Monday, July 30, 2007

BMAI is not in a good position at the moment...

the odds are he (it?) won't be able to win this round, but it does still have some chance of winning this round, right? what should it do?

* Next Turn * Player: bmai *AI* *111111101001000001100 as of 9-22-03* * Next Turn *
Button Man: Jellybean Score: -15 (-28.6 sides) Rounds Won/Lost/Tied: 0 / 0 / 0 (out of 3 round(s))
Captured Dice: None
Dice Poison
20-sided die
V Swing
(with 6 sides)
X Swing
(with 4 sides)
Value 3 2 4
Dice 6-sided die 10-sided die Poison
12-sided die
20-sided die X Swing
(with 4 sides)
Value 1 8 2 13 3
Player: ElihuRoot *Dead Dude* *Fanatic*
Button Man: Lucky Score: 28 (28.6 sides) Rounds Won/Lost/Tied: 0 / 0 / 0
Captured Dice: Shadow 20-sided die

Friday, July 27, 2007

I think 2-3 posts per week is all I can consistently manage -- what should D. have done?

I'll do my best to post a puzzle when I can; I also want to go back and offer some comments and replies on older puzzles (though it's probably best that I don't give my own opinions too soon). Finally, I need to write a few more detailed strategy essays (like telling you what that essay left out about Crab)

In the meantime, here's something from a recent game. (say, challenge me to a match to help me generate more of these situations! Pick whatever buttons you think lead to interesting problems. I don't care about the odds, I'll take either side, though if you give me a ridiculously outmatched button, I'd mildly prefer the match to be "just for fun" -- or we can play both the game and the reverse match.)

In the game below, Desdinova just made a power attack that, unfortunately for him, rolled high enough for me to recapture it with my own 20-sided die -- on the other hand, it forces me to reroll that die and puts it at risk. He could still eke out a tie. (actually, if I reroll a 2, I suppose there's a chance he might win!) Was there a better move D. could have made?



Button Men Game #600869

Tournament Legal challenge, copying communication from game 600484

Skills in this game: Poison, Shadow, X Swing
Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Caine (ps4 ps4 s20 s20 sX) Score: 26 (8 sides) Rounds Won/Lost/Tied: 0 / 1 / 0 (Out of 3 wins)
Your Captured Dice: 16-sided die, X Swing 4-sided die
Poison Shadow
4-sided die
Shadow
20-sided die

Shadow X Swing
(with 4 sides)
3 17
4
Captured last turn
Poison Shadow
6-sided die
Poison Shadow
12-sided die
20-sided die
1 1 18
Opponent: Desdinova
Button Man: Bluff (ps6 ps12 16 20 X) Score: 14 (-8 sides) Rounds Won/Lost/Tied: 1 / 0 / 0
Captured Dice: Shadow 20-sided die, Poison Shadow 4-sided die, Shadow X Swing 4-sided die

Results from last turn
Desdinova is performing a power attack with a 20-sided die showing 10,
targeting ElihuRoot's Shadow X Swing 4-sided die showing 4.

The 20-sided die is rerolled and the new value is 18.

Desdinova takes ElihuRoot's die.

Wednesday, July 25, 2007

From a game today -- what would you do?

Maybe this is obvious, but I do think there's a point worth making here, too.


Should I take his die with value 17 using mine with value 18? Should I take his
die with value 9 using mine with value 10? Any other bright ideas?

Button Men Game #600484

Reverse Battle From Game 599998

Skills in this game: Option, X Swing
Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Aylee (8 10/20 12 12/20 20) Score: 50 (5.3 sides) Rounds Won/Lost/Tied: 2 / 0 / 0 (Out of 3 wins)
Your Captured Dice: 20-sided die
8-sided die 12-sided die Option 12/20
(with 20 sides)
20-sided die Option 10/20
(with 20 sides)
4 4 10 18 6
Captured last turn
20-sided die 20-sided die X Swing
(with 4 sides)
17 9 4
Opponent: Desdinova
Button Man: Dirgo (20 20 20 X) Score: 42 (-5.3 sides) Rounds Won/Lost/Tied: 0 / 2 / 0
Captured Dice: Option 10/20 20-sided die

Monday, July 23, 2007

a little later in the same round as one of Friday's posts

D's turn is coming up, and he has to take my 20-sided die with a value of 1. Which die should he take it with? This is pretty straightforward, isn't it? You can go through the computation
to get the exact chance of winning with each decision, but is there a general principle you can extract that would allow you to more easily figure out the best move in similar situations?

