Backgammon, Part 7


Ok, where are we?

We have a backgammon board with 2 players, 15 stones each, both taking turns rolling two 6-sided die that average 7 per turn, with a 2.5% chance of double 6’s and a 16.7% chance of any doubles at all. The game has three stages: starting, mid-game and bear off. And there are two primary strategies: play a back game, or break into a running game. Plus, there’s two kinds of risk: The risk that a blot can be sent to the bar, and the possibility your blot getting on the bar and not being able to get back into the game. It’s not always wise to hit every blot that you can (you could get hit back, or you could fill up your own home field with the enemy’s stones).

Let’s look more at the mid-game, and what happens if you hit too many blots

If the goal of the start game is to take advantage of the first 2-3 turns and set yourself up against your opponent using standardized responses (as described in part 2), then the mid-game is where the jockeying happens to get you to where you can start bearing off.

The kind of jockeying depends on whether the start stage put you into a better position for initiating a running game, or if you’d rather try for a back game. In a running game, you want to pull in your farthest two stones from the backfield (24-point for Red, 1-point for White) and try to avoid leaving blots that can be hit by your opponent (if White moves both stones from 1-point to 4-point, then it’s more-or-less safe to start leaving blots behind him on the 1-, 2- and 3-points). But, for a back game, you want to leave both stones on the 24-point as long as you can, and move everything on the 13- and 8-points into your home field to make up a big wall of blocks, two stones each on 6 consecutive points. Then, hit your opponent’s blot to put him on the bar and not let him back into the game until after you start bearing off.

So, that jockeying in the mid-game can vary from game to game, and the success of each strategy will depend largely on the dice you get. Just because your strategy is good doesn’t mean you’ll always get the right dice to continue carrying it out. That is, the 2.5% chance that something will go wrong repeats with every turn, and after 50 turns, it WILL happen. You can try to minimize risk, but you can’t eliminate it entirely.


(Start.)

Ok, the game starts, White goes first and rolls 6-5. He moves one stone from 1-point to 12-point. Red gets 1-2, moving a stone from 24 to 23, and one from 13 to 11. White gets 1-3, moving a stone from 17 to 20, and one from 19 to 20, making a block. Red gets 3-4. Generally, he’d want to use the 2 blots to make the block on 20-point, but that’s already covered. He could play it safe and move one stone from 13-point to 6-point, but that puts him in an inflexible position. He takes the risk and moves from 13 to 10 and 13 to 9. That leaves three blots, and a 33% chance any of them will get hit. White rolls 6-2, and moves one stone from 1-point to 9, hitting the blot there and putting it on the bar.


(Red is on the bar and needs to get back on the board.)

Red isn’t too worried. There’s a 32/36=89% chance of getting back on the board, with the option of making a block anywhere on the 21-, 22-, 23- and 24-points. But, he rolls 6-6 and is stuck on the bar. White rolls double 1’s, hitting Red’s blots on 10- and 11-points, putting them on the bar as well, then continues to 12-point, and moves one stone from 19- to 20-point.

Generally, this would look grim for Red. But, he rolls a 1-2, making blocks on the 23- and 24-points. White rolls 3-4, and moves one stone from 6-point to 19-point. Red rolls a 4-3, putting the last stone back on the board, and making a block by moving one stone from 24- to 21-point. It should be obvious now that White has a problem. Any blot on his side of the board is going to be vulnerable, and two of the points in his home field are now blocked so it’s going to be harder to initiate a running game.


(White’s jammed up his home field with the enemy’s stones.)

White rolls 1-6, and continues to play it safe, again going from 13-point to 19-point. At this stage, there’s nothing stopping Red from leaving blots. He rolls 3-4, and moves the two stones on 13-point back to 10- and 9-points. White gets double 1’s, and moves the two stones on 17- to 19-point. Red gets 1-3, and moves stones from 8- and 6-points to make the block on 5-point. White gets 6-3, moving from 12- to 18-point, and 13- to 15-point, leaving 2 blots. White rolls 5-1, and moves from 12-point to make the block on 18. Red gets 5-2, and makes the block on 4-point. White gets 1-6, and moves one stone from 12 to 18, and one from 19 to 20. Red rolls 6-4, and makes the block on the 3-point. White rolls 5-2, and moves one more stone from 12 to 19.

(The tide turns.)

