On June 19, 2022 at 7:19:15 AM UTC-6, Tim Chow wrote:

> A secondary reason is that Chess960 is still
> basically chess, so the best Chess960 players
> are pretty much the best chess players.

This made me look at game complexity (i.e. skill
required vs luck) from yet a different perspective:
"how long a game lasts on the average".

Wiki says: "10 to 60 minutes for casual games,
10 minutes (fast chess) to 6 hours or more for
tournament games" both for regular chess and
chess960.

For backgammon it says "5 to 60 minutes".

For Ludo, Mensch ärgere Dich nicht, etc. it says
"about 30 minutes".

I don't know how they came up with these but
they seem reasonable to me.

In chess, the low 10 minutes is for the variant
"fast chess" or if a huge skill difference between
the players leads to a quick defeat.

In backgammon, the low 5 minutes is also and
only for a variant "gamblegammon" played with
cube. No cubeless backgammon game will be
over in 5 minutes even with big skill differences
between the players or if played fast by equally
skilled players.

Just the act of rolling the dice uses up time in
Ludo also which is probably why it doesn't end
in 5 to 10 minutes even when played between
unskilled children.

Clearly gamblegammon with the cube is more
of a game of luck than even Ludo...

MK

On 6/21/2022 9:57 PM, MK wrote:
> This makes better sense to me than the approach used
> in the Wiki page I previously gave a link to. Being based
> on actual results, it seems more realistic than the ones
> based on theoretical/mathematical extrapolations.
>
> Did you come up with this? If so, is 25% a random pick?
> Or is this actually used to rank players in some games?

I did not come up with this. I don't know who first came up with
it, but it dates back at least to Bill Robertie in 1992.

https://web.archive.org/web/20190112044437/https://thegammonpress.com/comparing-games-skill-chance/

The concept is also discussed in the book "Characteristics of Games,"
by Elias, Garfield, and Gutschera, where they call this measure the
"length of the skill chain." The number 25% is a random pick; it's
what Robertie used, but Elias et al. use 40%. Actual ranking of players
is always done by something like the Elo system, in every game that I
am aware of.

Elias et al. make some simple but important observations. The first
is that the length of the skill chain depends not just on the game
itself, but the community of players. Tic-tac-toe has a longer skill
chain among kids than among adults. For games like chess, the skill
chain may change over time as people learn more about the game and
the size of the playing population changes.

Another point is that the win percentage of Player A over Player B
depends on the duration of a playing session. The more skillful
player is going to have a better chance of winning a best-of-5 match
than a single game. So if Game 1 has a longer skill chain than Game 2,
we may be able to change that by replacing Game 2 by best-of-5 matches
of Game 2. This again shows that the length of the skill chain is not
an intrinsic property of the game, but depends on "external" factors
such as how long people are willing to spend on a playing session.

---
Tim Chow

On 6/21/2022 10:39 PM, MK wrote:
> This made me look at game complexity (i.e. skill
> required vs luck) from yet a different perspective:
> "how long a game lasts on the average".

In the book, "Characteristics of Games" by Elias, Garfield, and
Gutschera, the duration of a game is the very first characteristic
of a game that they consider. This is not an accidental choice,
since often the very first question a new player has when offered
the opportunity to play a game is, "How long will the game last?"

I think you'll find a lot of interesting stuff in this book.

---
Tim Chow

bks@panix.com (Bradley K. Sherman) writes:

> Related:
> | ...
> | In any competition including academic tests, athletic
> | events, and company management where there is an element of
> | luck that causes performances to be an imperfect measure of
> | ability, there is an important difference between
> | competitions among people with high ability and
> | competitions among people of lesser ability. If four work
> | friends play a round of golf and one player is much better
> | than the others, the winner is determined mostly by
> | ability. If four of the top golfers in the world play a
> | round of golf, the winner is determined mostly by luck.
> | This is the paradox of luck and skill: the more skilled the
> | competitors are, the more the outcome is determined by
> | luck.
> | ...
> <https://mindmatters.ai/2019/08/the-paradox-of-luck-and-skill/>
> (Written by Econ Prof, Gary Smith)

Add-on: If two clueless backgammon players compete, the outcome is also
determined mostly by luck.

Best regards

Axel

MK <murat@compuplus.net> writes:

[Ludo, Pachisi, ...]

