New 3bv Limits/New rule for lucky boards?

Suggest ideas for the World Ranking
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RonnyDeWinter
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Re: New 3bv Limits/New rule for lucky boards?

Post by RonnyDeWinter » Wed Nov 04, 2009 2:13 pm

My Internet broke down yesterday so I had plenty of time to finish it, but off course I couldn't upload it.

Anyway, you'll find the 3BVO and HumanZiNi analyzes linked below:

http://members.ziggo.nl/ronny_de_winter ... 0trial.pdf

I don't have much time now, so I'll post it on the guestbook later. I hope you guys like it.
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Re: New 3bv Limits/New rule for lucky boards?

Post by Cryslon » Thu Nov 05, 2009 7:04 am

Nice job, Ronny! I like the section where you count optimal weight of opening, it's a very interesting question.

I've some remarks:
1) World ranking isn't very reliable input. Of course, records are usually set on easy boards, but imo 'board present in world ranking' is not perfect definition of 'easy board'.
2) I still think new methods of limiting should be aimed to exclusion of dreamboards. Benchmark should not only give lower than average results for boards on which you set your records, but also give MUCH lower results for extremely easy boards. Iff benchmark satisfies these demands, then limits based on it are good.
3) I also think we should study deviations of benchmark/s for individual player. The lower the deviation, the more consistent benchmark is, isn't it?

And you considered only H.ZiNi? I think G.ZiNi is worth studying too.

---

I hope Schu will write down his description of OBV which (if i understand it correctly) is another attempt to consider impact of openings on the difficulty of board.
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Re: New 3bv Limits/New rule for lucky boards?

Post by RonnyDeWinter » Thu Nov 05, 2009 2:40 pm

I don't think you should underestimate the World Ranking when trying to find out which indicator best describes what are easy boards and which aren't. It's the result of hundreds of players playing hundreds of boards each and isn't effected by any subjective selection on what people find 'extremely easy' boards.

For instance, on Intermediate I had found an optimized HumanZini indicator that concluded that the average World ranking board only occurs randomly once per 268 boards. This is pretty insane, because if the indicator wouldn't be effective at all, you would only find 3 or 4 people with a record on such a low (or lower) HumanZini value, but instead about 500(!) people have a record on such a rare board. Also we find multiple boards that only occur like once per 100.000-1.000.000 times randomly in a selection of just 400 boards, so it surely can detect the extremely easy boards by the simple fact that they occur in the world ranking, when you statistically would expect none at all.

I haven't checked G.ZiNi, do you think it's better? Also it would be nice if Schu would give me a description of OBV so I can check it's effectiveness.
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Re: New 3bv Limits/New rule for lucky boards?

Post by Cryslon » Thu Nov 05, 2009 3:55 pm

OBV formulas:
beg: 0.07 * <numbers> + 0.43 * <3BV> + 2.27 * <openings>
int: 0.20 * <numbers> + 0.32 * <3BV> + 1.38 * <openings>
exp: 0.38 * <numbers> + 0.23 * <3BV> + 0.99 * <openings>

<numbers> is number of openable cells which contain a number, lol. It's Clone counter...
Thx Yuuki Nakagiri for posting these formulas in a place where we can find them!
RonnyDeWinter wrote: I haven't checked G.ZiNi, do you think it's better?
Well, i don't think it's 'better' or 'worse' than some another benchmark, because i don't see obvious definition for 'better' and 'worse'. But i'd like to see some research on G.ZiNi as well :) IMO, ZiNi should fit well for board limiting, since it seems to be a good approximation to minimal number of clicks.

About world ranking: of course, indicators based on number of clicks are effective. No doubt that people set records on boards which require less clicks. But imo, eg, my 55 wasn't set on very easy board. I've seen much easier ones, and that 55 was just a consequence of good form and average board. And that 'extremely easy' isn't so subjective, just look at the dreamboard thread. I'm pretty sure you can do sup6 3bv/s on my board, maybe even sup7. But your normal 3bv/s is around 2.5, right? So i conclude that 3BV (and anything what looks like 3BV+smth) isn't good enough. 3BV of that board is 111, 3BVO is 113. 3BV or 3BVO limits don't save us from this type of boards. But such a board surely should be rejected by our new limits, right? Else, why do we want new limits at all?!
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Re: New 3bv Limits/New rule for lucky boards?

Post by RonnyDeWinter » Thu Nov 05, 2009 6:58 pm

Result for (Greedy)ZiNi and OBV compared to the other indicators.