At this stage, Red has 4 consecutive blocks, and a (6-1, 6-2, 6-3, 6-4, 6-5, 6-6, 1-6, 2-6, 3-6, 4-6, 5-6, 4-2, 2-4, 5-1, 1-5 = 15/36) 42% chance of hitting that blot on point 15. He rolls 6-5, moving both stones from point-21 to points 16 and 15, moving them out of his back field and putting White’s blot on the bar. White needs a 1 or 2 to get back on the board, which is 1 out of 3 turns.

There’s not a lot of reason to play the full game out. White is all jammed up around points 18 through 20, while Red is in a much more flexible position. Even if White can get back on the board, it will be difficult to get out of Red’s home field, while Red is focused on putting blocks on the 1- and 2-points. When White does get that lone blot past that wall of Red blocks, Red will probably just send it back to the bar again. Red’s plan is to have blocks on points 1- through 5-, and then start bearing off. If White does get on the board, it will be on point-6, BEHIND Red, turning this into a running game that Red is more likely to win.


(Red preps for a running game and bearing off. White just wants Red to make a mistake.)

There is still some strategy at this point. With 3 stones on the 5 point, Red will have a problem if he rolls a 5-6 – he’ll have to bear off 2 stones from the 5-point, leaving a blot that White has a 1/6 chance of hitting. The ideal is to constantly move stones in from the highest point number without having an odd number of stones on that point. Another reason for avoiding an odd number of stones on the highest point is if you have 5 stones and roll high doubles – you bear off 4 stones and leave a blot behind. In this game, Red doesn’t need to worry too much if he is sent to the bar because he has an 80% of getting back on the board in one turn, and a 50% chance of getting past White’s current wall. Red still has the advantage in the running game, and could still survive White’s hitting him on the way back to his home field.

BUT… There’s a chance (maybe 5-10%) that Red couldn’t get off the bar while White builds up blocks in his own home field. This is why Red wants to play a conservative game while bearing off, avoiding odd numbers of stones on the highest point of the wall until White is on the board behind him and no longer a threat.

Another option is to use the doubling cube. When White is on the bar and Red is starting to bear off, Red challenges White to double the game. If White accepts and then loses, it’s at twice the points as before. If he declines, he automatically loses the game and Red doesn’t have to worry about how the dice would turn out. If the idea is to win money, Red would want to double the game a bit earlier than this, making White struggle over whether to accept. If Red is already bearing off, then White will probably decline the challenge and forfeit the game. Red wouldn’t get the extra money, but it does let both players go on to the next game and start over again.

To be continued.

Bokaro P ni Naritai, vol. 1


Hmm. You’d think that a company that sells books and stuff would WANT people to cross link to images in their bookstores, but no…

(Image used for review purposes only.)

Bokaro P ni naritai is a new installment series out from Shopro, the same conglomerate that operates the Weekly Shonen Sunday manga magazine. The title translates to “I want to become a Vocaloid P”, where “P” presumably stands for “Producer”. If you’re not familiar with the Vocaloid series (and if you’ve been reading my blog, you should at least know about Miku Hatsune), it’s a collection of “singing synthesizer” packages. You type out the lyrics, and instead of just having some instruments plus a singer on a separate voice track, Vocaloid sings the lyrics as well. There are several voice styles on the market now, both male and female, with Miku being the most popular in Japan.

The installment magazine from Shopro introduces a new Vocaloid character – Rana. Over the course of the 30 magazines, which are scheduled to come out every other week, you get to learn how to use the Vocaloid engine, Singer-Songwriter for Rana, and Miku-Miku Dance (a 3-D modelling program that lets you create your own dance videos using the Rana model). The first 10 issues bring you up to speed as a beginner on all three packages. The next 10 walk you through the writing process for different music genres (rock, j-pop, jazz, etc.), and then the last 10 focus on the finer points of the applications.

The first issue is 800 yen ($8 USD), while the rest are all 1,500 yen. So, the full series is going to be close to $450 USD, spread out over a little more than 1 year. You may be tempted to skip issues and only buy the ones you need. However, the idea is to clip the proof of purchase markers from the magazine covers and glue them onto the included postcard. If you collect all 30 issues and send in the postcard, you’ll receive serial numbers for upgrading to the fully-functional versions of the Vocaloid software (rather than the crippled “lite” versions that come with the magazine). The first 3 volumes have DVD-ROMs, and after that it’s just going to be the magazine by itself.

Vol. 1 comes with the DVD-ROM with the installers of all three packages (Vocaloid, Singer-Song Writer and MMD), with movie files showing how to do the installs and then dabble with the included demo data files. The movie for MMD is particularly necessary, since there’s no install wizard for it – you have to do some weird tweaking in Visual Studio by hand, instead. I haven’t tried that yet – it took over an hour just to get the other two done.

