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Jan 25, 2020, 3:35:04 AM1/25/20

to

On January 23, 2020 at 5:10:23 PM UTC-7, Tim Chow wrote:

> In any case, it shouldn't be that hard to write

> a program from scratch to compute exact cubeful

> equities in Hypergammon. I might do that sometime.

I'm pretty sure that you can't.

So, in order to help you get started with an easier

task, I invented an even simpler BG variant than

HyperGammon: HypestGammon..!! :)

Players start out with only one man on the 24-point

and roll only one die.

To decide who gets the opening roll, they play rock

paper scissor.

The rest is the same as regular BG, except there will

be obviously no doubles possible with a single die.

Let's see if you can write a program from scratch to

compute exact cubeful equities in "HypestGammon".!? :)

MK

> In any case, it shouldn't be that hard to write

> a program from scratch to compute exact cubeful

> equities in Hypergammon. I might do that sometime.

I'm pretty sure that you can't.

So, in order to help you get started with an easier

task, I invented an even simpler BG variant than

HyperGammon: HypestGammon..!! :)

Players start out with only one man on the 24-point

and roll only one die.

To decide who gets the opening roll, they play rock

paper scissor.

The rest is the same as regular BG, except there will

be obviously no doubles possible with a single die.

Let's see if you can write a program from scratch to

compute exact cubeful equities in "HypestGammon".!? :)

MK

Jan 25, 2020, 1:42:46 PM1/25/20

to

On Saturday, January 25, 2020 at 3:35:04 AM UTC-5, mu...@compuplus.net wrote:

> I'm pretty sure that you can't.

I'm not as easily manipulated as you are.
> I'm pretty sure that you can't.

---

Tim Chow

Feb 1, 2020, 1:13:33 AM2/1/20

to

On January 25, 2020 at 11:42:46 AM UTC-7, Tim Chow wrote:

> On January 25, 2020 at 3:35:04 AM UTC-5, mu...@compuplus.net wrote:

>> I'm pretty sure that you can't.

> I'm not as easily manipulated as you are.

You sound like you have just realised that you have

been manipulated to claim something you can't do. :)

Or, perhaps, you manipulate yourself..?? ;)

MK

> On January 25, 2020 at 3:35:04 AM UTC-5, mu...@compuplus.net wrote:

>> I'm pretty sure that you can't.

> I'm not as easily manipulated as you are.

been manipulated to claim something you can't do. :)

Or, perhaps, you manipulate yourself..?? ;)

MK

May 21, 2020, 12:57:25 PM5/21/20

to

go ahead and write a program to compute the equities.

In fact, I did so in two different ways. The first way was to write down

a mixed integer program and then solve it with CPLEX. The second way was

to write an iterative program along the lines of what Tom Keith sketched.

Both methods gave the same numerical answers. It seems intuitively clear

that the equities should exist and be unique, but I don't actually have a

rigorous proof of that fact.

Note that in HypestGammon, checker play is deterministic. So cube decisions

are the only nontrivial decisions.

Note also that since there is only one checker, it doesn't really make sense

to talk about a gammon; a gammon is the same as a single win. But it does

make sense to talk about a backgammon; if I bear off my checker when my

opponent is on the bar or in my home board, then I win a backgammon. It is

easy to rerun my code with whatever backgammon value you want.

I can make the equities I computed available on my website if anyone is

interested. As a spot check, I find that if you win the initial rock-paper-

scissors game and get to go first, your cubeful equity is about 0.26081.

If you are allowed to double after winning rock-paper-scissors but before

rolling the die, then you should not double. Doubling decreases your equity

to about 0.03044.

In the meantime, I discovered that GNU Backgammon comes bundled with a program

called "makehyper" that computes cubeful equities for HyperGammon. That has

reduced my incentive for beefing up my program(s) to handle HyperGammon.

---

Tim Chow

May 21, 2020, 1:58:45 PM5/21/20

to

When learning concepts, it's often best to focus on them in isolation.

So the game might be a great tool for teaching doubling to beginners.

Since only the doubling is non-trivial, the game makes it possible to

focus on the doubling concept in isolation without being distracted

by checkerplay concepts. Alternatively, I've thought of the idea of

introducing skill into snakes and ladders, by playing it with a doubling cube.

