Lucky mode

Anything to do with minesweeper...
Posts: 12
Joined: Mon Apr 02, 2012 7:19 pm

Re: Lucky mode

Post by dg211 » Wed May 02, 2012 1:32 am

First of all, I don't think it is helpful to constantly belittle other people's opinions by implying they don't have an encyclopaedic knowledge of the wiki or some obscure bit of minesweeper lore, especially when you are bringing up irrelevant points.

Secondly, I'd like to clarify a few things. I recognize that practice is an extremely important factor in improving, I have never denied this. Players like Tommy and [name removed]are much, much better than I am, and in very large part this is due to an awful lot of hard work on their part. I do not expect that lucky mode would be a short cut to improving my times, and I do not expect that it could magically allow me to beat my records in a week or compete with elite players. And I am not getting hung up on individual games lost to 50-50s. I can't even bring to mind an occasion when I have missed out on a good time, and I would like to think that if I blasted say a 43 or something that I would be philosophical about it and treat it as a motivation like Tommy suggests. But what is happening is that I am getting a tiny bit frustrated thousands of times because of things we know how to avoid, and there is a cumulative effect.

You keep saying that the benefit to completion rate of lucky mode depends on the fraction of boards you blast through mistakes like misclicks, but I don't think that is true. Unless you believe the probability that you will make a misclick or other mistake on a board with no 50-50s is different from the probability on a board with 1 or more 50-50s (and I see no reason to believe there would be any significant difference), then the two effects are independent. For example, assume you have a probability p of blasting through a misclick and consider a distribution where 40% of boards have 0 50-50s and 60% have exactly 1. (For reasons of simplicity I have assumed a single probability p, but it would work equally well with a distribution, and I have absorbed multiple 50-50s into a larger probability for a single 50-50, but the analysis would be much the same with the full distribution of 50-50 prevalences that qq determined). So, the total fraction of boards you blast will be

( p * fraction of 0 50-50 boards ) + ( p * fraction of boards with 1 50-50 which you guess correctly if you get to it) + ( 1 * fraction of boards with 1 50-50 which you guess incorrectly if you get to it)

= 0.4 p + 0.3 p + 0.3

So, the total fraction of boards blasted is

0.7 p + 0.3

Or, the fraction of boards completed is

1 - ( 0.7 p + 0.3 )
= 0.7 - 0.7 p
= 0.7 ( 1 - p )

If the guesses were removed, then you would complete a fraction 1 - p.

So the increase in completion rate would be

( 1 - p )
_______ = 1 / 0.7

0.7 * ( 1 - p )

a result which is independent of p.

Posts: 121
Joined: Thu Sep 23, 2010 4:17 pm

Re: Lucky mode

Post by qqwref » Wed May 02, 2012 2:29 pm

OK, most of what EWQ said was just random insults and stuff that has nothing to do with the argument, so I'll reply to the useful stuff:
EWQMinesweeper wrote:only looking at all boards isn't enough here. you willingly ignore that depending on where you start you might blast, that sweepers make mistakes and do not see patterns. this probably accounts for the vast majority of blasts.
Of course the vast majority of blasts are due to someone's own mistakes or risky behavior - nobody's disputing that. What matters is that, out of every board you might have completed without making a mistake,, you WILL fail some 30% of them due to misguessed 50-50s. Maybe you won't fail them all at the end, but if you do the thought experiment with the 50-50less world you will see what I mean. So, with them removed, you will complete significantly more games. Do you honestly think that completing about 3/2 as many games would be irrelevant to people?
EWQMinesweeper wrote:pretty wrong. 3bv calculation and mousepath are easy to understand, cl's displays is something that afaik only i really use (in the sense that i can play many different solving styles at different speeds), correctness is easy as well, slowed-down replays is nothing that top sweepers should need and is often used by slower sweepers. daily averages are pointless.
Can you please read my post, at least once? I said that those things are not useful to sweepers who are not very good, not that they are hard to understand. These factors really don't matter until you get to the point where you need to pay close attention to your style to get better. If I see a player who is trying to get on the world rank, I'd certainly not tell him to pay close attention to mousepath or cl/s or correctness, or to slow down his replays to see what mistakes he's making. The point is that features are worth including even if only the top players will use them.
NF player. Best scores 1-10-39.

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