Button Men Game #599998

Tournament Legal challenge, copying communication from game 599661

Performing a power attack
ElihuRoot is performing a power attack with a 20-sided die showing 9,
targeting Desdinova's 12-sided die showing 7.

The 20-sided die is rerolled and the new value is 14.

ElihuRoot takes Desdinova's die.

Your Dice:Opponent's Dice:
20-sided die showing 14
20-sided die showing 1
8-sided die showing 6
Option 10/20 10-sided die showing 7

Rounds Won/Lost/Tied: 1 / 0 / 0 (Out of 3 wins)
Your Score: 72 (15.3 sides)
Opponent's Score: 49

What's Zegota's best move?

OK, this is an easy one, isn't it?

What should he do? What are his chances of winning?

Player: Zegota, score: 41 (-0.6 sides)
capture dice: 20-sided die, focus X-swing (with 15 sides)
Dice 4-sided die8-sided die
Value 4
3

Dice 4-sided die4-sided die8-sided die
Value 412
Player: ElihuRoot, score 42 (0.6 sides)
captured dice: 4-sided die, 20-sided die, focus X-swing (with 10 sides)

here's the filler:

Button Men Game #309173
Tournament #5695: #32
Current Round: Round 3. (organized by bowler190)

Tonase vs. Tonase

Rounds Won/Lost/Tied: 2 / 2 / 0 (Out of 3 wins) (for both of us, obviously)
Most recent move:
ElihuRoot is performing a skill attack with a 4-sided die showing 2 and a 8-sided die showing 2, targeting Zegota's 4-sided die showing 4.

The 4-sided die is rerolled and the new value is 1.
The 8-sided die is rerolled and the new value is 2.

ElihuRoot takes Zegota's die.

Friday, July 20, 2007

Speed dice #1: Does this article on "countering speed dice" make any sense at all?

I almost thought we were playing a different game!


I think this article may have been written before the growth of the buttonmen.com web game -- back when people thought Tirade was really strong, etc. But still, the notion that what you want are lots of dice of different sizes! There MIGHT be something to the idea that you want
to get initiative: any speed attack your opponent can make is also a skill attack you can make on her, if you go first --Bunnies is actually a pretty good button against recipes with speed dice, both since it will get initiative and because the dice don't change when you reroll them.

Still, your main hope in defanging Bennett is that you won't be a target -- and if all your dice are large, it's much less likely that they'll be vulnerable to a massive speed attack.

Forgetting poison, etc, for the moment, look at Bennett's record against Soldiers buttons:
Bennet wins against all of them, but there's a big difference between winning 56% of his
games, or even 59%, and winning 76% or more. Admittedly, I suspect
Changeling, in particular, is not well-played against Bennett -- maybe all of these numbers would be a little lower with better play (I think Bennett is much easier to play in all these matchups than his opponent) -- I'll also confess to being a little puzzled by Kublai's relatively good showing on this list - maybe it's that "disparate dice" thing!
Hammer (Soldiers)78/61 = 13956.11%







Kublai (Soldiers)13/9 = 2259.09%
Shore (Soldiers)58/40 = 9859.18%







Karl (Soldiers)16/8 = 2466.66%







Changeling (Soldiers)13/4 = 1776.47%







Iago (Soldiers)24/7 = 3177.41%







Avis (Soldiers)51/12 = 6380.95%







Stark (Soldiers)56/14 = 7080%







Bauer (Soldiers)19/4 = 2382.6%







Clare (Soldiers)32/7 = 3982.05%







Hannah (Soldiers)20/4 = 2483.33%







Niles (Soldiers)21/3 = 2487.5%







Kith (Soldiers)14/1 = 1593.33%

And note that Giant, whose overall record against ALL buttonmen is about 56%, does nearly that well against Bennett:
Giant (Brom)51/42 = 9354.83%
And Yeti does BETTER against Bennett than its overall record of about 60%:
Yeti (Majesty)52/146 = 19826.26%
(though the question there might be what percentage of these Yeti-Bennett games were played by Anders as this is pretty close to HIS average value with Yeti...)


aside from what button to play, there's also the question of how to play the button against speed dice -- of course, all things being equal, you want to try to take speed dice early, though small speed dice may not be that big a threat. And you want to be very alert when rolling your dice how much risk you are exposing yourself to -- you want to minimize the chance that you roll into a speed attack. That usually means you'd prefer to roll as few dice as possible and you are alert to the values on your unrolled dice -- ideally they add up to as few threatening values as possible. Some illustrations might make this more clear, but I'll either have to construct
them or play a bunch of games against speed dice to generate examples.