Paul

May 21, 2020, 2:44:26 PM5/21/20

to

On Thursday, May 21, 2020 at 1:58:45 PM UTC-4, Paul Epstein wrote:

> Hypestgammon doesn't sound like a bad game at all.

> When learning concepts, it's often best to focus on them in isolation.

> So the game might be a great tool for teaching doubling to beginners.

> Since only the doubling is non-trivial, the game makes it possible to

> focus on the doubling concept in isolation without being distracted

> by checkerplay concepts. Alternatively, I've thought of the idea of

> introducing skill into snakes and ladders, by playing it with a doubling

> cube.

It also occurs to me---and perhaps this was Murat's point---that it provides
> Hypestgammon doesn't sound like a bad game at all.

> When learning concepts, it's often best to focus on them in isolation.

> So the game might be a great tool for teaching doubling to beginners.

> Since only the doubling is non-trivial, the game makes it possible to

> focus on the doubling concept in isolation without being distracted

> by checkerplay concepts. Alternatively, I've thought of the idea of

> introducing skill into snakes and ladders, by playing it with a doubling

> cube.

a nice testing ground for investigating non-equilibrium strategies. For

example, one could see what happens if we pit the equilibrium strategy

against some simple strategy such as "double if my DMP winning chances are

>50% and take if and only if my DMP winning chances are >25%."

A more subtle question would be, suppose I want to publish a sequence of

(say) 25 consecutive games that seems to demonstrate that I can "beat the

bot." What strategy should I use to minimize the waiting time until I get

such a sequence? It probably isn't the equilibrium strategy. Almost surely

I want to increase variance at the expense of expected value. Offhand, I'm

not sure what kind of learning algorithm would work well to discover such a

strategy. Naively, I could start with some doubling/taking strategy, then

randomly change some decisions to see if it helps, but this seems like it

would take an inordinately long time to converge, because I might have to

simulate a lot of games to decide if my random change helped.

---

Tim Chow

May 24, 2020, 3:37:06 AM5/24/20

to

On May 21, 2020 at 10:57:25 AM UTC-6, Tim Chow wrote:

> On January 25, 2020 at 3:35:04 AM UTC-5, mu...@compuplus.net wrote:

>> On January 23, 2020 at 5:10:23 PM UTC-7, Tim Chow wrote:

>>> In any case, it shouldn't be that hard to write

>>> a program from scratch to compute exact cubeful

>>> equities in Hypergammon. I might do that sometime.

I never thought you would try even being dared. And, as you

confess, you wouldn't have if your colleague hadn't expressed

interest in it. So, if any credit may arise from your effort,

he/she should get it. Unless he requires to remain anonymous,

may we know who this "colleague" is?

More importantly than his name, I would like to know what was

the nature of his interest? Was it plain/scientific curiosity

to know/learn whithout any presuppositions? Or did he already

have an idea what the result would be and just wanted to find

out if he was right/wrong?

I'm sure we will later question and interpret your methods and

results after the fact. With that, what lead to the experiment

may be as worthy and meaningful as what came out of it.

> In fact, I did so in two different ways. The first way was

> to write down a mixed integer program and then solve it with

> CPLEX. The second way was to write an iterative program along

> the lines of what Tom Keith sketched.

Since you have already put in an effort into this, would you go

the extra step to explain and document what you have done? Even

if it may be too complex for non mathematicians at first, thru

future discussions, others may also understand eventually.

> Both methods gave the same numerical answers.

Was there ever the possibility in your mind that they woudn't?

If yes, by chance, have you even began to ask the question what

then..?

> It seems intuitively clear that the equities should exist and

> be unique, but I don't actually have a rigorous proof of that

> fact.

Well, at least you started on it. Hopefully more will follow.

> Note also that since there is only one checker, it doesn't

> really make sense to talk about a gammon; a gammon is the

> same as a single win. But it does make sense to talk about

> a backgammon; if I bear off my checker when my opponent is

> on the bar or in my home board, then I win a backgammon. It

> is easy to rerun my code with whatever backgammon value you

> want.

If it's going to make cube decisions more like regular gammon,

(and it it would be meaningful doing it), a new rule can be

injected to differentiate between single games and gammons. If

the checker has at least made into the loser's home board, then

it would be a single game vs. gammon lost otherwise, etc.

> I can make the equities I computed available on my website if

> anyone is interested.

Yes, plase. I would be very interested in not only the computed

equities but any and all other info you can make available, such

as program codes, etc.

