# Luck in Games – Part II

Thinking of games simply in terms of skill vs. luck is an oversimplification.  With the help of my kind commentors, I have made the chart below to illustrate some of the many components of games that belie the image of a monolithic component called “skill”.   Below the table I will describe each of the categories.

Game Complexity

Games differ in complexity due to the permutations of possible moves and outcomes.  In the left-hand orange column are two scales to mathematically rank a game’s complexity.  The purple numbers are the GameTree (GT) complexity – which I arbitrarily used to sort this list.  The yellow numbers are the State Space (SS) complexity — I barely understand the math, so read the wiki article if you are interested).  The numbers represent the log to base 10.

Luck – Skill Spectrum

The red-blue blurred spectrum bar is meant to imperfectly illustrate the fact that luck and skill blur.  Adjusting for luck in a game is a skill in itself.

Skill Sets

In the white columns are 7 components of the game which I feel illustrate the variety of skill involved in playing various games.  The sum of these components add up to 100%.  Only the first column would be considered “pure” luck, the rest I would consider skills of different types.  The numbers in these boxes is totally fabricated by me in an intuitive way — thus error laden.  But I hope they illustrate the theme of this post.  Here is a brief elaboration of the categories I invented:

• Random Elements:  roll of the dice, deal of the cards and such
• Hidden Information:  For instance, your opponent holds a set of card which you can not see.
• Bluffing Skills:  Some games involve bluffing, face reading and such
• Memorizing Skills:  During the game, how much use of memory is needed.
• System Particulars:  The idiosyncrasies of the games rules will generate particulars that a player needs time and experience to understand and remember.  They are not apparent simply by understanding the rules.
• Pattern Recognition:  This is looking at the big picture of the game and weighting your moves appropriately.  It can involve seeing familiar patterns that are difficult to calculate.
• Calculations:  In Weiqi we call this “reading”.  It means playing out as many possible moves you can in the game tree to make the best calculated move.

After setting out this table, I see that I tend not to like games with random elements or memorizing (a weakness of mine).  Looking at the complex set of skills in games helps make it clear why different folks like different games.

Important Caveat: Any given player, will change the game to match their skill sets.  So, for example, in my WéiQí game I may only do 30% calculating and increase my pattern recognition to 50%.  However,  if I did more calculating, I would be better.  Nonetheless, but of “style” is how we all compensate our skill sets in response to our opponents.  Thus these percentages are artificial in yet this sense too.

Filed under Philosophy & Religion

### 13 responses to “Luck in Games – Part II”

1. Only time for a superquickie….

Poker has no hidden information, and requires no bluffing skills? Can I play you at poker some time? 🙂

You can give gametree sizes for Poker, they are large, on the order of chess. And both scrabble and backgammon have tree sizes larger than checkers. We can solve checkers (spoiler: it is a draw), but not those other games.

2. Hjalti

Well, regarding chess (and I’m only talking about “western chess”), I don’t think that bluffing plays a big part (but of course it helps a little bit, like if you see that you’ve just blundered and curse out loud, the opponent might figure it out :P).

I would say that memory plays a bigger role, that is memorizing opening variations (understanding what’s going on in the opening is of course vital, but knowing variations helps alot). Although it of course plays no role later on in the game.

3. Not a bad taxonomy. I would’ve lumped together “pattern recognition” and “memorization skills”, since pattern recognition is what happens when memorization becomes automatic. Your 8kyu weiqi ranking requires good pattern recognition, as well as a fairly strong working memory for the ability to read ahead in battles, but I think I see the distinction you’re trying to make.

I see that I tend not to like games with random elements or memorizing

I’m with you on this. Since a very young age, games that had a large chance component would bore me to death. It always seemed that there was no point for me to bother playing if it was all chance, since it was really the dice or the spinner doing the playing. If it’s all just spinning the spinner and going that many spaces on the board, I might as well let a robot (or a freakishly honest sibling) play the entire game, and then I could come back and see how it all played out. Maybe that proves I was a determinist even as a kid 🙂

In fact, my youngest is the opposite. If I don’t want to play “life” or whatever other game, she’ll play her part and mine (and anyone else who will participate), and then tells us who won in the end. 🙂

My memory is one of my strong suits, but games that rely on memory also bore me.

My favorite games are games that rely on creativity and mind-reading.

4. johnl

After participating (= getting my clock cleaned!) in a high-level backgammon tournament, I began to believe that the best players of these high-random games have some ability to influence events like the roll of dice. I read a book called Backgammon for Blood that reinforced this notion. (I don’t have any experience with Craps (dice game), but I think I might be good at the Chinese dice game 大小(Big-Small).

5. @ Ian
Ooops, thanx. I threw that together last night, too late. I fixed it. Of course the numbers are just made up. Any further tweaks on numbers are welcome!
Perhaps I should add to skills “Bravdo” (I guess that comes under “Bluff”) — as in your challenge to play Poker. 🙂

@ Hjalti
Thanks, I tweaked a little. Bluffing probably is less in Chess than Wéiqí. I loved the example of a bluffed curse!

@ JS Allen
Thank you. I have a terrible memory but I can recognize patterns to some degree. I can’t keep track of cards played but I recognize patterns without being able to verbalize them. That is why I separated those — but I understand your thought. Heck, I considered putting 3 into 1: memorize, system preferences and pattern and just call it memorize.
I laughed hard at your daughter playing several players alone — my daughter does the same. She is a very good sport in games but my son is a very bad sport — he cares, while she is there for the social fun.