Am I in good shape here? What should I do?

Maybe the next move is obvious here... but do you think I'm in a good position in this game?

Button Men Game #599998

Tournament Legal challenge, copying communication from game 599661

Skills in this game: Option, X Swing
Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Dirgo (20 20 20 X) Score: 50 (3.3 sides) Rounds Won/Lost/Tied: 1 / 0 / 0 (Out of 3 wins)
Your Captured Dice: Option 12/20 20-sided die
20-sided die 20-sided die 20-sided die
X Swing
(with 20 sides)
9 10 1
18
Captured last turn
8-sided die Option 10/20
(with 10 sides)
12-sided die 20-sided die
3 2 5 8
Opponent: Desdinova
Button Man: Aylee (8 10/20 12 12/20 20) Score: 45 (-3.3 sides) Rounds Won/Lost/Tied: 0 / 1 / 0
Captured Dice: X Swing 20-sided die

Thursday, July 19, 2007

Did you ever see this article on buttonmen strategy?

It's very pretty! And I do understand that there's a world of Legend of the Five Rings outside of buttonmen (though I have no idea what it's all about -- how could it possibly be as interesting as buttonmen, anyway?). And I'm not *necessarily* objecting to how wordy it is, or how much time is spent saying the obvious (I'm known for doing that, myself).

But.. but... but... some of it isn't true -- and see what he says about my beloved Crab! He doesn't understand her at all!

http://www.geocities.com/stormson_2000/buttonmen.html#strategy

Maybe I'll have to do some Crab examples -- but I don't have any saved (I've sort of been cleaning out my garbage pile this week -- well, it's more of an archaeological excavation, I suppose. These are snippets and situations, not necessarily deep, that I happened to have saved temporarily at the time of the game, but forgot to delete them. )

Wednesday, July 18, 2007

This one may be harder to agree on:

The previous examples I posted were all at or near the end of the game -- which gives us the ability to actually compute the exact probability of winning -- or at least make a pretty decent approximation. It's harder (for me, at least), to be so precise at the beginning of a turn.


Game #166629 from June 2003, and something called "IBMF (provisional)" -- I had to search the message boards to remember what that was!

Anyway, it's the start of the last round of the game, I have the initiative -- but what do you think I should do? I know what I *did*, and I have my reasons, but I'm not going to promise you it was the right thing to do.

Player: randomlife *Fanatic* *Pesky* *Teen Girl Squad*
Button Man: Sailor Mercury Score: 23 (10.6 sides)
Rounds Won/Lost/Tied: 2 / 2 / 0 (out of 3 round(s))
Captured Dice: None

Dice 4-sided die8-sided die8-sided die
12-sided die
10-sided die
4-sided die
Value
3
7
8
2
8
4

Dice 10-sided diePoison
20-sided die
20-sided die
20-sided die
X Swing
(with 4 sides)
Value 109
20
91
* Next Turn * Player: ElihuRoot *Fanatic* *Dead Dude* * Next Turn *
Button Man: Crusher Score: 7 (-10.6 sides)
Rounds Won/Lost/Tied: 2 / 2 / 0
Captured Dice: None

Tuesday, July 17, 2007

Is this an interesting position?

(Again, I don't think I'll be maintaining this pace of posting in the future).

I can't tell if this one is obvious or not -- insert favorite math joke here. It's still a somewhat similar idea.


OK, in this game, it's DanaMorrigan's turn to move. Her move is forced, she's going to have to take my Stinger 8-sided die with her X Swing 7-sided die. What's the best thing I can do in response? (Of course, it might depend on what she rolls -- she might even roll a 7, too high for me to catch it with my own X swing...). What are my chances of winning in the worst case? What is the worst case?