> As a spot check, I find that if you win the initial rock-paper-

> scissors game and get to go first, your cubeful equity is about

> 0.26081.

Can we also speak in MWC also, if not instead.

> If you are allowed to double after winning rock-paper-scissors

> but before rolling the die, then you should not double. Doubling

> decreases your equity to about 0.03044.

Since it's not allowed, why would you even want to know that?

Are you trying to create strawmen already..??

> In the meantime, I discovered that GNU Backgammon comes bundled

> with a program called "makehyper" that computes cubeful equities

> for HyperGammon.

I saw that too. In fact, it refers to 1, 2 or 3 checker HyperGammon.

> That has reduced my incentive for beefing up my program(s) to

> handle HyperGammon.

Nonsense. How do you know Gnubg does it right? There is no way to

compare my HypestGammon to Gnubg's 1-checker HyperGammon, (since,

I assume it uses two dice), but you can improve your programs to

handle 1, 2 and 3 checker HyperGammon, and compare the results.

MK

> On January 25, 2020 at 3:35:04 AM UTC-5, mu...@compuplus.net wrote:

>> On January 23, 2020 at 5:10:23 PM UTC-7, Tim Chow wrote:

>>> In any case, it shouldn't be that hard to write

>>> a program from scratch to compute exact cubeful

>>> equities in Hypergammon. I might do that sometime.

>> So, in order to help you get started with an easier

>> task, I invented an even simpler BG variant than

>> HyperGammon: HypestGammon..!! :)

>> task, I invented an even simpler BG variant than

>> HyperGammon: HypestGammon..!! :)

>> Let's see if you can write a program from scratch to

>> compute exact cubeful equities in "HypestGammon".!? :)

> One of my colleagues expressed interest in HypestGammon,

> so I did finally go ahead and write a program to compute

> the equities.

This renews my hope and interest to continue debating in RGB.
>> compute exact cubeful equities in "HypestGammon".!? :)

> One of my colleagues expressed interest in HypestGammon,

> so I did finally go ahead and write a program to compute

> the equities.

I never thought you would try even being dared. And, as you

confess, you wouldn't have if your colleague hadn't expressed

interest in it. So, if any credit may arise from your effort,

he/she should get it. Unless he requires to remain anonymous,

may we know who this "colleague" is?

More importantly than his name, I would like to know what was

the nature of his interest? Was it plain/scientific curiosity

to know/learn whithout any presuppositions? Or did he already

have an idea what the result would be and just wanted to find

out if he was right/wrong?

I'm sure we will later question and interpret your methods and

results after the fact. With that, what lead to the experiment

may be as worthy and meaningful as what came out of it.

> In fact, I did so in two different ways. The first way was

> to write down a mixed integer program and then solve it with

> CPLEX. The second way was to write an iterative program along

> the lines of what Tom Keith sketched.

the extra step to explain and document what you have done? Even

if it may be too complex for non mathematicians at first, thru

future discussions, others may also understand eventually.

> Both methods gave the same numerical answers.

If yes, by chance, have you even began to ask the question what

then..?

> It seems intuitively clear that the equities should exist and

> be unique, but I don't actually have a rigorous proof of that

> fact.

> Note also that since there is only one checker, it doesn't

> really make sense to talk about a gammon; a gammon is the

> same as a single win. But it does make sense to talk about

> a backgammon; if I bear off my checker when my opponent is

> on the bar or in my home board, then I win a backgammon. It

> is easy to rerun my code with whatever backgammon value you

> want.

(and it it would be meaningful doing it), a new rule can be

injected to differentiate between single games and gammons. If

the checker has at least made into the loser's home board, then

it would be a single game vs. gammon lost otherwise, etc.

> I can make the equities I computed available on my website if

> anyone is interested.

equities but any and all other info you can make available, such

as program codes, etc.

> As a spot check, I find that if you win the initial rock-paper-

> scissors game and get to go first, your cubeful equity is about

> 0.26081.

> If you are allowed to double after winning rock-paper-scissors

> but before rolling the die, then you should not double. Doubling

> decreases your equity to about 0.03044.

Are you trying to create strawmen already..??

> In the meantime, I discovered that GNU Backgammon comes bundled

> with a program called "makehyper" that computes cubeful equities

> for HyperGammon.

