibly) unbalanced nature of scenarios in this tournament adds certain ingredients of realism into the game it also brings along a new type of unrealism, which is impossible in balanced games. In the real world you would not assume that an enemy task force hits the area as soon as you get there. You would take some precautions, but the assumption would be that you'd be ok. In this tournament if you would get an occupy task such as the one described above, you'd suspect that something terrible is waiting for you. We'd still have to havesomething happening in each game. Therefore it would be somewhat unrealistic to have you waiting for the worst. Which brings us to the third important point: orders. For the sake of realism it is very important that you have reasonable orders. The occupy order given above is not reasonable - in the real world when something surprising happens you should contact your superiors. You can't do that in CM. There are two ways to handle that situation: fallback orders and having elements of surprise since the very beginning. Fallback orders tell you what to do if something goes wrong. These are also a delicate issue since fallback orders should not always apply - hence the possibility of surprise. The second way is to have the element of surprise there immediately, and to give immediate orders on how to deal with the surprise. Sometimes this second option is just a lot more realistic and natural way to handle orders. Fallback orders are at their best when the probability of a threat is fairly high. You can't give fallback orders for every possible situation. Now we come, finally, to your question regarding the placement of units. Now, assuming that an element of surprise is there since the very beginning it would be unrealistic to have you place units yourself. You would know what the surprise is, and the resulting unit placement would be so far from what it would be in the real situation that the idea would be spoiled. So sometimes you just have to start at fixed - that is, locked - positions. The problem here for the scenario maker is to have reasonable and realistic starting positions. Since what is reasonable and realistic is largely a matter of opinion, the initial placement will probably not make some people happy. But the placement is the same for all players playing on the same side. Remember, your result is compared against those guys. Also, sometimes units are just placed in different spatial locations because they would be naturally there. Some obstacle may prevent you from exchanging their positions. In such cases the placement can be restricted to certain areas. There are also other issues related to this, but these are the most important ones. I know that this message has become ridiculously long,but this is important. Did this answer your question (I'm afraid to even ask )? [ 11-02-2001: Message edited by: Nabla ]</p>

<blockquote>quote:</font><hr>Originally posted by WineCape: In appreciation for Nabla's scoring system that we are using in Wild Bill's Rumblings of War Tourney, plus the diligent work of a certain Number 155 in other well run tourneys, as well as the fact that most of these Nords like warm stuff (coffee excluding), I'll put up 6 bottles of fine South African wine for the winner on recommendation, postage paid by me. Sincerely, Charl Theron <hr></blockquote> Charl, This is a perfect first prize for any tournament. I am extremely grateful for this wonderful contribution, as is without a doubt also the ultimate winner of this tournament (and his wife / girlfried ). The spirit of the CM community keeps amazing me.

Not that many Danes here... I just made a marketing attack to get some enlisted. If you know any Danes just challenge them.

<blockquote>quote:</font><hr>Originally posted by Juha Ahoniemi: Proposal: In each first round section should contain a participant from every participating country. So in ideal case I can play agains guys from all other countries. What do You think? Of course it seems that Finns are the most bloodthirsty nation so far (most of those who signed up are Finns)...<hr></blockquote> Yes, this is what I had in mind as well. It is also essential if we are to announce a winning team after the first round.

Adding a placeholder for Pixie (Finland), who is waiting for his registration on this board.

<blockquote>quote:</font><hr>Originally posted by Treeburst155: The four section winners will have a playoff at the end using ultra-balanced, custom meeting engagements designed by me, unless Nabla wishes to create them. This is because Nabla's brilliant scoring system will not work well in the playoffs due to the limited number of games. IOW, we need accurate median scores for the system to work.<hr></blockquote> This is something we'll have to think about later on. In theory, we could use the highly competitive rule in the playoffs. That is, for four players and three scenarios, in each scenario you get one point if you play better than the other guy playing for the same side. But we have a lot of time to consider what is the best way to arrange the playoffs.

<blockquote>quote:</font><hr>Originally posted by tero: Will there be separate scoring for national teams and individuals ? <hr></blockquote> An excellent idea! Although the final winner will be an individual, I think we will also announce the winning team based on the results of the first round.

<blockquote>quote:</font><hr>Originally posted by Peter Svensson: I'm Swedish, and I'd like to take part, but I'm not sure I have the time. What's the deadline for applications? <hr></blockquote> Let's say that the deadline is next Wednesday, 7.11. <blockquote>quote:</font><hr>Originally posted by Peter Svensson: How about making it the Vodka Belt Championship, the stronger cousin of the Winecape tournaments?<hr></blockquote> Not a bad idea. I don't think we have any vodka manufacturers here, do we? But we have not yet decided on the material award (fame and power not included), and this is a strong candidate.