Once again I've calculated the rareness of the average of all World ranking boards compared to the normal distribution of 1.000.000 random boards with the same indicator. The rarer the boards of the world ranking are, the better the indicator.

Intermediate level:
3BV = 1:152
3BVO = 1 : 255
hZiNi = 1 : 193
hZiNi+1,5*O = 1:268
ZiNi = 1 : 212
ZiNi+1*O = 1: 273
OBV = 1:122

Expert level:
3BV = 1:56
3BVO = 1:58
hZiNi = 1:69
hZiNi+0,5*O = 1:70
ZiNi = 1:73
OBV = 1:27

OBV seems to be rather pointless, but I'll try to see if the 3 weight factors in the formulas are just incorrectly chosen or whether it just is simply not a good method.
To me the formula for expert: 0.38*<numbers> + 0.23*<3BV> + 0.99*<openings> looks pretty silly. Because every indicator that I've tested showed that 3BV generates a much bigger deviation than the shapes, sizes and number openings do. However on OBV the influence of:

openings = (numbers-3BV+openings)*0.38 + (openings)*0.99
3BV = (3BV-openings) * 0.38 + (3BV)*0.23

For example if you have a board with 312 numbers / 144 3BV / 12 openings, then the influence of :

openings = (312-144+12)*0.38 + 12*0.99 = 80.28
3BV = (144-12)*0.38 + 144*0.23 = 83.28

So in this case the shapes, sizes and number of openings produce 49% of the OBV value and 3BV the remaining 51%. My research however showed that the influence of openings is small on expert and definitely not (almost) as much as 3BV.

Looks like ZiNi works significantly better than HumanZini. On expert level I also tried to optimize ZiNi by trying different amount of clicks per opening, but without improvement.
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Re: New 3bv Limits/New rule for lucky boards?

Post by Cryslon » Fri Nov 06, 2009 10:43 am

RonnyDeWinter wrote:The rarer the boards of the world ranking are, the better the indicator.
For me this statement isn't that undoubtable.
RonnyDeWinter wrote:OBV seems to be rather pointless
AFAIK, formula was born in attempts to minimize deviation of OBV/s for individual players. Hope Schu will bring some light on the matter.
I also tried to optimize ZiNi by trying different amount of clicks per opening, but without improvement.
Have you tried to subtract openings from ZiNi? :) That would be some voodoo...
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Re: New 3bv Limits/New rule for lucky boards?

Post by Tommy » Fri Sep 03, 2010 10:06 am

I'm posting this here because of the 2000 character limit on the guestbook...
It's a reply to an entry from Bertie submitted at August 30th 2010, 09:41:11 AM.

Not quite, they make boards as easy as the current easiest boards more rare, but exclude boards that are even easier.

I want a 3bv limit of ~120 and a reasonable ZiNi limit (ie, the board has to be harder both in terms of 3bv and ZiNi).

At worst, those easy scores will remain in the ranking, but future generations might still beat them.

At best... I might not be the right person to suggest that, given that I would arguably benefit from it...

But if I had one of these scores, and new 3bv/ZiNi limits were to be introduced, I'd agree to have it taken from the ranking. I'm not asking this of anyone, I just have the hope that others might do that (and, I don't think I can overstate that, I do NOT want that decision to be taken by ANYONE but the player who got that highscore).

I want 50:50es to stay in the game.
I see two ways to deal with them.
One, the minesweeperlive way, is to generate only solvable boards in the first place. We all know how much easier that makes boards, and while the board generation algorithm might rule out too many solvable boards, we also know that the information that the board is solvable itself can be used to solve some patterns.
I think that that is pretty much out of the question for classic minesweeper for the reasons stated above.
The second possibility is to detect when the player had no choice but to guess, and resolve that guess in the players favor.
I'll call that kind of game a "lucky game" for the rest of this post.
This approach is much better than the first, but still suffers from a couple of problems:
1.) It doesn't matter where you go next.
In a classic game, if you see a 50:50, you resolve it as fast as you can, because of the possibility that you will lose the game (and all the time invested solving other parts of that board) doing so. In a lucky game, you can just do it whenever you want - reducing the whole game to just clearing out squares, when in a classic game you have to prioritize areas, but still factor in path, etc.
2.) What about situations where you have to guess, but opening one particular square will resolve the whole situation, while the others will just leave you with another guess? I think they definetly belong in the game.
The more you play for consistency, the more all of this matters. And it is possible to be very consistent on expert even with 50:50es. Ask christoph :D If you're not, it is still most likely your fault.

