Just a quick heads-up about a revisal of my Sínat game. After one commenter, Hans, rightly noted that the probability distribution of numbers thrown by the four ancient Egyptian casting sticks were not the same as the even distribution of a die, I went to work readapting the game to reflect this.
My game now allows multiple moves whenever 1, 4 or 5 is thrown. This better reflects Kendall's original rules which are apparently inspired in part by a similar modern Arabic game called Tâb. I honestly had never conceived that there would be a difference between sticks and dice. I just blindly assumed that numbers should show up with equal frequency which made the extra turns on 1, 4 and 5 too obscure a rule for me to include but all that's changed.
For those interested in the programmatical solution to this, it's merely a matter of telling the computer to find a random number from 0 to 15 which in binary is represented as the numbers from 0000 to 1111. By conceiving of the four sticks as a single binary number of four bits, we can then isolate any particular bit with boolean bitwise operators and add up the total of 1's. We also have to remember to convert 0000 to "5" since this represents the four sticks facing down.
13 Mar 2009
Subscribe to:
Post Comments (Atom)
Hello Glen.
ReplyDeleteYour rules (hereafter RG) differ from those devised by Kendall (hereafter RK).
Also, I found different sets of rules, with 6 instead of 5, and blocks of three pawns (hereafter RW).
RK (not fully explained in your link) state that pieces landing on 28 or 29 go back to the water, or to the ankh.
RW's sixes are not a bad idea, as the sticks are supposed to be semicircular.
The descriptions of tâb I found on the Internet were incomplete. So maybe Kendall really was inspired by it.
However, it struck me that neither RG nor RK have much in common with tâb.
Only
- the boustrophedic movement
- the sticks
There are more similarities with ludo and especially
le jeu de l'oie, the Royal game of Goose.
- The pawns (geese) switch places
- The pieces need exact throws at the end
- Le puits
I played this game with my brothers and sisters, nearly half a century ago. When someone fell into the well, he could get out of it by throwing a six, or by being rescued by another unlucky player.
Sinat, like the jeu de l'oie, is a good game for children.
I don't think these (RG or RK) can be the rules of a game that fascinated Egyptians for more than 3000 years.
7vs7 or even 10vs10 will not add much to it, I think (My friends don't want to play this very boring game anymore, so I can't test.). Nor will an extra rule of three pawns blocking (RW).
Can you add a description of the rules for hitting pieces on 28/29/30 when 15 is occupied? Just for completeness.
I would like 7vs7 and 10vs10 versions, with a three-piece blocking rule. But I estimate this is just too much work for only a few Sinat lovers.
As for strategy: Whatever way you play Sinat, it almost invariably ends 1vs1, the well being the deciding factor. "Running as fast as you can" wins by a narrow margin, but really only when you count the opponent's pieces left on the board.
According to what I found on the Internet, le jeu de l'oie probably did not exist before about 1470.
Now: Back to Etruscan. Far more interesting!
Hans: "Also, I found different sets of rules, with 6 instead of 5, and blocks of three pawns (hereafter RW)."
ReplyDeleteThere are many sets of rules online and off. I'm only personally interested in ones most based on historical facts however.
I've been also comparing Sinat to the Babylonian Game of Ur (clearly a related game) and notice that "four" must have been considered a lucky number as a whole. In the Game of Ur, each "special square" occurs every four squares while its entire board has 20 squares (nb. 20 is the holy number of Shamash) and is coincidentally divisible by 4. In Sinat, rolling four gets you out of Par Maw (water). When rolling a four from the Par Nāfara (initial entry into the 'Temple'), it is yet again lucky since it lands on the last square, the square of the sun, Atum-Re (cf. Game of Ur's 20 square board and the Shamash symbolism again). As per the use of sticks in modern Tâb, four also gives us further turns. Everything in the version I present seems pretty consistent.
"Sinat, like the jeu de l'oie, is a good game for children."
And... when enough incentive is offered... a great game for adults.
Look at all the zombies playing VLTs at your local casino, pushing the same buttons over and over and over. Many children's games are easily converted to adult forms with added incentives like money or sex. Eg. Monopoly → Strip Monopoly, Baseball → Baseball Bets.
So back to Sinat, as previously commented by someone, it was a gambling game too, and I suppose, just as with the VLT players, no profound strategy is required to infatuate people for hours (or days) if you believe you're the next great winner.
We should really be discussing actual historical facts concerning our choice of which rules are most accurate. Otherwise it's just an endless pursuit of what is most idly "entertaining" over what is most "historical".
"As for strategy: Whatever way you play Sinat, it almost invariably ends 1vs1 [...]"
But can you *prove* that your assertion is true? You keep repeating this over and over again without basis or references. Is there some insight from Game Theory that I need to know?
Obviously some strategies are still better than others so the question remains: Is there a strategy (complex or not) that enables someone to win the given rules of Sinat (ie. in "RG" rules, hehe) better than the average player. For the purposes of coding the computer play, that's all I need to know. And the rest, as I say, is a matter of historical accuracy.
Hello Glen
ReplyDelete"As for strategy: Whatever way you play Sinat, it almost invariably ends 1vs1 [...]"
But can you *prove* that your assertion is true? You keep repeating this over and over again without basis or references. Is there some insight from Game Theory that I need to know?