Player: ElihuRoot *Dead Dude* *Fanatic*
Button Man: Buck Score: 53.5 (8.6 sides) Rounds Won/Lost/Tied: 2 / 2 / 0
Captured Dice: 20-sided die, 12-sided die, Stinger 8-sided die
Dice Stinger
8-sided die
Stinger
10-sided die
X Swing
(with 9 sides)
Value 386

Dice Stinger
10-sided die
X Swing
(with 7 sides)

Value 14
* Next Turn * Player: DanaMorrigan *Dagda* *Ms. Funny Pants* * Next Turn *
Button Man: Buck Score: 40.5 (-8.6 sides)
Rounds Won/Lost/Tied: 2 / 2 / 0 (out of 3 round(s))
Captured Dice: 20-sided die, 12-sided die

Monday, July 16, 2007

What's gryphon's best move?

Granted these very-near-the-end positions are perhaps too straightforward, if you stop and compute what to do. But how many people do that consistently?

And is this situation any muddier? Would you take my 10-sided die or my 20-sided die? Does it make much difference?

* Next Turn * Player: Gryphon * Next Turn *
Button Man: CynCyn Score: 34 (3.3 sides)
Rounds Won/Lost/Tied: 0 / 1 / 0 (out of 3 round(s))
Captured Dice: 12-sided die, 6-sided die
Dice 6-sided die20-sided die6-sided die
Value 3201

Dice 10-sided die20-sided die
Value 96
Player: ElihuRoot *Fanatic* *Dead Dude*
Button Man: Sailor Jupiter Score: 29 (-3.3 sides) Rounds Won/Lost/Tied: 1 / 0 / 0
Captured Dice: Doppleganger 10-sided die, X Swing 4-sided die

Results from last turn:
ElihuRoot is performing a power attack with a 20-sided die showing 10,
targeting Gryphon's X Swing 4-sided die showing 4.

The 20-sided die is rerolled and the new value is 6.

What's my opponent's best move?

Don't expect so many of these, in general! Maybe I can post two or three a week, normally.

Here's another one, maybe it's a similar theme to the last one -- maybe not! This is from a long time ago, I don't really know why I saved this position to my online notes -- and I didn't have the graphics, so pardon my quick and sloppy attempt to make it look a little like the game screen.

It was game 167611 from tournament 4706. I had BANG (p(4,4), 6, 12, 12, X), my opponent, SG_1, was playing AGATHA (4, 6, (8,8), 20, X). It's the first round, first my X swing was set to 4, his was set to 20. I had just performed a skill attack with a 6-sided die showing 3 and a X Swing 4-sided die showing 1, targeting SG_1's 6-sided die showing 4. after the reroll, things looked [something] like this:


Me: ElihuRoot
My Button Man: Bang (p(4,4), 6, 12, 12, X) Score: 39 (2 sides)
Rounds Won/Lost/Tied: 0 / 0 / 0 (Out of 3 wins)
My Captured Dice: (8,8) twin die, 6-sided die, X Swing die (20 sides)

ice Poison Twin Die
(Both with 4 sides)
6-sided die X Swing
(with 4 sides)






Value 2 5 1

Dice 4-sided die 20-sided die
6-sided die
Value 4 16
(4) captured last turn
Him: SG_1
His Button Man: Agatha (4, 6, (8,8), 20, X) Score: 36 (-2 sides)
Rounds Won/Lost/Tied: 0 / 0 / 0 (Out of 3 wins)
His captured dice 12-sided die, 12-sided die


So: what should he do? He has five possible power attacks, two with the 4-sided die and three with the 20-sided die.

OK, here's a sample "what's the best move?"

Maybe this isn't the best example, but it just came up online in a game I was playing. I'm pretty sure I made the "best" move under these circumstances, what do you think it was?

So: In the below situation, you are me ("ElihuRoot"). [And, for those unfammiliar with buttonmen.com notation, the 20-sided die on the top right has just been captured by Anders]. You have eight different possible power attacks, and one possible skill attack. What is the move that maximizes your probability of winning this round?