> I can't offer any branching numbers, etc. but I have the feeling
> that it can get pretty darn complicated...

I imagine that the "terrain", as perceived by an optimizer, is very
flat, meaning that the equity difference between the (few) possible
moves will be tiny, similar to long races such as this:

The score (after 0 games) is: gnubg 0, axel 0
Move number 1: axel to play 11

GNU Backgammon Position ID: sG+3AACwb7cAAA
Match ID : cIkEAAAAAAAA
+24-23-22-21-20-19------18-17-16-15-14-13-+ O: gnubg
| O O | | O O O O | 0 points
| O O | | O O O |
| O | | O |
| O | | |
| O | | |
| |BAR| |v (Cube: 1)
| X | | |
| X | | |
| X | | X |
| X X | | X X X | Rolled 11
| X X | | X X X X | 0 points
+-1--2--3--4--5--6-------7--8--9-10-11-12-+ X: axel
Pip counts: O 106, X 106

There are more than 40 moves within 0.01 equity of the best move.

Best regards

Axel

On August 13, 2022 at 7:21:13 AM UTC-6, Axel Reichert wrote:

> MK <mu...@compuplus.net> writes:

> [Ludo, Pachisi, ...]

>> I can't offer any branching numbers, etc. but I have
>> the feeling that it can get pretty darn complicated...

> I imagine that the "terrain", as perceived by an
> optimizer, is very flat, meaning that the equity
> difference between the (few) possible moves
> will be tiny, similar to long races such as this:

I will argue the exact opposite but let's talk about
your backgammon example first.

> GNU Backgammon Position ID: sG+3AACwb7cAAA
> Match ID : cIkEAAAAAAAA

> There are more than 40 moves within 0.01 equity
> of the best move.

Thank you, thank you, for this example perfectly
supporting my argument about "branching factor
inflation" in backgammon.

I categorically question the accuracy of all equity
estimates but 0.01 here meaning tiny/negligeable
difference suits me just fine.

There you have not 40 branches but 40 twigs and
your opponent has also 40 twigs... I wonder how
many possible positions there will be until the end
of this game. A few hundreds? A few thousands?
Gods forbid, even more?

Now, on to Ludo. As I mentioned before, there are
40 squares on the board with the possibility of all
16 men being on the board.

1) Considering that all 4 players are opponents of
one another, this is would be a very crowded board.

2) Each player may adopt a strategy of having 1, 2,
3 or 4 of his men on the board. Thus, every other
player needs to adjust his own strategy according
to the combination of startegies adopted by the
other 3 players.

3) You can't stack your pieces to make points to
save your blots or block your opponents. Every
piece on the board is a blot, ripe for picking by
any of the 3 opponents.

4) After making your move, you have to wait 3 turns
until it's your turn again. Unlike once in backgammon,
3 times the chance of getting it.

5) Even if you have to choose between moving one
of two pieces to either follow one opponent of to
jump ahead of another opponent will be much more
than a tiny equity difference.

6) I'm sure we could come up with many more
arguments for the complexity of Ludo...

I totally understand your obsession with cube skill
theories, equities accurate to several decimals, etc.
in gamblegammon and your need to exaggerate the
skill level needed in order to make yourself feel better
about not being just an addicted gambler settling for
an inferior skill game than chess, etc. because that's
all you can handle...

I bet it would really upset you if Ludo proved to need
more skill than gamblegammon but why should you
even worry about it? It's also a game of luck played
by rolling a die. You can concoct a "doubling cube
theory for Ludo" using tinyly accurate equities and
then just switch to gambling with gambleludo... ;)

MK

MK <murat@compuplus.net> writes:

> On August 13, 2022 at 7:21:13 AM UTC-6, Axel Reichert wrote:
>
> I bet it would really upset you if Ludo proved to need more skill than
> gamblegammon

Just because equity differences between moves are tiny (think "greedy"
bear-off versus optimal bear-off) does not mean that the game is a
difficult and skillful game.

Imagine a toin coss experiment where prior to the toss the player has to
skillfully select (by visual examination) one of 11 imperfect coins
(yielding heads with 0.495, 0.496, ..., 0.504, 0.505 probability,
respectively). Then the coin is tossed, head wins.

Skillful? Maybe.
Dominated by luck? For sure.
Boring? You can bet.

Most stages of Ludo to me fit this picture.