Obviously some strategies are still better than others so the question remains: Is there a strategy (complex or not) that enables someone to win the given rules of Sinat (ie. in "RG" rules, hehe) better than the average player. For the purposes of coding the computer play, that's all I need to know. And the rest, as I say, is a matter of historical accuracy.
My "proof":
I played Sinat for many hours (Yes, almost like a zombie, I have to admit.).
I just counted the numbers of wins and losses. An accepted method, though it gives no more than an empirical "proof".
I imitated (while playing against myself; my friends already are bored) Mordrigar's two-three theory.
Mordrigar's two-blocks and three-blocks are an optical illusion.
Ultimately the blocks will have to move, so they really are not blocking anything at all. Also, they allways fall apart, either by bad throws or by badly timed twos and threes, or, of course because they reach 26.
Mordrigar's strategy, however, has some merit. A "running" player should play in such a way that he can play a Two or a Three, if possible.
Of course I played against your program.
It should not surprise you that your program loses quite often. Your program tends to keep pieces on 30, 29, 28 (and even 27). These pieces often are hit, and thereafter have a one-in-11 chance to escape (More often they are rescued by the opponent).
Another feature of your program is its tendency to build a "caterpillar" at 21 to 26. Often the program has only one "one": into the water.
Playing a strategy of switching pieces as often as possible, you sometimes get an advantage (but very, very rarely, and only against opponents who refuse to do this.).
I also played against an improved version of your program.
Building blocks around Ten and around 24/25/26, but avoiding the water, so not leaving pieces on 28/29 etc.
I tried combinations.
I have not tried to imitate the "retarded monkey" (This would require an extra procedure to determine the move chosen by the monkey. I am too lazy for that).
"Running" wins. Narrowly if you only count wins and losses; by a considerable margin if you count the pawns left on the board.
Of course sometimes a runner has choices to make to win most. I already mentioned 25. This square generally is to be avoided, especially in the middle stages.
Some very difficult decisions have to be made when an opposing block has formed near 26/25/24.
Also, if you can choose between 28 and 29, choose 29. 29 is hit twice for every three times 28. Also it can be taken out three times for every twice 28.
All in all it does not matter much.
The game (far too) often ends in 1vs1.
In the very long run, the better player/strategy will win.
But even the "retarded monkey" is a formidable opponent.
I've made updates in the past few days. See Sinat - Graphics revised and computer algorithm enhanced.
ReplyDeleteMy new algorithm Seth is definitely better than the retarded monkey. Switching at every opportunity may in fact be a good overall strategy, despite what you say since I've actually tested it against the retarded monkey (completely random play) and it won 68% of the time in 25 plays by an average of a 2-piece gain.
Hello Glen.
ReplyDeleteSwitching at every opportunity may in fact be a good overall strategy
You are right. You should switch (almost) every time you can. This effectively is a form of "running".
There are few exceptions.
One is when you want to keep intact a small block to protect your pieces from long range (4 or 5) hits.
, despite what you say
My clumsy English...
since I've actually tested it against the retarded monkey (completely random play) and it won 68% of the time in 25 plays by an average of a 2-piece gain.
When I tested the retarded monkey, it won a a few % more. But this was a long time ago.
Still, 32% is an enormous result for a clueless monkey!
Generally, humans play better than the monkey, so even very bad players lose only slightly less than 50%.
I will try Seth, when I find the time. Thanks!
Hans: "There are few exceptions. One is when you want to keep intact a small block to protect your pieces from long range (4 or 5) hits."
ReplyDeleteI was thinking about this and it might be a next step. One of these next few days, I'll have to think about how I might translate that into a better algorithm. However, it seems that "running" is the core of the best strategy and everything else are add-ons and tweaks. Hmmm.
"Still, 32% is an enormous result for a clueless monkey!"
Yes, but naturally a game with an element of chance (ie. the casting sticks) is going to improve the odds for the poor retarded monkey.
"Generally, humans play better than the monkey, so even very bad players lose only slightly less than 50%."
Exactly. However, I'm merely using the retarded monkey algorithm (ie. Lateesha; random moves) as something to test against to improve my computer player. That way I know if I've either found a better or worse strategy in a scientific way.
"I will try Seth, when I find the time. Thanks!"
It's been beating me a little too much and I'm afraid that maybe I now may be the retarded monkey.
Take it easy, Glen!
ReplyDelete1) I played 7 games against what at first I thought was Seth.
"Seth" beat me 4 times. He seemed to play incredibly bad. He must have hypnotized me.
2) I misanalysed. Landing on 25 is not nearly as bad as I thought. Effectively you are not waiting for a One, but for a One-plus-x.
3) Who is Lateesha named after?
Hans: "Effectively you are not waiting for a One, but for a One-plus-x."
ReplyDeleteMore accurately, my "AvoidWater" function, added to the general strategy, simply erases from its memory the possibility of moving from 25 to the waters on a roll of "1" UNLESS it's the ONLY move left.
"Who is Lateesha named after?"
No one in particular. I've been watching too much Jerry Springer lately. Lol. It was just a name I pulled out of my head. I could have called it Bob, Cassandra, or Ming Yu too, but I didn't.