@ johnl
The immersion of belief in the ability to control dice roll shows the perversions of the human cognitive system. 🙂 But who can deny experiencing such illusions. Getting others to believe you have such power may take away their confidence and add to the bluff. Thus playing with that illusion is a powerful technique.

6. @hjalti – You need to memorize standard endgame patterns too. Otherwise you’d miss a R vs. N mate, say.

@sabio – On the game complexity, here are some data from a survey paper I have – Go: 10^171, Chess: 10^47 (Chinese Chess: 10^48, Shogi: 10^71), Poker: 10^67, Mahjong: ?, Pente: 10^105, Reversi: 10^28, Checkers: 10^20, Scrabble: ?, Backgammon: 10^20, Yahtzee: 10^49, Tictactoe: 10^3. Scrabble is very hard to calculate, because it depends on the dictionary so much, but the scrabble board is huge, so it would be very big, a quick (and wrong) calculation tells me around 10^100. Mahjong I don’t have data on, and I don’t know well enough to estimate.

I wonder what the bluffing skills are in the perfect information games? I would have put them all at zero, but I do tend to think about games in terms of computer play.

Reversi and Checkers at a high level definitely involve memorizing openings. I’d be surprised if Pente didn’t too.

Generally, a nice grid, and pretty intuitive numbers, I think.

7. I don’t think luck is an independent variable in many of these games; I think it has to be twinned with how the element is used, which is a skill. For example, to prove to another that winning at Bridge was not based on luck, I wagered and won a bet that against another team, my partner and I would win 25 straight 4-rubber Bridge games. Although the element of luck is considered a part of the game – meaning what cards end up where – capitalizing on ‘good’ and ‘bad’ random distribution of cards is an integral part of showing one’s skill level. And part of that skill set is understanding and utilizing what isn’t said, what isn’t done, what isn’t revealed. Straight up games like chess and checkers and Go lack this significant challenge but I don’t see the grid reflecting why this necessary skill set adds to a game’s sophistication but equates it with mere ‘chance’.

8. @ Ian:
Thank you again. I found the wiki article and modified my chart.
I WeiQi you can bluff by playing moves to distract and suggest to the opponent you are playing a different strategy than you actually are.

@ tildeb
Your points are very important. I agree and have tried to capture them by adding a spectrum bar at the top which I explain in the text. I wish I had the complexity scores for Bridge — if you find them, I would be very glad to re-order the table.

Games can be like religion — they are very personal to us. I chuckle at our fervent defense of what we hold precious. 🙂

I have played all these games to some degree [albeit, poorly] — have you played WeiQi to any degree?

9. Ah didn’t see the wiki article – thanks. I would ignore game tree complexity, however. It used to be important for computer play, but isn’t any more. And it has never been the way people have played.

In go, say, you can make two moves in any of two different orders, and be left with the same board position. Choosing the right order is important, but after you have played both, it doesn’t matter a jot which order you chose: just where the pieces are at that time. Game tree complexity counts all of the possible futures from that point twice: once for each order of moves you got there. State space complexity treats the ways you got there as irrelevant, and just counts the ways forward.

Because when considering making a move, you don’t take into account the sequence of moves leading up to that point (except in general psychological terms to work out how good the player is), you don’t ‘feel’ the game tree size, just the state space size.

Just as a matter of interest, where did you get the Scrabble complexity figure from?

Bridge’s complexity is in the same order as Poker. Both involve a deck-shuffle, and resulting assignments of cards. Not quite that simple, but as a ballpark estimate.

10. Hey Ian !

(1) Complexity Theories
I will leave both ratings for historical reasons and cite your comment. Thank you.

(2) Scrabble
The scrabble number is an estimate YOU provided ! 🙂

(3) Other Factors
(a) In Bridge, you have hidden information about not only you opponent but also your partner — so I wonder if this complicates the game a bit more than poker. Bridge also has the ability for silent communication and learning each others habits and strategies.

(b) Sometimes I wonder if the high number of possible moves entices people to stop calculating and guess more or rely on pattern recognition in a way as to add more luck. In other words, just because a game is calculatable with concentration, doesn’t mean that is how most people play it.

Scrabble, for instance, I am curious if they have studied the strategies of good players. I, for one don’t try too, too hard. I have a few heuristics that I work through casually and hope that my heuristics and vocabulary are better applied than my opponent — I don’t go for maximum.

So though a game may be one with little luck, I wager that most play games in far luckier ways than they need to.

11. Earnest

I can beat most elemetary school chess players I play against but I think the pattern number for WeiQi is just crazy. Each piece placed on the board changes the whole game in the beginning of each game, then the effect of each piece decreases as the game continues.

I sometimes wonder if the calculations that Sabio describes could become a sort of pattern recognition if one was deeply immersed enough in the game. How much calculation do you really need in a binary system, where the pieces can only exist or be removed once they are placed?

So I think those numbers of calculation and pattern recognition could be reversed and still be true.

12. Oh, but I see you had already thought about the points I was trying (in haste) to make. I like tour table! But I don’t know how accurate it is not least because I don’t know most of the games above. As for coin flipping (my favorite game ! 🙂 ) take a look at this.

13. @ Takis,
Glad you see that I thought about those issues. (I took a look, thx)