The magazine is part advertising for the installment series, and part Vocaloid history lesson. The only really necessary sections are those describing how to get the upgrade serial numbers, and the page on how to get the limited-edition (not free) calendar (end of October deadline). You can personalize Rana in MMD with a unique serial number that appears on her cheek, by clicking on the “Get Rana SN” button from the DVD-ROM menu screen.

It is possible to get a head start on each of the software packages – once you activate them with the included serial numbers, they’re ready to go, and the DVD-ROM also has sample music files you can play with. On the other hand, the volume 2 magazine is a step-by-step guide on how to run and use Singer SongWriter Lite, and that’s actually being released on Sept. 23. It should be reaching Kyushu by the 25th, and I’ll start seriously playing with Vocaloid at that point. Interestingly, the Vocaloid installer lets you pick Japanese or English, so there’s no language barrier there on that count.

If you live in Japan (to avoid the 2x’s import mark-up) and want to learn how to make music using the vocaloid system, and ultimately uploading your own dance videos to youtube (or the Japanese version, Nico-Nico Douga), it may be a good idea to get I Want to Become a Vocaloid Producer. It’s going to be expensive for what you get, since the commercial versions of the software might be closer to $300 for the total package, but the magazines act as a classroom study, and it’d cost more if you went to a school that teaches Vocaloid. Me? Personally I’m waiting for the volume on how to write house, techno and trance.

140925 Updates


A bit of new activity going on at Gakken this week.

First, a couple updates on the Otaku no Kagaku facebook page. One is an announcement of the Theo Jansen film shown in Kyoto on Sept. 21st, accompanying a “beests” workshop the same day. The other includes a couple photos of the film and workshop venue on the day of the event.

Next, the Otona no Kagaku website now has the details for the latest kit, the electronic steel drum. The official release date is Sept. 29, meaning that I won’t see it in Kyushu until Oct. 1. 3,300 yen ($33 USD), plus tax. Looks like it’s a small stand to hold a drum plate, with a guitar-style pickup in the base. The pickup plugs into a signal processor for clean-up and amplification. Output is either to a guitar amp, or wireless to an FM radio. (The box has a jumper for selecting 1 of 4 FM frequencies: 88.2, 88.4, 88.6 or 88.8 MHz.) It’s powered with a single CR2032 button battery. I’m not really happy with that, because it means changing more expensive batteries more often. I think one mod is going to have to be attaching a regular AA battery case to the main unit. The kit instructions give a 30-minute assembly time.

The mook will have an overview of steel pans, an interview with Yann Tomita, a look at how the kit works, suggestions for other surfaces to use as drum pads, and an article on electronic drum kits. There’s also the next manga from Yoshitou Asari in the Manga Science series.

One thing that I don’t like is that Gakken pulled the link on the “Next Up” kit. Hopefully this just means that they’re trying to keep some suspense until after the steel drum comes out, rather than showing that they don’t have a “next kit”…

————-

Also, Newsletter #161 just arrived in my email. It starts out by asking if readers have had fun playing with the last kit, the Auto Writer, and then mentioning that the free app on the website allows you to make your own writing cogs for drawing pictures or writing letters. Anyone that hasn’t used the app is encouraged to.

TOC
1) The Cute Electric Steel Drum goes on sale Sept. 29
2) Big hit mini-Theremin kit gets reissued
3) “Twin V-Engine” workshop report
4) 100,000 Rainbow Loom Starter Kits sold!


1) The Cute Electric Steel Drum goes on sale Sept. 29
The editors ask if readers are familiar with steel drums, which became popular in the second half of the 20th century. There’s a bit of history about how they first came to use in 1939 in Trinidad, and then this turns into a commentary on how Gakken decided to make the kit. The main focus of the column is on how the pick-up works.
Mook: A4 size, 100 pages
Release: Sept. 29
3,300 yen plus tax

(no photo yet)
2) Big hit mini-Theremin kit gets reissued
200,000 of the mini-theremin kits have sold so far. To commemorate this event, Gakken is releasing an updated, fully assembled version for people that don’t like building things. New features will include an earphone jack, a 3 octave range, and a mint chocolate-colored outer case.
Pamphlet: 16×12.8 cm, 24 pages
Release: Sept. 30
2,500 yen plus tax

 


3) “Twin V-Engine” workshop report
On Aug. 24th, Gakken partnered with Mercedes Benz to present a workshop for school kids. The first hour was spent assembling the Gakken Twin-V steam engine kit. The second hour consisted of presentations on how Indy 500 race cars work.
Location: Mercedes Benz Connection, Tokyo
Attendees: 24 pairs of children and adults, 48 people total