> That has reduced my incentive for beefing up my program(s) to

> handle HyperGammon.

compare my HypestGammon to Gnubg's 1-checker HyperGammon, (since,

I assume it uses two dice), but you can improve your programs to

handle 1, 2 and 3 checker HyperGammon, and compare the results.

MK

May 24, 2020, 4:48:51 AM5/24/20

to

On May 21, 2020 at 11:58:45 AM UTC-6, Paul Epstein wrote:

> When learning concepts, it's often best to focus on

> them in isolation. So the game might be a great tool

> for teaching doubling to beginners.

It's ironic that I pushed for it as a tool to "unteach"
> When learning concepts, it's often best to focus on

> them in isolation. So the game might be a great tool

> for teaching doubling to beginners.

you all... :))

Using an analogy, I believe that you guys started to

button your shirts (your bots) wrong after TD-Gammon v1.

After that, as you keep buttoning more holes (improving

various in-bred bots based on TD-Gammon v2), you keep

elaborating on the fallacy, without a chance to realize

that you are "progressing" in the wrong direction.

I could never get you guys to backtrack one button at a

time, which would be almost impossible anyway. That's

why I kept arguing that we all need to go back to the

beginning and start over with "buttoning a new shirt".

When there are countless books written about a fallacy

that is so established, nobody wanting to listen to

hear anything against it was easy enough to understand

but difficult to overcome the frustration and give up.

Never too late, HyperGammon being claimed to be a simpler,

solved version of BG, with perfectly calculatable cubeful

equities could be a tool for making my point easier for

you all to listen and begin to understand.

Then, better yet, I came up with HypestGammon, which at

last grabbed the attention of a mathematician collegue

and may give me some traction...

> Since only the doubling is non-trivial, the game makes

> it possible to focus on the doubling concept in isolation

> without being distracted by checkerplay concepts.

shoul learn cubeless BG first, focusing on checker play

concepts without being distracted by cube play concepts.

> Alternatively, I've thought of the idea of introducing

> skill into snakes and ladders, by playing it with a

> doubling cube.

calculated equities come out the same... :)

Doubling cube is a gambling tool, with the same simple

strategie that can be applied to any game "externally".

It doesn't add anything to any game that can be called

"skill" other than paying more attention to your winning

odds at any point, which you would need to know anyway.

In BG for example, a traditional cubeless match would be

5-points for a quick one, 7-points will prove skill more

and a real challenge would be best 2 of 3 5-pointers. A

good player would know and use his equity to vary his

checker play strategy.

In cubeful world, at championship level, 25-point matches

are the standard. Why? Because cube magnifies luck and

allows luck to truncate skill. A cubeless 7-pointer, even

sometimes a 5-pointer can last as long as a cubeful

25-pointer.

If it's not for money/gambling, cubeful BG is less enjoyable.

If it's for money/gambling, why bother playing BG anyway?

Just roll the dice, or flip a coin, or cut a deck of cards...

Knowing your cubeful equity more accurately may be claimed

to be additional level of skill but the problem is, except

simple positions such as in late games, you can't calculate

it. Or at least, not the way you are doing it now. So why

keep pretending?? Why not give up the bullshit and try to

do it right??

MK

May 24, 2020, 4:58:57 AM5/24/20

to

On Sunday, May 24, 2020 at 9:48:51 AM UTC+1, mu...@compuplus.net wrote:

....

This opinion of yours is almost universal. Almost every backgammon

book, aimed at complete beginners, covers checkerplay before the cube.

I was trying to develop a different approach.

Very few people learn anything about the cube before they have thoroughly

understood checkerplay so you're advocating something that people already

agree with.

Paul

....

> Again, it's ironic that for years I advocated that people

> shoul learn cubeless BG first, focusing on checker play

> concepts without being distracted by cube play concepts.

...
> shoul learn cubeless BG first, focusing on checker play

> concepts without being distracted by cube play concepts.

This opinion of yours is almost universal. Almost every backgammon

book, aimed at complete beginners, covers checkerplay before the cube.

I was trying to develop a different approach.

Very few people learn anything about the cube before they have thoroughly

understood checkerplay so you're advocating something that people already

agree with.