Edit:
I should add that higher 3bv/ZiNi limits will also significantly reduce the luck factor in getting a high score - because every player gets many more shots at the easiest available boards - without having an impact on gameplay.
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Re: New 3bv Limits/New rule for lucky boards?

Post by dcalafiore » Sun Sep 05, 2010 1:24 am

I have just finished to read again the article by Ronny (link: http://www.minesweeper.info/articles/3B ... _Trial.pdf).
It convinced myself 3bv limit of 120 is the one as much rare as 30 on intermediate (considering average number of openings in exp, 14 in my clone stats (see article), and the smaller percentage of wins).
I don't think introducing a Zini limit is a good idea, because Zini is not implemented in msx, clone and vienna, and they aren't no more upgraded. There are 2 possibilities: the only official version will be arbiter, or Damien will have to check zini value of ALL the videos submitted (that's a long and boring work!). I dislike both options. The same for 3bvo and any other standard.
If any old record won't fit in the new limits, I think leaving it in the rankings is more fair to players who did those records: rules were that way, and we can't disregard it. If we want to take them away, at least let's leave inactive players. I like the idea to ask them.

about the guesses....

I want guesses to remain, in order to keep the way you play minesweeper (i.e. let's not create a different game, or we have to call it a different way!). But I like the idea of eliminating 50-50s because they are the situations you have least information (if a square is safe or a mine) and they are the most of the guesses ( which you can't eliminate in any way). See this article: http://www.minesweeper.info/articles/Mi ... action.pdf , table at page 8. We could also eliminate those 34% (does he mean 33,333%?), to keep only sup50% guesses (note I'm writing only about what are called "craps shoots" in the article). We could have lower suicide percentage among minesweepers! :D
I suggest to create algorithms that generate only boards without 50-50s. They could generate boards in the usual way, but if a generated board contains 50-50, they eliminate it e generate another one. I don't think this would slow-down clones. This solution solves "lucky game" problems, and shouldn't give too many additional information like the minesweeperlive way, but it will make game less stressful and more fair (and of course people like Bertie more happy :D )
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Re: New 3bv Limits/New rule for lucky boards?

Post by Tommy » Sun Sep 05, 2010 8:57 am

The problem with eliminating 50:50es:

Code: Select all

____
bx10
bx31
a**1
Numbers stand for the corresponding number on a minesweeper board, underscores stand for the top edge of the board, letters are hidden squares, asterisks ("*") are squares known to be mines. The two "x"es are the fields contained in the 50:50 situation I will discuss.

We know that if a is a mine, the resulting situation is a 50:50. Therefore, if we know that our clone doesn't generate 50:50es, a is always free.
Even worse, opening a will probably give us a lot of information - consider that we know that the two squares next to a are mines - we probably know more about the board than revealed here.
Odds are, we have something like

Code: Select all

____
bx10
bx31
a**1
c321
c%00
d...
Dots are whatever (and in this case can only be numbers because of the adjacent blanks), percent ("%") is any number.
We now know what d contains and can probably use that information to solve quite a bit more.

Worse though very unlikely, if we have

Code: Select all

____
bx10
bx31
a**1
dc31
fe10
we can still open a - and now imagine that it's a one.

Consider that a could in fact be surrounded by squares that are still hidden (except for one mine) - and still be safe.
I know that this is an extreme case, but it could easily happen.
Imagine playing that flagging:
uncover a, flag the mine next to a, chord. Seven squares with one chord.
I'm considering to build that into my technique even in classic. But I think it should be a healthy risk to do that.
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Re: New 3bv Limits/New rule for lucky boards?

Post by Cryslon » Sun Sep 05, 2010 12:55 pm

I think it's my turn to write long and nonsensical post.
dcalafiore wrote:It convinced myself 3bv limit of 120 is the one as much rare as 30 on intermediate.
3BV limits are bad. There are baby boards with >200 3BV.
I don't think introducing a Zini limit is a good idea, because Zini is not implemented in msx, clone and vienna, and they aren't no more upgraded.
I think a clone with no maintainers is crap and doesn't deserve to be "official".
There are 2 possibilities: the only official version will be arbiter, or Damien will have to check zini value of ALL the videos submitted (that's a long and boring work!).
I think it's not that long, imho it's pretty easy to write a script for zinicalc which counts ZiNi for each submitted score. We only need Curtis to make zinicalc work with MVR format.
The same for 3bvo and any other format.
I think to refuse any solution just because of clonemakers' laziness is a very very bad way.
I want guesses to remain, in order to keep the way you play minesweeper (i.e. let's not create a different game, or we have to call it a different way!).
I don't think Lucky Mode changes game in any significant way. You solve the same boards, and do the same work as before: determine 50/50 patterns and guess. Well, maybe your path might be slightly affected as TK said, but imo that price is worth paying to make game prettier.
I suggest to create algorithms that generate only boards without 50-50s.
That's exactly mslive way, and many people see big differences in mslive boards and normally generated boards. Also, there are new patterns like one TK pointed out. This approach imo changes game more significantly than Lucky Mode.
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Re: New 3bv Limits/New rule for lucky boards?