 


4) 100,000 Rainbow Loom Starter Kits sold!
This section is a repeat announcement for the Rainbow Loom kit, for making bracelets, and the fact that 100,000 units have sold so far.
Mook: A5 size, 28 pages
Ages: 6 on up
1,200 yen plus tax

NSX-39 – Programming Comments


Time to revisit the NSX-39, otherwise known as the “Singing Synthesizer Keyboard Pocket Miku“. I was rereading the “Pocket Miku Perfect Guide” book, and looking at the section on controlling the kit using MIDI commands from a sequencer app (I think the author was using Garage Band). Since the only app I have is Sonar X1 LE, which didn’t play well together with the NSX-39, I figured that I might as well repurpose my Kaossilator Pro Java arpeggiator as an NSX configurator/controller.

The overall concept works, but I’ve been struggling to get all the commands discussed in the documentation to work. One of the problems is that, although all the docs I can find are in Japanese, there aren’t that many to begin with. The starting doc is the Perfect Guide itself, which reprints several of the tables from the Yamaha MIDI parameters sheet, and offers a couple of example instructions. The next doc is the Yamaha MIDI parameter sheet, which lacks examples. I was able to track down the Gakken NSX-39 MIDI Guide, which does discuss programming the NSX in more detail, but the examples are pretty much the same as the ones in the Perfect Guide. The NSX-39 MIDI Guide has links to additional docs stored somewhere on Google, but access to those is controlled by someone, and they’re not giving me permissions to the files.

Having said that, I’m still very impressed with the Pocket Miku. The heart of the kit is the Yamaha NSX-1 chip. It supports eVocaloid, General MIDI, and one or two sound banks (the spec. sheet says that there’s the general purpose MIDI sound bank, RAS (real acoustic system) and a drum kit. RAS seems to be disabled, and the drum kit bank is the same as the percussive instruments you get when selecting channel 9 in the general MIDI sound bank).

With MIDI, you specify 1 of 16 channels to send messages to. Since, the NSX-39 uses USB, in Java you open up a receiver to the kit and send messages that way. Meaning that all 16 channels for that receiver go straight to the NSX-39 – you can play 16 instruments simultaneously on just the one Miku. Channel 0 is eVocaloid (in the Yamaha documentation, channel numbering starts at 1, not 0), and channel 9 is the drum kit. All other channels give you the general MIDI instruments.

The Perfect Guide and the Yamaha spec. break up MIDI commands into 4 major groups: regular MIDI messages (change volume, change program, note ON/OFF, etc.); control change messages (used to access reverb, modulation and brightness); NRPN messages (Non-Realtime Parameters, accessed via control change messages, that let you change the low frequency filter and vibrato) and SysEx (System Exclusive messages, that supposedly let you control pretty much any aspect of the NSX-39). For the most part, the only features that I’ve been able to get working consistently are: NoteON/OFF, pan, reverb, modulation, vibrato, LFO filter frequency, the drum kit, changing the eVocaloid vocabulary and reassigning the NSX-39 key sounds (kind of like having a “keypressed beep”).

A lot of the other stuff, like chorus, variation, and 90% of the SysEx features, are specific to the eVocaloid voice, and I can’t tell why Chorus and Variation aren’t doing anything. I really wish I had more examples to work with, and more complete documentation.

But, what I do have working makes for a pretty good DAW box as it stands. I can switch between the general MIDI instruments, drum kit and eVocaloid, and I can set up a sequencer to run all 16 channels at once. Which, given that the NSX-39 is only $50 USD, including tax, makes it a good deal for the price. Running the sounds through the modulator, adding reverb and then filtering the results is fun.

I’ve even added the Java code for implementing the Roland A-300 keyboard support, and assigned the A-300 sliders to the various NSX-39 settings. There are one or two minor bugs that I want to work out, plus I’ll eventually get around to implementing channel after touch. Then, I need to learn how to play a keyboard…

(Sidenote: When I was experimenting with the A300 support code, I wanted to add an external file for holding the control names as strings in a separate class, so that the main file wouldn’t be so cluttered. I’m using Netbeans as the programming environment, and it got really slow on me. Thinking that the new class file wasn’t working right, I tried deleting it and by mistake ended up irretrievably deleting my project source file. That sucked. I didn’t have backups, so I had to retype the entire NSX-39 controller project all over again from scratch. That took me the better part of a day and a half, but I fixed some mistakes along the way, and added a few new features that I wanted to add anyway. Note to self: Make more backups.)