Paul

May 24, 2020, 5:26:14 AM5/24/20

to

On May 21, 2020 at 12:44:26 PM UTC-6, Tim Chow wrote:

> It also occurs to me---and perhaps this was Murat's

> point---that it provides a nice testing ground for

> investigating non-equilibrium strategies. For example,

> one could see what happens if we pit the equilibrium

> strategy against some simple strategy such as "double

> if my DMP winning chances are >50% and take if and only

> if my DMP winning chances are >25%."

Well, you may be able to do such experiments now using
> It also occurs to me---and perhaps this was Murat's

> point---that it provides a nice testing ground for

> investigating non-equilibrium strategies. For example,

> one could see what happens if we pit the equilibrium

> strategy against some simple strategy such as "double

> if my DMP winning chances are >50% and take if and only

> if my DMP winning chances are >25%."

HypestGammon but when I was talking about regular BG,

I was arguing that:

a) Statistically, you will never lose the equity/edge/lead

you gain very early in the game.

b) Current calculations of cubeful equities for very early

or even for some middle game positions are inaccurate and

useless.

That's why this whole discussion here: let's see if you

can begin to calculate opening equities for HyperGammon,

or even HypestGammon, and then we can go from there to

talk about if you can calculate them in regular BG.

> A more subtle question would be, suppose I want to publish

> a sequence of (say) 25 consecutive games that seems to

> demonstrate that I can "beat the bot." What strategy

> should I use to minimize the waiting time until I get

> such a sequence? It probably isn't the equilibrium strategy.

meaningless, especially you can't extrapolate from it

that transitively you can beat the humans players who

are beaten by the bot.

I played tens of thousand of games to accomplish that

just by playing my way, unlike the bot, without having

to know or show how I did it.

From there I progressed to experimenting with doubling

after opponents opening 63, 62, 64, etc. The reason I

picked 63 to experiment with first for example, is because

I noticed that TD-Gammon v1 cubeless opening roll equity

calculations showed it to be a bad opening roll.

> Offhand, I'm not sure what kind of learning algorithm

> would work well to discover such a strategy. Naively,

> I could start with some doubling/taking strategy, then

> randomly change some decisions to see if it helps, but

> this seems like it would take an inordinately long time

How about doing what I have done. If you agree with me that:

1) Statistically you will never lose the equity you gain at

any point in the game, including very early in the game, for

the rest of the game.

2) If opening 63 is a bad roll in cubeless rollouts, no

subsequent cube actions in that game will change that fact.

Why waste time with totally random cube decisions, instead

of using more likely possibilities based on previously

calculated cubeless equities through random play already,

such as my above 63 example??

Why don't you plug a few of these into your algorithm to

see what you may start to discover and then you can go

from there...

MK

May 24, 2020, 7:56:56 PM5/24/20

to

On Sunday, May 24, 2020 at 5:26:14 AM UTC-4, mu...@compuplus.net wrote:

> a) Statistically, you will never lose the equity/edge/lead

> you gain very early in the game.

I don't understand what you're claiming here.
> a) Statistically, you will never lose the equity/edge/lead

> you gain very early in the game.

Are you saying that if you acquire an edge at some point in the game,

then the probability is >50% that you will retain an edge all the

way to the end of the game, without ever at any point ceding the edge

to your opponent?

---

Tim Chow

May 24, 2020, 8:18:26 PM5/24/20

to

On Sunday, May 24, 2020 at 3:37:06 AM UTC-4, mu...@compuplus.net wrote:

> More importantly than his name, I would like to know what was

> the nature of his interest? Was it plain/scientific curiosity

> to know/learn whithout any presuppositions? Or did he already

> have an idea what the result would be and just wanted to find

> out if he was right/wrong?

He was interested in learning more about AlphaZero, coding up a simple
> More importantly than his name, I would like to know what was

> the nature of his interest? Was it plain/scientific curiosity

> to know/learn whithout any presuppositions? Or did he already

> have an idea what the result would be and just wanted to find

> out if he was right/wrong?

version of it himself, and he was looking for suggestions of simple games

to try it on, so I mentioned hypergammon and hypestgammon. He thought it

would be interesting to compare the AlphaZero strategy with the exactly

computed equilibrium equities, so I volunteered to compute the latter.

> Since you have already put in an effort into this, would you go

> the extra step to explain and document what you have done? Even

> if it may be too complex for non mathematicians at first, thru

> future discussions, others may also understand eventually.

week. The C code was for the iterative method.

I could also post the linear programming code but that seems less useful.