Post by EWQMinesweeper » Sun Sep 05, 2010 4:49 pm

i want to keep the current rules. i lost a 39 as well as 4.40 3bv/s on LC 50/50. my lowest 3bv for an exp time record was 114 and my current record is on 148 3bv. the rules imo worked well so far and you should be extremely careful about changing them.

the more you play, the less important forced guesses and extreme 3bv become.
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Re: New 3bv Limits/New rule for lucky boards?

Post by Tjips » Mon Sep 06, 2010 3:37 pm

Okay, it seems that there is some uncertainty about what exactly a "lucky mode" entails and should be. Thus I think this would be a good time to outline what exactly the lucky mode, which I am proposing, is; what it's aims are, and how exactly it will work. The best place to start, however, is to give a good outline of what a lucky mode should be.

The most basic and general aim of a lucky mode is to eliminate the effect of forced guesses from a ranking which is meant to measure skill, not luck. While it is true that forced guesses are not the only (and probably not the most important) probabilistic element in the system as we have it today, it is imo by far the most annoying. This is why I've been working on a way of eliminating forced guesses from the gameplay itself based on the constraint satisfaction approach discussed in Raphaël Collet's article, "Playing Minesweeper with Constrains" (even before my blast :P). Well, the first thing I want to discuss is what can be defined as a good lucky mode, and why. It is important to note that this definition is in the context of speedsolving. But it doesn't really lose much of it's appeal in other contexts.

Here is an ad hoc list of general properties to illustrate this definition:
  • The most important property of a good lucky mode is that it has as small as possible of an effect on the distribution in the "speed-difficulty" (how hard it is to get a fast time) of boards faced by the player. At the moment the standard for measuring this is 3BV (and the emerging ZiNi implementations), and I will stick to that in this post. The reason for this is simply as was said before: We don't want to change minesweeper completely from what it started as.
  • The optimal strategies to deal with forced guesses is as far as possible unaltered. This is a gray point, because if one of these strategies is altered only slightly (not in such a big way as Tommy suggests), it takes the same close reasoning skills on the part of the player to realize this change and utilize it. It can easily be argued that if the gains of the two strategies in the two regimes are comparable, then the game was in fact not truly changed. This is of course very gray :D
  • Only forced guesses are eliminated. This is a very subtle condition, and has to be considered carefully in context of the previous points. The most important thing is to only eliminate guesses the player can possibly discern as being forced guesses, and to not eliminate them before this. This condition stems from the idea that players can skew the probabilities of unforced guesses of the same form to gain a considerable advantage. This condition excludes most MSlive-like approaches, as these approaches eliminate the need for the player to be able to recognize a forced guess above an unforced one.
These points are of course not the complete list, but they are a start. I feel it important to restate the point that only force guesses which the player can possibly identify, using the information available on the board, are to be eliminated. This basically means that the player still has to solve the problem of whether or not it in fact is a guess.

Okay, now for a basic outline of what the article of Raphaël Collet's says, and how it pertains to this problem...

The basic idea of the article is that a minesweeper game can be reduced to the solution of a set of equations which are determined by (1) the total number of mines on the board, and (2) the uncovered squares in the format
x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 = N(x0)
where N(x0) is the number in square x0, and x1-x8 can take the values 1 or 0 (1 for a mine and 0 for a safe square)

Example

Code: Select all

? ? ?          x1 x2 x3
? 2 2          x4 x0 x5
1 2 0          x6 x7 x8
would correspond to the following equation:

x1 + x2 + x3 + x4 = 2
This is, of course not the end of the story. It turns out that to do more advanced logical tricks (like the 1-in-a-hole) you need to group the squares adjacent to a number into appropriate subgroups (the "top row" etc) and generate further equations from them. Thus our example actually implies the following equations: (I'm not entirely sure about the two element groups, but kinks are for later :D)
x1 + x2 + x3 + x4 = 2
[x1,x2,x3] + x4 = 2
[x1,x2] + x3 + x4 = 2
[x1,x4] + x2 + x3 = 2
[x1,x4] + [x2,x3] = 2
The reason for this is that some of the logical tricks rely on groups of squares sharing mines.