Backgammon, Part 6


There are actually two kinds of games in backgammon, the running game and the “back game”. In the back game, you want to keep the stones on the 24 point (if you’re Red; the 1 point for White). This makes your opponent more cautious about leaving blots at his side of the board (1-6 for Red, 19-24 for White), and make it harder for him to build blocks in that region. So, both sides tend to work the back game while preparing for a running game. If White rolls a 6-5 at the beginning, he’s more likely to move one stone from 1 to 7 to 12. Do this again in the next turn, and he’s probably going to go for that running game, leaving Red to play a back game. Eventually, most games turn into running games at the end, anyway.

But, both sides will still remain cautious, and White will work on building new blocks, or only landing on existing blocks, until Red starts moving the stones off of 24 and a little closer to the 19 point. After that, White will throw stones in the region behind Red (points 23 and 24 where possible) just to improve the odds for that running game.

So, just exactly what happens with running games and bearing off?

Again, a running game starts when neither side has the option for hitting the opponent’s blots. This happens when none of the opponent’s stones are mixed in with your own. Let’s say that White was setting up for a running game while Red was playing a back game. Red hit one of White’s blots and sent him to the bar, allowing Red to bring all of his stones into his home field. White gets back onto the board and the running game starts in full force. Notice that there’s no longer any chance of Red or White hitting their opponent’s blots.

Because Red has all of his stones in his home field, he can beginning bearing them off, which just means that he’s rolling the dice to remove the stones from the board and return them to the carry tray. The rules here are that you have to:

“Make the best use of the dice”
Move the stones the number of points based on the numbers on the dice
Remove as many stones per roll as possible

That is, if you’re Red and you roll a 2-1, take one stone from the 2-point and one from the 1-point and put them in the tray. If you roll 6-5, remove one stone from the 6-point to put into the tray, and move one stone from the 6-point to the 1-point. If you roll doubles, you can move one stone 4 times, or four stones 1 time each.

Look at that last sentence again. If you roll doubles, you can move one stone 4 times, or four stones 1 time each. Now, look at the board. White can’t bear off until that last stone on the 7 point reaches his home field. After that, he’ll be on fire. While Red is going to need a lot of 6’s, White will be bearing off at LEAST 2 stones per turn, and if he gets ANY doubles, he’ll be able to take off 4 stones per turn.

I mentioned previously that to get a feel for who has an advantage in a running game that you add up all the points for both sides. For Red, that’s (3×1 + 5×2 + 7×6) 55. For White, (7×1 + 7×2 + 1×18) (where “1” is the point in that home field closest to the tray) 24. If we assume that the highest usable number per die is “6”, and that we’re rolling two dice each round with an average of 7, that Red will take 55/7 = 8 rounds, and White 24/7 = 4 rounds to bear off. White should win, then.

What happens for White?

Obviously, this assumption is wrong, but White still has the advantage. To get to his home field, he needs to move 12 points. He can do that with double 6’s, which also gives him 2 extra rolls to bear off the stone from the 6-point, and then one more from the 2-point. So, in one turn, with 6-6, White can reach home and take off two stones. The odds of this are 2.5%, but it does happen. It’s slightly more likely (5%) that he’ll get 6-5, which brings him to 18-point. In the next round, any combination of numbers will put him in the home field and he’ll probably bear off a stone from the 1- or 2-points. A 6-4 will get him to the 17-point, and he still might bear off one stone in the next turn. However, since the average of two 6-sided dice is 7, probability says that each of his rolls will average out to 7, so maybe he’ll get a 1-2 on the first turn, a 6-3 on the next, and 2-3 on the third. Figuring an average of 7 total for each turn, it will take 2 turns to get to the home field, and he won’t be able to bear off until the 3rd turn. If the stone on the 7-point lands on the 19-point by the end of the second turn, then what happens next depends on the dice. If the third turn dice are 6-1 or 6-2, White will remove the stone from the 19-point and one stone from either the 23- or 24-points. If it’s 4-3, then White HAS to move the stone from 19-point to 23-point, then take off one stone from the 23-point.

Recap: White COULD roll double 6’s, and bear off two stones in turn 1. It’s more likely that it will take three turns and only bear off 1 stone. The thing is, in all cases, he’d be bearing off the only stone NOT on the 23- and 24-points. After that, he’d average 2 stones per turn (as long as the numbers on the dice are 2 or higher he’d be bearing off stones from the 23-point. When those are gone, he’d bear off those still on the 24-point.  If any of the dies come up one, he’d bear off the 24-point). Since there are 14 stones remaining, it will take a maximum of 7 turns. And we already know that the odds of getting doubles is 1/6. So, White can expect to get some kind of doubles at least once, and that will act like a free turn, bringing down the total number of turns to bear off to 6, or even 4. In summary, White can take one to three turns to start bearing off, and then win the game in four to seven turns. Expect the game to be over in 5 to 10 turns, with a win for White.