I wrote it in Maple, which is a proprietary language, and it's not very

readable because I was coercing it to produce CPLEX LP files. But it's

easy enough to explain what I did, at least to someone who knows a little

bit about mixed integer programming. One introduces floating-point variables

for all the equities, and binary variables for the cube decisions, and writes

down the obvious constraints relating the variables.

> > Both methods gave the same numerical answers.

>

> Was there ever the possibility in your mind that they woudn't?

> If yes, by chance, have you even began to ask the question what

> then..?

it's not hard to show that it can't, although I haven't actually worked it

out---then equities are certainly well defined. I wasn't expecting this to

happen even though I hadn't mathematically ruled it out.

But there could be another issue---there might be some other solution

(besides the true equities) that satisfies all the obvious constraints.

If there is, then either the mixed integer programming solver or the

iterative algorithm might converge to the spurious solution. This also

seems unlikely, though less unlikely than the nonexistence of equities.

> > As a spot check, I find that if you win the initial rock-paper-

> > scissors game and get to go first, your cubeful equity is about

> > 0.26081.

>

> Can we also speak in MWC also, if not instead.

done so far corresponds to playing a single money game, not a match.

> > If you are allowed to double after winning rock-paper-scissors

> > but before rolling the die, then you should not double. Doubling

> > decreases your equity to about 0.03044.

>

> Since it's not allowed, why would you even want to know that?

> Are you trying to create strawmen already..??

ordinary backgammon, we roll dice to determine the first player, and it

is understood that you can't double after you roll the dice. But if you

play rock-paper-scissors to determine the first player, then the first

player is determined *before* the die is rolled, so it's not immediately

clear whether the first player is allowed to double before rolling. It's

your game, so if you say no, then the answer is no. But since you didn't

say so explicitly in your original description, I figured I would mention it.

> > That has reduced my incentive for beefing up my program(s) to

> > handle HyperGammon.

>

> Nonsense. How do you know Gnubg does it right? There is no way to

> compare my HypestGammon to Gnubg's 1-checker HyperGammon, (since,

> I assume it uses two dice), but you can improve your programs to

> handle 1, 2 and 3 checker HyperGammon, and compare the results.

that I'm doing this in response to a colleague, who is willing to trust GNU

Backgammon at this point.

---

Tim Chow

May 25, 2020, 3:25:08 AM5/25/20

to

On May 24, 2020 at 2:58:57 AM UTC-6, Paul Epstein wrote:

> On May 24, 2020 at 9:48:51 AM UTC+1, mu...@compuplus.net wrote:

>> Again, it's ironic that for years I advocated that people

>> shoul learn cubeless BG first, focusing on checker play

>> concepts without being distracted by cube play concepts.

What I found ironic is the contrast coming back at me as

the opposite concept.

If you take the cube out of cubeful BG, you end up with BG.

If you take the BG out of BG, you end up with "cube skill",

"a naked flasher"... :))

I know what BG is without the cube. Perhaps you can explain

to me what the "cube skill" is without (independent of) BG?

For clarification and for the record: I have never ever read

even a single book on BG, or cube skill, or both.

I have read quite a few short articles in BG archives but

with "mental gloves" at that, for fear of getting infected! ;)

Tom Keith's writings about HyperGammon was perhaps the longest

article I have ever read, along with some papers about neural

nets, TD-Gammon, etc.

Since we are talking about "cubeful backgammon" and not

"backgammonful cube", it's natural that the books would first

teach the basics of backgammon but I still have a feeling that

they probably start introducing the cube into BG too soon for

what I meant in any case...

> I was trying to develop a different approach.

Fine. Now, as I have done with Chow, I am daring you to follow

through with it!

Let's see you "introduce skill" into snakes and ladders with

the doubling cube.

Before you start though, I want you to realize that you are

talking about "introducing the cube into snakes and ladders",

not "introducing snakes and ladders into the cube"! Got it??

With that said, let's see what you will come up with? I'll

be waiting very impatiently... ;)

MK

> On May 24, 2020 at 9:48:51 AM UTC+1, mu...@compuplus.net wrote:

>> Again, it's ironic that for years I advocated that people

>> shoul learn cubeless BG first, focusing on checker play

>> concepts without being distracted by cube play concepts.

> This opinion of yours is almost universal. Almost every

> backgammon book, aimed at complete beginners, covers

> checkerplay before the cube.

