Video Game Update December 2016

Well, video games have been a little weird for me this month.  I ended up playing Heroes of the Storm again, primarily to unlock the Oni skin for Genji in Overwatch, but with the nice side effect of also unlocking Zarya in Heroes of the Storm.  I see that they're in a new competitive season, so I might go get ranked in that. 
I think that I'll be finishing my Civ 5 game in the 1st 2 weeks of January. 

Video Game Update November 2016

So, in an odd turn, I felt compelled to play my copy of Civilization V.  I never did finish a proper game of it.  (I'm not counting my training-wheels game from when I first got it.)  I'm pretty far along in my current game.  My biggest opponent for any victory conditions is England, who's currently oppressing 2 other countries. 
This, unfortunately, means that I haven't played much Minecraft this month.  December is looking to be less busy, but still pretty busy, so I'm not sure when I'll get a chance to just Minecraft out again. 

Video Game Update October 2016

So, recently, I dug up Minecraft.  It turns out that I haven't played in about 2 years.  I had to spend a fair amount of time trying to remember what I was doing in that world, but I was starting to get back into the swing of things.  Unfortunately, I got smashed by a bunch of mobs while I was trying to re-explore a cave, and I had no idea where I was, so I think that everything de-spawned by the time that I got to what I suspect was the general area of my death.  I also hadn't made a new backup since 2 years ago, so I'll be starting over; thankfully, I hadn't done much real work, so re-doing what I'd done won't be too bad. 

Video Game Update July 2016

I mentioned like 2 months ago that I'd be playing Overwatch and Battleborn this year, which is odd for me mostly in that I don't usually play the new shinies.  Well, the short version is that Overwatch runs better than Battleborn, has shorter rounds, and has shorter queues, and I've only got so much time in my day, so it's been winning out for me. 
As for other games, I did recently scratch my FTL itch a few times, and I still keep up on Hearthstone and the Sentinels of the Multiverse weekly one-shot, but that's pretty much it for now. 
Yay boring updates! 

Life Update May 2016

There's not going to be a third post this month.  I was planning to blog last week, actually, but a bit of a crisis came up.  Don't worry, I'm safe, but I'm trying to help some friends of mine in real life, and things have been a bit trying of late.  I was going to write a sudden short story last week, actually, but I really haven't been in the mood for it lately. 
A bit of a clarification on that:  For the past ... few years, really, I've almost never written a sudden short story truly suddenly, usually because I'm far, far away from the keyboard when I think of it, so I jot down a note and actually write the story a bit later.  For instance, I have a sudden short story note written down right now, but I won't be getting to it this week. 
But, yes, expect 4 posts next month, since I'll be making up this month's missed post. 

Regarding Battleborn & Overwatch

I mentioned last month that, during this month, I'd talk a bit about the new games that came out:  Battleborn (by Gearbox) and Overwatch (by Blizzard).  Unfortunately, I haven't been able to play either game nearly as much as I'd like, but I think that I can give something of a summary of my impressions of these games. 
In short, Battleborn is better if you're after strategic depth and long play, but Overwatch is better if you're after a more tactical experience and shorter games.  I've also found both games to have noticeable shortcomings.  In Battleborn's case, a typical match is 5v5, but, in the interest of not constantly resetting matchmaking, if someone drops, then the game can continue as 5v4, but the team that's a man down isn't compensated in any way, meaning that they're always fighting at a severe disadvantage.  For Overwatch, it comes back to the character vs. class issue:  While it's possible to play a highlander-equivalent mode in a custom game, custom games require inviting people; quick-play matches have no character limits, and there's no way to quick-join a character-limited match. 
I hope to have deeper reviews at some later point, but that'll have to wait until next month, as I don't have the time right now to play these games enough to do the reviews justice. 

My Video Game Status for May 2016

Well, I haven't touched Minecraft in ages, but I'll soon be playing 2 upcoming FPSes:  Battleborn and Overwatch.  (The short version of why I got both is:  I pre-ordered Overwatch before I heard about Battleborn.)  This does mean that I'm almost certainly looking at a long hiatus on TF2, since I have 2 different ways to get my shooter fix. 
My life is currently quite disorganized, which is why, when I've played video games, it's been a lot of quickies:  Hearthstone here, Heroes of the Storm there, but never zenning out on Minecraft or attempting FTL again.  I'm getting things organized, but it's tough, so it's still going to be at least a couple of months before I get back into those again. 
That's all for now.  I'll probably report back on the new shooters at the end of May.  ;)