What happens for Red?

Red is already in his home field and can start bearing off. But, say he rolls a 3-4. He has to “make the best use of the dice”. He doesn’t have anything on the 3- or 4-points, so he has to move one stone from 6-point to 2-point. There’s still nothing on the 4-point, so he moves another stone from 6-point to 3-point. If he rolled a 6-1, then he’d bear off a stone from the 6-point and another from 1-point, thus removing 2 stones. This means that either way he has to keep bringing his farthest stones in closer to the tray. He might bear off 0, 1, or 2 stones per turn. The average when rolling a 6-sided die is (1+2+3+4+5+6/6 = 21/6) = 3.5. Seven stones on the 6-point (7*6/3.5)/2 gives roughly six-seven turns to bear off just those 7 (assuming that Red doesn’t roll high doubles). After those 6-point stones are gone, it’s another 4 turns to clear off the rest of the board. That’s ten or eleven rounds, with a probability of getting doubles twice. Summary: Red can bear off the farthest away stones in 7 turns, and then the rest in 4; With double 6’s twice, he could wrap up in six. Expect the game to be over in 6 to 11 turns, with a win for Red.

Reality? In reality, the chances of Red getting double 6’s twice is less than 1%, so don’t count on it. But, double 6’s do turn up consistently in the yahoo game, at better than 2.5%. From a purely statistical viewpoint, we can say that in the majority of games with this set-up that White will bear off in 6 or 7 turns, Red in 9 or 10. White wins most of the time. And the numbers aren’t that far off from the original assumption of point counting. (White in 4, Red in 8.)

To be continued.

 

Programming the Pocket Miku


I’ve had the “Singing Keyboard Synthesizer Pocket Miku” for months now, and I’ve played with it a bit as a handheld synth keyboard off and on when I’ve had the time (which hasn’t been all that often). Recently, I decided to write a Java app for accessing the different features available via MIDI commands, and I’ve kind of run into a wall regarding documentation. That is, there doesn’t seem to be anything useful in English.

The Miku, also known as the NSX-39, is based on the Yamaha NSX-1 chip, which is used in a number of other products, including a Vocaloid-style Speak and Spell game in Japan. While Yamaha has posted the NSX-1 timing sheet, product brief and MIDI spec online, they haven’t made the NSX-1 User’s Manual publicly available. The MIDI spec is the only one in English, and while it’s good for things like the Control Change and SysEx messages, it lacks example usages, and there’s nothing for specifically controlling the NSX-39.

Gakken has a go-to author for synth-specific issues who goes by the name Polymoog. Poly wrote a MIDI guide for the NSX-39 which is very detailed, but is in Japanese. He also makes reference to a number of spec docs hosted on Google docs that aren’t publicly viewable. I’ve tried requesting access to them, but haven’t gotten a response back. I’ve also tried asking on the Yamaha Synth forums whether anyone has these docs and, again, haven’t gotten an answer back.

Now, I’m willing to accept that the NSX series synths are only available in Japan, and that the demand for English documentation is very low. But, it would be nice to have all of the Japanese docs so I can at least get a better shot at figuring out what’s going on, on my own.

Fortunately, I do have the Pocket Miku Perfect Guide, which includes a few of the data tables, and some example SysEx messages. Unfortunately, a lot of the information was lifted directly from Polymoog’s MIDI guide, and contains the same typos Poly made.  So, I can get working about 50% of what I want to accomplish, but I have no idea what else the Miku is capable of, and I don’t know why the other 50% isn’t functioning correctly.

This brings me to my point. I’ve been compiling a lot of notes on the NSX-39 Control Change and SysEx messages, and I’m slowly translating, for myself, the key operations of the NSX-39 from Polymoog’s guide. I’m going to start up a new series of blog entries here, alternating with the backgammon series (due to wrap up in a few weeks), consisting of these notes. What I’m really hoping is that this will help connect me with other English-speaking NSX-39 owners, and we can get something of a community started up. Worst case, I’ll just have my notes available here in the blog as back up if my laptop ever gets fried.