Once these equations have been set up, it is a simple matter of recursively finding an equation in the entire set which has only one term on the left, and implying it throughout the entire set. You of course need to give it some starting information, but that's not the point.

After reading this in his article I realized that this is exactly how we solve minesweeper boards! Beautiful heh? Interestingly, Sudoku is a similar constraint satisfaction problem.....

But I digress.....

This brings me to the relevance of this to our current discussion. The key is to notice that in situations where a player is forced to guess, the set of equations describing that position will reflect this. More specifically, the set of equations will contain a subset which is under-determined and disjoint from the rest of the equations in the set excluding the equation dealing with the number of mines on the whole board, which the set of solutions of the subset will leave unchanged. (this is very vague, but I'm not going into programming grit here....)

Just quickly for those not familiar with the terms..... Under-determined: There are more variables than equations..... disjoint: the variables in the subset don't appear in it's compliment (outside it)

That basically describes the basis of the lucky mode I propose... The specifics of it's implementation are of little importance at this stage....

In our discussion of this idea, Cryslon and I have found only 2 serious con's in this approach. The first is the problem Tommy mentioned:
Tommy wrote:What about situations where you have to guess, but opening one particular square will resolve the whole situation
Well, because of the stringent nature of a guess being defined as "forced", this problem has a very small effect, and is arguably rendered moot due to the similar close reasoning required to arrive at negligibly different results.

The second is the problem of "surrounded square" forced guesses (or, as I like to call them: "Traps"), and their linked nature. Basically, if you have more than one trap on the board they together will form a forced guess if all other squares are open. The problem is that these can only be resolved right at the end of the game, even though they are also forced guesses on their own. The plus side of this problem is that always resolving these as lucky will cost such a high price to players that they probably wouldn't utilize it much in serious play, and it would thus not affect the statistics :D

There may be more, but I've not found them....

A positive of this method is that the problem Tommy states in the previous post does not exist in this implementation, because what he shows is not necessarily a forced guess (in his expanded picture). The very fact that "a" can influence, and is influenced by the squares of the 50/50 shows this.

Anyhow, that's lucky mode as I see it. And in case you where wondering, I'm completely in favor of eliminating limits on int and exp completely, and leaving that job up to pure statistics; removing 50/50's completely in the way I've just proposed; and in eliminating the probabilistic effects of 3BV-like properties on the measurement of skill which is a world ranking.... (but more on that some other time)
The number of minesweeper boards:
Exp: 140055249834355336357264746443955277014822625680974475320364702381803619892657792049596418323789908370400 (1.4e104)
Int: 13115156192346373485000211099954895788134532256 (1.3e46) &
Beg: 18934455246 (1.9e10)
:D

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Re: New 3bv Limits/New rule for lucky boards?

Post by dcalafiore » Thu Sep 09, 2010 7:30 pm

I must admit I was completely wrong about generating only boards without 50-50s. (thank you Tommy).
Now I agree with lucky mode, and I like Bertie's suggestion about how to formalize it mathematically.


About the issue by Tommy
What about situations where you have to guess, but opening one particular square will resolve the whole situation, while the others will just leave you with another guess?
note that if we only apply lucky mode to 50-50s which have 2 possible solutions (like 3-1s in corners), imo the most annoying, there is no problem. This because if in a solution a square is mined in the other it is not, so opening a certain square always resolve the whole situation. So I suggest to apply lucky mode only to such patterns.

If you don't like that idea, please let's only apply it for patterns in which probability of success is <= 50%, or 60% or something similar, keeping the others. This because being aware of probabilities and clicking where non-mined squares are more likely is part of minesweeper's skills. Keeping the most succes-probable patterns we keep the need of this skills and also we have only solvable or nearly solvable boards. This seems to me a good compromise.
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Re: New 3bv Limits/New rule for lucky boards?

Post by Tommy » Mon Sep 13, 2010 3:48 pm

The other big problem I see...

Didn't Lanye LC a sub40 on a 50:50? :roll:
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Re: New 3bv Limits/New rule for lucky boards?

Post by Cryslon » Wed Sep 29, 2010 9:07 am

Tommy wrote:The other big problem I see...

Didn't Lanye LC a sub40 on a 50:50? :roll:
I see no problem. If there's a video, we will just award him a sub40, what's wrong with it?
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Re: New 3bv Limits/New rule for lucky boards?

Post by areout » Mon Oct 11, 2010 4:40 pm

Hahah come on what are you doing, awarding record to someone who blew it (albeit being unlucky)?!

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