Yahtzee

At lunch today the subject of Yahtzee came up.  I won a game last night against my girlfriend and eventually we drifted to score differentials.  It lead me to wonder. 

What’s the worst possible score a person could achieve playing a perfect strategy at Yahtzee

After a bit of thinking I settled on the score of 15 and here’s the logic behind it. 
Warning: This is not a mathematical proof or really a proof of any kind so please don’t read it as such (it lacks rigor).  It’s just a fun exercise I went through. 
The key to getting the lowest score is to get to a position where there is at least 1 roll of the dice which meets no category and forces a scratch of some category on the score sheet.  Once this the roller is in this position bad luck has them roll that set of dice N consecutive turns where N is the number of categories which have yet to receive a point or be scratched.
Ignore Chance for now as it’s a catch all and is unavoidable.  The perfect player would use Chance whenever they had either a very low or no scoring option and the sum of the dice was significant as compared to the max achievable Chance value.  The max achievable chance value is the highest sum of the dice which meets no other category (6,6,5,5,4=26). 
With chance out of the way the rest of the bottom half of a Yahtzee score sheet can be avoided by a roll of the dice which produces 2 pairs.  For example 1,1,2,2,3.  This matches none of the rest of the bottom and forces a scratch of a category, chance or use of the digit count category at the top.  The sequence 1,1,2,2,3 is chosen as the target roll because it has the lowest possible sum of any sequence which meets none of the bottom half of the yahtzee score card and hence will produce the lowest chance score. 
Now that we have a roll which doesn’t meet the bottom we need to eliminate it from the top with the lowest possible score.  Ideally we want a situation where 1,2 and 3 are filled up with the smallest values. 
Lets play our game.
Roll 1: 1,2,2,3,3
Here the player is at a loss.  In the top half of the score card you need to average 3 ticks for every digit category in order to hit your bonus.  If you only get one 1’s you are 2 point in debt, while if you get one 2 you are 4 points in debt (and one 3 has you 6 points in debt).  In this situation its best to take the one 1 because while all of the losses are equal the higher value dice have more upside with equal probability of hitting two or more in the same roll. 
Also the chance score here is 11 which is less than 1/2 of the maximum chance score of 26.  So the perfect player puts 1 tick in the 1 digit category.  
Roll 2: 1,1,2,3,3
Using the same logic as above, the perfect player puts 1 tick in the 2 digit category. 
Roll 3: 1,1,2,2,3
Using the same logic as above the perfect player puts 1 tick in the 3 digit category. 
Roll 4+: 1,1,2,2,3
This roll can go no other place than chance.  Eventually the perfect player is forced to take their chance of 9. 
Total Score:
1+2+3+9 = 15

Whose going to take that bone?

I bought my dog a chew bone today.  I thought this would be a win/win situation: he'd have some fun chewing it and I'd have some time to relax on my computer. 

Unfortunately this turned into a lose/lose situation.  He's apparently paranoid someone will take his bone.  Or at least he's acting paranoid by running around the apartment with the bone in his mouth whining and crying.  I've watched him try and bury the bone a few times but being unsatisfied retrieved it and dug it back up. 

I'm not sure who he's afraid of.  He's currently the only dog in the house and I gave him the bone.  Maybe he's remembering the times Mira bullied him out of his toy and is preemptively hiding it from her.

Eventually I helped him realize his fears by taking the bone away from him.  This turned out to be a win/win because I didn't have to listen to him whine anymore and losing the bone apparently was much better than being afraid of losing the bone because he immediately calmed down.

One minute later I gave it back and now he's happily devouring it on the floor in front of me. 

Who knows. 

Unnecessary use of Elevators

Please stop using the elevators to go up or down a single floor.  Especially when the stairs are next to the elevator.  It really slows down my 4 floor trip.  Thank You.

Part of the Pack

I often wonder how my dogs perceive me.  Am I their friend, master, playmate, pack member or some combination?  Recently I found a new way to analyze this through our pack relationship. 

Dogs work in packs.  According to many dog trainers, an owner should attempt to establish themselves as the clear alpha member of the family pack.  My wife and I take that approach, to greater and lesser success, with our dogs.  For the most part it works.  The dogs appear to consider us one pack and we do have constant struggles with Mira (the female) for dominance of the pack. 

The dogs though seem to treat people and dogs differently with respect to packs.  Whenever a person approaches us, Mira will happily jump up and show affection in hope that she can sneak in a quick lick or two.  However she often will react negatively to other dogs which seek to approach us. 

Why the difference?  Do my dogs view themselves as different than us?  Why are they afraid of new dogs but not new people?  Do they consider other people beneath themselves?

Where have you been?

Funny you should ask.  I've been pretty busy over the last bit and have continually neglected to update my personal blog.  I made a commitment to get my professional blog to a much higher cadence and succeeded.  But I've since neglected doing anything on my personal blog.

That doesn't mean that I haven't had anything to say (stop laughing Mom).  But I should be getting back on track here shortly.

Jason's Blogging (updated)

My brother Jason just started blogging.  Right now he's talking about sports but we'll see if he diverges a little bit as he goes on. 

Since my original post he started a new blog.  You can see it here.

http://jasonparsons.blogspot.com/

Favorite Quote, Not Favorite Book

I was playing around on facebook today and I ended up stumbling through some of my friends "Favorite Quotes" section.  Can it really be your favorite quote when it takes up half of the space in my web browser.  Seriously, if it's more than 30 words, it's no longer a quote, it's a rant, dialog or blathering.

Quotes are something to be remembered, enjoyed and able to quickly throw in your friends face to prove a point.  After 30 words, your friend is not convinced or shamed.  Instead they are laughing at your ridiculous attempt to insult them. 

For instance, one of my favorite quotes is "Hope is the denial of reality".  Short, to the point and of course, said by a Fantasy character.  Mind you it's very rarely won me or been used in an argument.  But at least when people started laughing at me I was at least done saying the quote.  Can't say the same for ...

Find a guy who calls you beautiful instead of hot, who calls you back when you hang up on him, who will stay awake just to watch you sleep. Wait for the guy who kisses your forehead, who wants to show you off to the world when you are in your sweats, who holds your hand in front of his friends, Wait for the one who is constantly reminding you of how much he cares about you and how lucky he is to have you. Wait for the one who turns to his friends and says,".....that's her."

The best part is I didn't even add the ..., it was added by the person who put it up on facebook.