Backgammon, Part 5


Now, things can get more complicated fast. Say you have the following board. You can say whatever you like about this layout, but let’s pretend that Red has gotten bad dice while trying to start a running game, while White has been luckier. If we count points, White has 110 and Red has 135 (Red: 1×3 + 1×4 + 1×5 + 4×6 etc.) White is in a somewhat stronger position than Red, so it’s to Red’s advantage to bide his time, leave the stones on 18 and 13 and try to build blocks with the other stones.


(White leaves a blot on point-15.)

However, White rolls something plus a 3. He moves a stone from 12 to 15, leaving it as an unprotected blot on 15. Is he stupid, or what?

As I wrote in the last entry, there’s more than one kind of risk. Red would need a 3 to hit White’s blot from the 18 point. Because there’s a block on 17, Red needs 1-2, 2-1, or a 3 on one die (3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 1-3, 2-3, 4-3, 5-3, 6-3) = 13/36 = 36%. One out of every three turns should let Red hit that blot. So, yeah, White is stupid, right?

Well, White gets on the bar and in the next turn needs anything other than 6-6 to get back onto the board. In fact, landing on the 3-, 4- or 5-points will hit one of Red’s blots and put him on the bar instead. What are the odds? White needs any roll with a 3, 4 or 5 in it, or something starting with a 1 or 2 to get on the board plus a 1 to hit the 3-blot. In fact, the only roll where Red won’t get hit are 6-6, 1-6, 2-6, 6-1 and 6-2 = 5/35 = 13%. Or, rather, 87 out of 100 times, White will hit AT LEAST one of Red’s blots. For 3-1, 3-2, 1-3, 2-3 and 1-1, Red will get hit TWICE (there’s that 13% probably again, but now, it can cause some real damage).

Here, we’re seeing two kinds of risk. The first is that White gets hit on the 13 point and sent to the bar. Second is Red’s getting hit in return and not being able to return to the board. Look at White’s “wall” on the 19-22 points. Red would need a 1 or a 2 (33% chance) to return one stone to the board. If White hit two stones, Red would need 1-2, 2-1, 1-1 or 2-2 (11%) to get both back on the board in one turn, otherwise White gets at least one round to bring in the stones on 12 and 17 and block the entire region from 19-24, preventing Red from getting on at all.

White is BEGGING Red to hit that blot on 15. It would destroy Red’s chances of winning. If things remain the way they are and White puts blocks on 23 and 24, he could continue bringing in his remaining stones at his leisure and start bearing them off the board. Red could get lucky and hit White one more time, but the odds for it are low.

The risk to Red is so great that White expects a 0% chance of that blot on 15 getting hit. In business terms, this is an “opportunity cost”. The impact of getting hit versus not being hit. As you play the game, you have to continuously weigh both.

Earlier, I mentioned taking risks at the start of the game and how this helps you build up blocks. As shown on the board above, having those blocks later on can offset the cost of being hit in the first 1 or 2 turns. Later on in the game, taking bad risks becomes much more costly, as in the case for Red here.

To be continued.

 

Making the steel drum kit


Gakken posted a short video of the factory line producing the tops of the new electric steel drum kit. No other news out, yet. I can’t get the Facebook video embed code to work here, so you’ll have to go to Facebook to see it for yourself.

 

Backgammon, Part 4


Risk.
The chance that your opponent may land on one (or more) of your blots and send it (them) to the bar.

Backgammon is all about probabilities. It plays a huge role in the game. First, let’s look at the dice.

The game is played with two 6-sided die, that are numbered 1 though 6, each. Each die has the same chance of coming up as a 1, as it does coming up as a 6. The die are unrelated to each other, so getting a 1 on the first die has no impact on whether the second one also comes up as a 1. And, the previous rolls have no influence on the next roll, so if you get double 6’s before, you still have the exact same odds of getting double 6’s next time, too.

If we chart out the possible permutations, we get:
1-1, 1-2, 1-3, 1-4, 1-5, 1-6
2-1, 2-2, 2-3, 2-4, 2-5, 2-6
3-1, 3-2, 3-3, 3-4, 3-5, 3-6
4-1, 4-2, 4-3, 4-4, 4-5, 4-6
5-1, 5-2, 5-3, 5-4, 5-5, 5-6
6-1, 6-2, 6-3, 6-4, 6-5, 6-6

There are 36 possible outcomes, but a little under half of them are identical as far as the game is concerned. That is, a 1-4 is the same as a 4-1. The order doesn’t matter.

So, if we want a 1-4 (or 4-1), the chances are 2 out of 36, 1 out of 18, or 5.6%. Put another way, out of 100 rolls, only 5 of them will be specifically a 1 combined with a 4. That’s not significant enough to plan a game around.

