Schierer Space

Cooties took a bit more effort to model in Excel than HHCO because the game has distinct states. The objective is to collect all the body parts of your Cootie bug which include: 1 Body, 1 Head, 1 Mouth, 1 Pair of eyes((A single molded piece)), 1 Headgear^[1] and 6 Legs. However, you must collect the Body followed by the Head before any other parts may be collected. Each part is selected based on the throw of a standard 6-sided die. If you successfully add a part to your bug, you get to roll again in the same turn. I didn’t model this, but rather did the statistics based on number of rolls required.

The average number of rolls required to complete the bug, based on 100 Monte Carlo runs, is 44 rolls. I’d estimate a tolerance of about +/- 5 rolls. Any individual player is not likely to reach this number, however, since any one lucky player at the table will end the game considerably earlier.

There is about a 20% chance of victory by 28 rolls for any single player. For four players, the game is over 60% of the time by this point. By 40 rolls, about 45% of players will have won meaning our table of 4 will have completed over 91% of the time. I did have one ‘simulation’ exceed my modeling table with no victory after 100 rolls. The next highest was 77 rolls, but the density increased significantly below that.

Now if we can just get Nate to settle down enough to roll when it’s his turn we might actually get through a game in under 30 minutes.

1. In the modern version this includes antenna, a hat or a bow. [↩]

Well this is the requisite Avatar response post since it seems like the primary thing to write about these days other than the impossibility of complete aircraft security.

Overall, my reaction was very positive. I’m notorious for pointing out the inconsistencies in computer generated effect and plot lines. But strangely, perhaps intentionally, it was the live-action sequences that felt out of place in this film. I’m not sure that I ever felt like the environment was truly photo-realistic, but it wasn’t cartoon-ish either. The film moved along at a steady pace, with the occasional ‘slow’ section was more than filled with eye candy. The same technique was used to distract you from the occasional plot hole… quick, change scenes to something pretty and the audience won’t notice the flaw. I saw the 3D showing (for the exorbitant price of $13), and the depth given by this illusion was worth it. The depth made the scenes more enveloping, and they didn’t kick you in the occipital lobe too often.

This is not a spoiler for anyone who has seen the previews, but stop reading if you’re the nervous type about such things.
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I just completed a relatively significant upgrade of the blog database as well as a normal WordPress software update. It looks like things are up and running, and if all went well, you won’t notice. Let me know if you do.

Yes really.

Nate got a series of classic kids games for Christmas: Hi-Ho-Cherry-Oh, Candyland, Memory and Cooties. With the exception of Memory, these are all games of complete and total chance. For those that haven’t played,^[1] three of them basically go like this:

1. Invoke a random event.
2. Execute required action.
3. Has victory condition been met?
   • If so, yippee.
   • If not, repeat from step 1.

For Hi-Ho-Cherry-Oh, the randomizer is a spinner with 7 positions. Four positions let you take from 1 to 4 cherries off your tree, two positions penalize you 2 cherries and the last causes you to loose all of your cherries. Once you have collected 10 cherries, you win.

So being the geek that I am, I found myself wondering the average number of cherries gained per spin. At first this is simple (1+2+3+4-2-2)/6=1. Unfortunately, there is that nasty bucket which is a variable penalty. Rather than create the entire statistical equation,^[2] I simply created a Monte Carlo simulation in Excel. After about 100 ‘games’ it was clear that the average payout is between 1 and 1.1 cherries per turn.((This is determined as the 10 cherries needed to win divided by the number of spins required to get there. Even though the last spin might put you over 10, you can’t get that many off the tree.))

The shortest game is three spins (4,4,4;4,4,3;4,4,2;4,3,3). There are 10 winning series as the spins could come in any order and 343 possible outcomes. The odds are 2.9% of winning in the minimum amount of time. Of course the odds of a shorter game improve with more players as the game ends if any of the players succeeds, so roughly this increases to 11%. The maximum game is theoretically infinite, but about 40% of the time 10 spins or fewer are required (85% of the time for four players). By 20 spins, a solitaire game is over 75% of the time (with four players this would increase to 99.6%).

Ok, I now return you to your regularly scheduled intra-holiday period.

Maybe I’ll work on Cooties tomorrow. Candyland is just too annoying.

1. Really? [↩]
2. Involving Markov chains, etc. [↩]

I can’t believe I haven’t posted since Thanksgiving. Time flies when you’re so freaking busy you can’t even think.

Here’s a quick photo-summary of what we’ve been up to….

• Thanks to the Davis’, there is now hardwood in the baby’s room. We started the work on Thanksgiving and put the majority of the floor in on Friday. I finished the rest over the remainder of the weekend. When I wasn’t working them as slave labor, we had some time for visiting too.
  
• Nate took some time to paint some baked ornaments for shipment.
  
• Later that weekend we made our annual run up to Critz Farm to drag home a Christmas tree. I think this is a new family record for us as it actually takes advantage of the high ceilings in the Family Room. Nate helped decorate over the next few days, and basically decided that all the decorations needed to be sorted by color.
  
• Nate enjoyed watching The Incredibles while getting his hair cut. Apparently Oreo liked his new do, as she’s starting to be much more tolerant of his ‘attention’.
  
• The following weekend we produced copious numbers of Christmas cookies so K could trade them with her MOMS club friends. Nate helped cut out the “stars”.
  
• Of course the church and the local green houses are all decked out in poinsettias and other festive flowers, so I’ve been having a field day with that. I combined several shots to make an HDR^[1] image of this greenhouse and tree farm in Manlius. We haven’t had much snow yet (as you can see), but driving past there with snow blowing is like watching a real-life piece of the Frosty the Snowman special.
  
• Today we went to the mall to look at the Festival of Trees and to let Nate drop a letter to Mr. Claus. Afterward, we wandered into the mall proper and Nate spoke with the man himself. He seemed a bit nervous, but Mr. Claus did a pretty good job getting him to warm up. In the end, he announced that he would like a guitar for Christmas. We’ll see what that jolly old elf can manage.
  

Lot’s more pics in the gallery. Just look at the recent updates.

1. High Dynamic Range [↩]