Button Men Game #599271


Skills in this game: Reserve
Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Diamond (4 6 12 20 r8 10 r10 20) Score: 52 (1.3 sides) Rounds Won/Lost/Tied: 1 / 2 / 0 (Out of 3 wins)
Your Captured Dice: 20-sided die, 12-sided die
4-sided die 6-sided die 20-sided die 10-sided die 20-sided die
3 3 17 10 1
Captured last turn
6-sided die 10-sided die 20-sided die
6 1 19
Opponent: Anders *ONE MILLION POINTS* *Fanatic*
Button Man: King Endymoin (6 10 20 20 r6 r10 12 r20) Score: 50 (-1.3 sides) Rounds Won/Lost/Tied: 2 / 1 / 0
Captured Dice: 12-sided die, 20-sided die


Thursday, July 12, 2007

it's my firm belief

that many people who play buttonmen understand the strategy of the game imperfectly -- I include myself, by the way! I have seen numerous errors in several strategy posts on the message boards of buttonmen.com, and even on web sites with articles about strategy. And I KNOW the online statistics for button-vs-button are not always very good indicators of the true relative strength of the buttons with optimal play.

Speed dice are dangerous, sure -- but they are not NECESSARILY as dangerous as you might think from the compiled statistics. People often misplay against speed dice and expose themselves to more risk than they need to.

Null dice are usually weak -- but they may not be as weak as everyone thinks!

Max is an easy button to play -- or to play against -- well, no, he isn't at all!

Maybe I'll get around to writing my own strategy articles; maybe I'll just occasionally make references to errors I've seen. I'd love to save occasionally interesting positions I've encountered.

Or maybe I'll never get around to any of this -- but it doesn't hurt to try!

From the "Moshe Con" booklet



Back when Morris had his bar mitzvah, we created two buttonmen for the "family game night" party we held. I like those buttons, both for the great artwork done by our friend Laura, for the way the recipes support the theme, and for the strategic balance the buttons have.

But not many of the people at the party actually PLAYED buttonmen, and I've often regretted that the little strategy summary I wrote for the event -- brief, based on a jewish text, yet not at all bad as a general statement of the principles of buttonmen -- has never since had a chance to be seen.







Until now: Here is the relevant material, taken straight from the convention booklet. (It seems to start a bit abruptly; in the context of the booklet, it followed an exposition of the rules of the game, and a description of the new buttons):


Strategy tips: For such a simple game, there is a surprising amount of mathematics and sophisticated strategy to Button Men. You don’t need to know all this to enjoy the game! A little farther down are links to buttonmen strategy details and an online game site where players happily offer informal tutoring.

But, in keeping with the premise in Koheleth (Ecclesiastes) that “there is nothing new under the sun” (Koheleth 1:9), one can find a concise summary of buttonmen strategy in this mishnah from Pirkei Avot:

Akavia Ben Mehalalel says: Contemplate three things, and you will not come to the hands of sin. Know from where you came, and to where you are going, and before whom you will ultimately give judgment and accounting. (Avot 3.1)

In this context, this means (in reverse order):

Judgment and accounting: Know the victory conditions – they are not simply to capture your opponent’s dice! Recall how dice are scored. The player who begins with more sides of dice has fewer points available to capture (“know from where you came”). This means that the player who begins with more sides must not only capture all his opponent’s dice, but must retain a sufficient number of his own dice in order to win. Try to know from the beginning of a round what specific outcomes at the end will result in victory.


Where you are going:
now that you know what you need to do, you need to think about how to get there! In early turns, skill attacks are more common and large dice are more vulnerable. Towards the end of the round, fewer dice are left. Try to steer the game to a favorable position in the end game. If your opponent begins with a high value on a powerful die, you need to try to get him to reroll it as soon as possible, while you are more likely to be able to capture it; conversely, you may need to think about how to protect your larger dice.


From where you came:
As mentioned above, the number of sides you begin with determines the ultimate victory conditions. Many buttons include swing or option dice, which allow you to vary the initial size of your dice. This is a powerful tool! Understanding the effect that your choice of swing die has on your victory conditions enables you to make it easier to push the game towards endings in which you can win!

This is pretty abstract – perhaps playing a bit will make things more clear! But if you want to learn more about buttonmen strategy, check out the essays at www.beatpeopleup.com/bmstrat.html and you can find opponents and teachers from around the world at http://www.buttonmen.com