If we want double 1’s, that’s 1 out of 36, or 2.8%

However, if all we want is any kind of doubles (double 1’s, double 2’s, whatever), that’s 6 out of 36, or a 1/6th chance, at 16%. So, for a running game, where the player that gets the most doubles will win, you can expect doubles every sixth role, which is almost guaranteed to happen at least once during the running game.

If we add the numbers up, we find that there’s only one way to get a 2 (1-1), two ways to get a 3 (1-2, 2-1), three ways to get a 4 (1-3, 3-1, 2-2), etc.

2 – 1 – 2.8%
3 – 2 – 5.6%
4 – 3 – 8.4%
5 – 4 – 11.2%
6 – 5 – 14%
7 – 6 – 18%
8 – 5 – 14%
9 – 4 – 11.2%
10 – 3 – 8.4%
11 – 2 – 5.6%
12 – 1 – 2.8%

So, while there’s only one way to get a total of 2, there are 6 ways to get a total of 7. Compare 2.8% versus 18%. That means that if your opponent’s blot is 2 points away from you, you only have a 2.8% chance of hitting it, right?

Well, not exactly. In backgammon, you move the number of points indicated on EACH die. So, when you’re figuring the chances of being hit, or hitting your opponent’s blot, you need to keep in mind the odds of getting all combinations of a specific number. So, if your opponent is 2 points away, you want a 2 on one die, or any combination that adds up to 2. (Any number followed by a 2, or a 2 followed by any other number, plus double 1’s).

That would be: 1-2, 2-2, 3-2, 4-2, 5-2, 6-2, 2-1, 2-3, 2-4, 2-5, 2-6, 1-1

12/36 = 33%.

Them’s good odds. Essentially, one out of every three rolls will give you a 2. The odds get better if you’re looking for a 6. (16/36 = 44%). Things get much weaker above 7, though. 8: 5/36; 9: 4/36; 10: 3/36; 11: 2/26; 12: 1/36.

This means that if your opponent is close to your blot (between 1 and 7 points away), you have a 30% to 40% chance of getting sent to the bar. If you’re looking at switching to a running game and you need to move one stone 12 points to get to your home field, you have a 2.5% chance of doing that in 1 roll (it’s more likely to take 2 to 3 turns to move one stone 12 points.)


(Really risky starting move for 3-4.)

If we look at the example from last week, it’s the beginning of the game, you’re moving first, and you rolled a 3-4. If you take one stone from 13 and move it to 10, and another from 13 to 9, you have 2 open blots – how likely is it that White can hit you?

Well, the only stones White has that endanger you are on 1. That means White needs an 8 or a 9. For an 8, that’s 6-2, 5-3, 4-4, 3-5 and 2-6. For a 9, that’s 6-3, 5-4, 4-5 and 3-6. 9/36 = 25%. So, you can probably get away with this gambit 3 out of 4 games where you start with a 3-4. Otherwise, when White DOES get 2-6 or 3-5, he’ll most likely land on the 9 point and send you to the bar. That’s not all that damaging, though, this early in the game.

So, this is one way of measuring risk, the statistical odds that a specific blot can be hit by the opponent. Let’s look at this more next time.

To be continued.

 

Kiri-e Escher


It’s been a while since I last did a kiri-e (cut paper picture), and there haven’t been any local class events announced on facebook, so I decided that I’d try my hand at something a little closer to my own interests. I’d been looking for various ideas, and one that I kept coming back to was for M.C. Escher’s repeating, interlocking mosaic murals. My initial intent was to make the pattern as individual pieces and then assemble them like tiles, but that proved to be too difficult to try just by hand (I may do something in the computer at a later date). Instead, I tackled this one of three-colored moths/butterflies.

The finished work is 8″ x 11″ (A4 sized), and took about 2 solid weeks to assemble. There are 29 moths, and each one took about 1 hour to cut out. Then maybe another 20-30 minutes each to clean up the lines, and another hour to put in the colored paper for the body-wings, and the wing “eyes”. It didn’t come out exactly the way I wanted, and I had a lot of trouble controlling the cuts of the black background paper, but it’s not too disappointing. Actually, the background sheet isn’t black. I was afraid that the picture would come out too dark, because of the amount of blue and red, so I chose a darker blue/dark gray paper. It didn’t cut the way I expected, and I’m wondering if there’s something inherently different between black paper and the other colors.

Just in case I ever feel like going back and redoing this design, after scanning it I pulled all the color out. This will make it easier to xerox, and do the cuts. Surprisingly, this version also looks perfect for use in a children’s coloring book.