Axel

On August 28, 2022 at 4:25:09 AM UTC-6, Axel Reichert wrote:

> MK <mu...@compuplus.net> writes:

>> I bet it would really upset you if Ludo proved to
>> need more skill than gamblegammon

> Just because equity differences between moves are tiny
> (think "greedy" bear-off versus optimal bear-off) does not
> mean that the game is a difficult and skillful game.

I don't see what are you trying to say with this comment.

In the previous posts, regarding Ludo you said: "the equity
difference between the (few) possible moves will be tiny";
and I responded: "I will argue the exact opposite".

Later in my reply, talking about equity difference in Ludo, in
paragraph #5, I said: "Even if you have to choose between
moving one of two pieces to either follow one opponent
of to jump ahead of another opponent will be much more
than a tiny equity difference."
> Imagine a toin coss experiment where.....

No need to imagine coin tossess. You had already given
an actual gamblegammon example using a position with
more than 40 moves within 0.01 equity of the best move.

Now let's apply your questions/answers to that example:

> Skillful? Maybe.
> Dominated by luck? For sure.
> Boring? You can bet.

I totally agree that these are true about gamblegammon
way too often. And I would also say more often than Ludo.

I was trying to argue that unlike in gamblegammon where
positions with more than 40 moves within 0.01 equity of
the best move are common, (making it a "Maybe skillful",
"Dominated by luck" and "Boring" game), in Ludo no such
"inflation of inconsequential decisions" would occur and
any equity differences between available moves wouldn't
be as "tiny" (i.e. 0.01) as gamblegammon.

> Most stages of Ludo to me fit this picture.

To each his opinion...

MK

MK <murat@compuplus.net> writes:

> On August 28, 2022 at 4:25:09 AM UTC-6, Axel Reichert wrote:
>
>> Skillful? Maybe.
>> Dominated by luck? For sure.
>> Boring? You can bet.
>
> I totally agree that these are true about gamblegammon
> way too often. And I would also say more often than Ludo.

Then please try your luck in rec.games.board, just around the corner.

Axel

On August 30, 2022 at 12:22:18 AM UTC-6, Axel Reichert wrote:

> MK <mu...@compuplus.net> writes:

> > On August 28, 2022 at 4:25:09 AM UTC-6, Axel Reichert wrote:

>>> Skillful? Maybe.
>>> Dominated by luck? For sure.
> >> Boring? You can bet.

>> I totally agree that these are true about gamblegammon
>> way too often. And I would also say more often than Ludo.

> Then please try your luck in rec.games.board,
> just around the corner.

You made many empty, unnecessary, unproductive
comments today. Trying to discuss things with you
is turning into a waste of time... :(

MK

On Wednesday, June 22, 2022 at 8:40:48 AM UTC-4, Tim Chow wrote:
> On 6/21/2022 9:57 PM, MK wrote:
> > This makes better sense to me than the approach used
> > in the Wiki page I previously gave a link to. Being based
> > on actual results, it seems more realistic than the ones
> > based on theoretical/mathematical extrapolations.
> >
> > Did you come up with this? If so, is 25% a random pick?
> > Or is this actually used to rank players in some games?
> I did not come up with this. I don't know who first came up with
> it, but it dates back at least to Bill Robertie in 1992.
>
> https://web.archive.org/web/20190112044437/https://thegammonpress.com/comparing-games-skill-chance/

I learned from Ken Regan that the idea of measuring the "depth" of
a game in this way seems to be due to Laszlo Mero, who described
the concept in his 1990 book, "Ways of Thinking."

---
Tim Chow

On September 19, 2022 at 7:23:42 PM UTC-6, Tim Chow wrote:

> On June 22, 2022 at 8:40:48 AM UTC-4, Tim Chow wrote:

>> it, but it dates back at least to Bill Robertie in 1992.

> I learned from Ken Regan that the idea of measuring the "depth" of
> a game in this way seems to be due to Laszlo Mero, who described
> the concept in his 1990 book, "Ways of Thinking."

Good to see the credit go to the right person.

Do you have anything new to say on the topic, by chance?
I'm disappointed that nothing more came out of it.

I looked for Ludo software but couldn't find anything other
than Android apps and no online servers, nothing to take
seriously anyway. It seems nobody plays Ludo competitively.
I guess it will stay at this unless we stumble onto something
more interesting about it in the future... :(

MK