Regarding The Three Indistinguishable Dice Puzzle: Reasoning

In my previous post, I gave my solution to the problem presented here, but I thought that it would be good to show the logic behind how I got the solution that I got. 
In the quest for an elegant solution, I was playing around with various functions over a,b,c.  One that I thought would be a good starting point was max(a,b,c)+min(a,b,c), since it would give a number 2 through 12 and wouldn't be biased upwards or downwards, since the median of a,b,c was what was being ignored.  I noticed that the distribution of results, if triples were ignored, was, indeed, symmetrical around 7, with 6, 7, and 8 occurring too often by multiples of 6, and with 2, 3, 4, 10, 11, 12 occurring too rarely by multiples of 6.  Of course, on this map, the excess from 6, 7, and 8 was 6 short of the deficit from the rest, but that's made up when we add the triples back in. 
I then looked at the patterns of groups that would result in 6, 7, or 8 and tried to find elegant ways to migrate them to the results that were coming up short.  This was pretty much trial and error, so one thing that I did was aim to end up with a rule saying that three of a kind makes 3, since that would be easy to remember. 
Any set of non-triples a,b,c is either a pair and another digit, which occurs 3 times out of every 216, or three different digits, which occurs 6 times out of every 216, so it was easy to move these things in whole lots of 6, and even to move them in lots of 3.  For instance, the rule that, if max(a,b,c)+min(a,b,c)=7 and a=b or b=c or c=a, then f(a,b,c)=min(a,b,c)+9 actually migrates pair of sets of 3, such as causing f(6,6,1) (or 6,1,6 or 1,6,6) and f(6,1,1) (or 1,6,1 or 1,1,6) to both be 10. 
So, hey, if you want to make a more elegant variation of my solution, mess around with ways to twist a,b,c where 5<max(a,b,c)+min(a,b,c)<9 to give the right number of missing results for 2,3,4,10,11,12 and put the triples somewhere and see if you can make one that uses fewer rules. 
Caveat:  Elegance is a matter of opinion.  I'm pretty sure that what I devised uses the simplest rules (though I could be wrong), so I'd anticipate that the other way to make a more elegant solution would be to have no if conditionals at all, though it probably involves math that's harder to do on the spot.  (I'm almost certain that such a solution would involve modular arithmetic, too, but I haven't actually looked at anyone else's solutions yet.)  So, I'd expect a "more elegant" variant of my solution to get it down to 3 or 2 rules, instead of my current 4. 
OK, have fun with that. 

Regarding The Three Indistinguishable Dice Puzzle

Recently, YouTube started recommending videos for me from Standup Math S.  Recently, I saw this video which presented an interesting problem.  Basically, it goes like this:  You roll three indistinguishable dice, to the point that you don't even know the order in which they returned results.  However, you want results as if you'd rolled 2d6.  That means not only that the results range from 2 to 12, but also that they be distributed like 2d6, i.e., that the odds of getting 3 be twice the odds of getting 2, that the odds of getting 4 be the same as the odds of getting 2 or 3, etc.  It's clearly possible with a lookup table, but the asker seeks a more elegant solution.

Last Friday at lunch, I came up with a fairly elegant solution, but I've been pretty busy, so I haven't gotten a chance to post it until now.  Here it is:

Let a, b, c represent the results of the dice, each an integer 1-6 inclusive, in any order.

f(a,b,c) =

• if a=b=c
• 3
• if a=b or b=c or c=a and max(a,b,c)+min(a,b,c)=7
• min(a,b,c) +9
• a≠b≠c≠a and either a=2i, b=2j, c=2k or a=2i+1, b=2j+1, c=2k+1, where i,j,k∈ℤ
• 2min(a,b,c)
• otherwise
• max(a,b,c) + min(a,b,c)

In layman's terms:

• If you get triples, then the answer is 3.  
• If you get doubles where low+high=7, then the answer is low+9 (a.k.a. high+low+low+2).  
• If you get all 3 even numbers or all 3 odd numbers, then the answer is 2*low.  
• Otherwise, add the highest and lowest numbers.  

I think that this solution is fairly elegant, even though it's in the form of 4 branches, because it's something easily understood (it doesn't even require exponents or modular arithmetic, let alone anything actually complicated) and 2 of the 3 non-main branches (triples and jumping straights) are fairly rare, all 4 branches are easy to solve, and there's some work overlap:  If you see doubles and add high+low to see if they're 7, if they're not, then you already did the math for your final answer.

And yes, I know that this is terribly informal and I didn't dig up all of the math symbols, but it's been a while since I did serious math, so I'm a bit rusty. 

EDIT 2016/Apr/30:  discovered and removed a touch of redundant text:  I had parenthetically said, in "if a=b or b=c or c=a and max(a,b,c)+min(a,b,c)=7", "(but not a=b=c)", but the max and the min would have different parity, so, duh.  

New Year's Resolutions 2016

• Write 3 blog posts each month:  I'm going back down to 3 this year, so that I can get more done.  
• Finish 12 books this year:  I've actually got 4 books half-finished right now, which is why I set the goal so high, and specified "finish".  I'm hoping that this will help me figure out a reading schedule that will itself allow me to get more book reading done, as I do so miss it.  
• Do at least 1 blog post on or before the 14th of the month:  This is something to help me stop stacking these in the last week of the month.  

I might edit this post later if I think of something else, but that's it for now.