I didn't mean to come across as I have invented the concept.
> backgammon book, aimed at complete beginners, covers

> checkerplay before the cube.

What I found ironic is the contrast coming back at me as

the opposite concept.

If you take the cube out of cubeful BG, you end up with BG.

If you take the BG out of BG, you end up with "cube skill",

"a naked flasher"... :))

I know what BG is without the cube. Perhaps you can explain

to me what the "cube skill" is without (independent of) BG?

For clarification and for the record: I have never ever read

even a single book on BG, or cube skill, or both.

I have read quite a few short articles in BG archives but

with "mental gloves" at that, for fear of getting infected! ;)

Tom Keith's writings about HyperGammon was perhaps the longest

article I have ever read, along with some papers about neural

nets, TD-Gammon, etc.

Since we are talking about "cubeful backgammon" and not

"backgammonful cube", it's natural that the books would first

teach the basics of backgammon but I still have a feeling that

they probably start introducing the cube into BG too soon for

what I meant in any case...

> I was trying to develop a different approach.

through with it!

Let's see you "introduce skill" into snakes and ladders with

the doubling cube.

Before you start though, I want you to realize that you are

talking about "introducing the cube into snakes and ladders",

not "introducing snakes and ladders into the cube"! Got it??

With that said, let's see what you will come up with? I'll

be waiting very impatiently... ;)

MK

May 25, 2020, 3:36:55 AM5/25/20

to

On May 24, 2020 at 5:56:56 PM UTC-6, Tim Chow wrote:

In the long run, yes. In fact, later in my same post I said

at any given point in a game instead of very early in a game.

The reason I said very early in a game was because the current

cubeful calculations of equity are most inaccurate/useless in

the early stages of a game rather than later.

I don't expect to argue against this since it's brainless simple

statistics. If player-A gains let's say 51% winning chances after

the fifth roll, calculated by roll-outs (statistics) based on

1296 or 4 billion tries, that number will never change as long as

it's calculated the same way, regardless of how many more billions

of tries, regardless of whether cubeless, cubeful, spoonful, cupful,

barrelful, etc....

Do you understand and do you agree now?

MK

at any given point in a game instead of very early in a game.

The reason I said very early in a game was because the current

cubeful calculations of equity are most inaccurate/useless in

the early stages of a game rather than later.

I don't expect to argue against this since it's brainless simple

statistics. If player-A gains let's say 51% winning chances after

the fifth roll, calculated by roll-outs (statistics) based on

1296 or 4 billion tries, that number will never change as long as

it's calculated the same way, regardless of how many more billions

of tries, regardless of whether cubeless, cubeful, spoonful, cupful,

barrelful, etc....

Do you understand and do you agree now?

MK

May 25, 2020, 10:31:58 AM5/25/20

to

the edge."

If I have a 51% edge, then practically by definition, it means that in the

long run, I'm going to come out ahead *at the end of the game* more often

than not.

However, a 51% edge doesn't automatically say anything about what might

happen *during the course* of the game. It might be that, during the game,

the advantage will *swing back and forth* between me and my opponent. I

might have the edge at first, and then my opponent might have the edge, and

then the edge might return to me. In the end I'll prevail more often than

not, but perhaps only after see-sawing back and forth a few times.

When one says "never lose the edge," it could mean that such see-sawing

never occurs. After all, you might say that I had an edge, then I *lost

the edge*, then I *regained the edge*, and that it's not true that I *never*

lost the edge.

So which do you mean? If you mean that if I gain an edge (let's say for

concreteness a 51% chance of winning the game at DMP) then, in the long run,

I will win 51% of such games, then I agree...this is almost tautological.

if you mean that if I gain an edge, then more often than not there will

*never be any see-sawing* then I don't agree.

---

Tim Chow

May 25, 2020, 2:03:24 PM5/25/20

to

On Sunday, May 24, 2020 at 8:18:26 PM UTC-4, I wrote:

> Okay, I'll clean up my C code a bit and post it on my website later this

> week. The C code was for the iterative method.

Okay, I've done this. Go to http://alum.mit.edu/www/tchow/fun.html and
> Okay, I'll clean up my C code a bit and post it on my website later this

> week. The C code was for the iterative method.

search for "Hypestgammon". (The web server seems to be a bit flaky today

so if you get a "Not Found" error, try again a few seconds later.)

---

Tim Chow

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