## 3BV, Gzini, and Hzini distributions

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Tjips
Posts: 72
Joined: Sat Apr 18, 2009 1:15 am
Location: South Africa

### 3BV, Gzini, and Hzini distributions

I did a run of 7'500'000 boards computing 3BV, Gzini, and Hzini values to generate distributions for these. Attached is a figure of the result.

The important values as found during these runs [min,max] - most_abundant:
3bv: [90, 289] - 172
Gzini: [79, 181] - 130
Hzini: [76, 179] - 129

I stored the boards but haven't gotten around to outputting usable format...

I'm gonna be doing few more runs (on the 16-core machine, hopefully), so this post may change...
Attachments
Normalized distributions for expert level (7,5e6 boards) plotted from 80 to 250
Screenshot.png (49.01 KiB) Viewed 7713 times
The number of minesweeper boards:
Exp: 140055249834355336357264746443955277014822625680974475320364702381803619892657792049596418323789908370400 (1.4e104)
Int: 13115156192346373485000211099954895788134532256 (1.3e46) &
Beg: 18934455246 (1.9e10)

Cryslon
Posts: 122
Joined: Sun Dec 28, 2008 7:41 pm

### Re: 3BV, Gzini, and Hzini distributions

Tjips wrote: Gzini: [79, 181] - 130
Hzini: [76, 179] - 129
How come ZiNi is bigger than HZiNi?!

Also, Ronny counted HZiNi distribution too, and he gives 128 as HZiNi avg. What's the truth?
Go IRC! (try mibbit)

Tjips
Posts: 72
Joined: Sat Apr 18, 2009 1:15 am
Location: South Africa

### Re: 3BV, Gzini, and Hzini distributions

Cryslon wrote: How come ZiNi is bigger than HZiNi?!
Well, I don't know. Remember that this doesn't mean that the value of zini is always 1 less than hzini. It could be that my implementation is incorrect, but I doubt it. It would be good to have someone else run this sort of thing using maybe the zinicalc implementation...
Cryslon wrote: Also, Ronny counted HZiNi distribution too, and he gives 128 as HZiNi avg. What's the truth?
Well, I didn't state what averages I got, now did I?
The averages I got we're as follows:
3bv - 173.58
gzini - 129.82
hzini - 128.22
The number of minesweeper boards:
Exp: 140055249834355336357264746443955277014822625680974475320364702381803619892657792049596418323789908370400 (1.4e104)
Int: 13115156192346373485000211099954895788134532256 (1.3e46) &
Beg: 18934455246 (1.9e10)

Tjips
Posts: 72
Joined: Sat Apr 18, 2009 1:15 am
Location: South Africa

### Re: 3BV, Gzini, and Hzini distributions

Ok, I did another run, this time with 22'500'000 runs (I'll be able to do more once I get around to optimizing the code. It's horribly slow...).

This time I wasn't after the distributions like in the previous ones, instead I computed the 2D distribution of 3BV vs. Hzini. All I did was to subtract the Hzini value from the 3BV value for each board and count it in that spot in the 2D array.

The resulting surface plot isn't all that special, but the contour plot give a very striking visual of the rarity of easy board. We see that a board like the 3BV 102; hzini 79 board on which I blasted a 43 is only seen 0-10 times per 22mil boards. (I'm NOT saying their rarity is 1 in 22mil)

In both the attached images the x-axis is 3BV and the y-axis is 3BV-Hzini
Attachments
Contourplot of 3BV vs. 3BV-Hzini for a run of 22'500'000 boards with levels at 1, 10, 100, 1000, and 10'000 counts, including lines of constant hzini for [70,180]hzini.
c_bv_hz_4e4Boards_with_const_zinis.jpg (97.57 KiB) Viewed 7664 times
Surfaceplot of 3BV vs. 3BV-Hzini for a run of 22'500'000 boards
bv_hz_4e4Boards.jpg (35.07 KiB) Viewed 7677 times
The number of minesweeper boards:
Exp: 140055249834355336357264746443955277014822625680974475320364702381803619892657792049596418323789908370400 (1.4e104)
Int: 13115156192346373485000211099954895788134532256 (1.3e46) &
Beg: 18934455246 (1.9e10)

Tjips
Posts: 72
Joined: Sat Apr 18, 2009 1:15 am
Location: South Africa

### Re: 3BV, Gzini, and Hzini distributions

Just a few comments on the (now updated) contour plot in the previous post...

Firstly, as Arj pointed out, this plot nicely shows why 3bv/s records usually come on high 3bv boards for flagging. We see that from about 220 upwards you'll not often see boards with hzini higher than 170, and thus with be doing the same amount of work on a [260,170] board as on a [220,170] board, but getting a bigger reward in terms of 3bv/s.

Secondly, the plot shows very nicely that (move along the hzini=80 line) 3bv limit's don't really do much in terms of eliminating the rare easy boards on exp (boards on the dark red contour in this case) as the boards of equal zini at 90 3bv and 100 3bv are also equally rare. This is not definite from the figure as the data isn't good enough, but it shows the principle to be valid and worthy of proper consideration.

Thirdly, considering the above kind of effect we see that a 3bv limit of >110 would only start having a real effect on the difficulty of the rarest boards.

Lastly, if we look at the spacing between the contours and stretch our imagination to the hzini=70 line we find that boards of 70 hzini are about 100 times rarer than hzini 80 boards. Putting this into perspective, if a hzini 80 board is a once in 3 year event, then an hzini 70 board is a once in 300 year event... Imo this shows that the pure numbers will do a better job of screening off the absurdly easy boards than our 3bv limits ever could.

Really lastly Comparing a 3bv limit of 100 with an hzini limit of 90 looks interesting.... (I still vote for no-limits )
The number of minesweeper boards:
Exp: 140055249834355336357264746443955277014822625680974475320364702381803619892657792049596418323789908370400 (1.4e104)
Int: 13115156192346373485000211099954895788134532256 (1.3e46) &
Beg: 18934455246 (1.9e10)