Luck versus Skill

Forum Archive : Luck versus Skill

The Bower Luck-O-Meter

From:   Gary Wong
Date:   12 August 1998
Subject:   Re: BG's gambling status
Google:   wtlnouveem.fsf@brigantine.CS.Arizona.EDU

Chuck Bower writes:
> Let's assign a number from 0 to 100 to every game, depending on the luck
> vs. skill factor.  Games like chess and golf will be very close to 0 (but
> maybe not exactly zero, as argued by both Gary and me).  Games like craps
> are very close to 100 (but even here you can make bets which vary in
> house edge and therefore some skill is helpful).  Four player contract
> bridge, poker, and backgammon are examples of games which fall well away
> from both zero and 100.
> Hopefully you realize I am not REALLY assigning a hard number.  I don't
> think this can be done in most cases.  But hopefully you get the idea.
> Now, somewhere on this scale you put a line and say "if a game is above
> this line, I define it:  GAMBLING."  Below this line the game is NOT
> gambling.  Where should I (or Edmond or Congress) put the line?
> Tough question?  Maybe. I put my line closer to 100 than most.  I believe
> that there is significant skill available (and enough to offset the house
> rake) in games like horse racing, sports betting, and blackjack.  Of
> course you must be quite skillful in these games to overcome the house
> advantage, but I believe it can be done.  Therefore I place my line high
> enough that these fall into the NON-gambling portion.  But that is just
> me.  I suspect if you asked a lot of people (and now I am assuming they
> understand my 0-100 scale) you would get a lot of different answers.
> So, my point is:  how do you define gambling?  I don't think EVERYONE
> does it the same way.  Surely NO ONE will argue that, will he???

I won't argue that, no :-)  I'm afraid I don't have a good definition.
Yours is about the best I've heard, but it's still not perfect.  It's
definitely a huge improvement over the laws in Oregon as mentioned in the
article referred to previously: "risking something of value upon the
outcome of a contest of chance".  It's not clear what is meant by a
"contest", but from my point of view, their definition would not rule out
investing on the stock market as gambling -- perhaps not even taking out an
insurance policy!

Your definition is much better, because it recognises that games make up an
entire spectrum involving varying amounts of skill and uncertainty.  The
problem of finding a suitable metric to quantify those concepts with is
certainly tricky, but even if we had one, we are left with a couple of
issues that might still need to be settled.

Firstly, are we measuring the skill in the _game_ or in the _players_?  The
game of Nim would be an interesting example.  Any skilled player could look
at a position and instantly tell whether it's a winning or losing one.
Therefore, a game between skilled players would be entirely a game of
chance (in deciding who moves first).  A game between one skilled player
and one novice would definitely be a game of skill -- the skilled player
would be a huge favourite.  But between two beginners, it becomes a game of
uncertainty again!  Is betting money on a game of Nim to be considered
gambling for some players, and not for others?  Whether you are skilled or
not, the categorisation of the game depends on your opponent!

Another problem is that if a game has a slight skill and large chance
content, then playing a long match of those games turns into one of large
skill and slight chance.  Suppose we're playing a money game, and late in
the bearoff, you double and I take.  After the game, you tell me you
believe it was a drop and offer to pay me a point and the cube to play it
as a prop. If it's late enough in the game, you can imagine it being a
definite game of chance with very little skill involved -- so, playing the
prop once for money would definitely be a gamble.  But if we played it out
enough times, then by the strong law of large numbers, the result will
almost surely converge to a win for whoever was right about the take/drop
decision -- pure skill!  So, a match that started out as a gamble gradually
turns into skill if we play it enough!

Let me finish with a story with a moral.  (I hope it has a moral, though
I'm not entirely sure what it is).

  It's getting late into the evening in Springfield.  Homer and Barney sit
hunched over a backgammon board in Moe's, just having started a series of
games at $5 a point.  They roll the bones.  They slide the chequers.  They
turn the cube.  They drink the Duff.  An hour later, Barney burps and
gammons Homer with the cube at 4 for the fifth time in a row.  Homer checks
the score and realises he's $200 down on the deal.  He tells Barney he's
had enough and wonders how to break the news to Marge that he's lost this
week's grocery money and Bart's birthday present.  He's about to leave

  "SIT DOWN, HOMER!" Chief Wiggum barks.  "I see you've been betting money
on 5 games of backgammon.  I note on my handy reference chart that 5 games
comes to 62 on the Bower Luck-O-Meter -- which is over the legal limit of
15 imposed by the state of (mumblesnarf).  Indeed, it would take 13 games
of backgammon to accumulate enough skill content for your activity to be
regarded by the law as a game of skill.  Now, you two get back there and
play another 8 games for the same stakes before I arrest you both for
illegal gambling!"

  Is Chief Wiggum's behaviour enforcing the letter of the law?  Quite
possibly, if that's where you want to draw the boundary between a game of
chance and a game of skill.  Is it enforcing the spirit of the law?  Not
according to my interpretation.  Is forcing them to _continue_ playing
for more money in order to render their game one of skill upholding social
responsibility?  I don't see how ANYBODY (uh oh, that word again) could
think so...

        Gary Wong, Department of Computer Science, University of Arizona
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Luck versus Skill

Are good players just luckier?  (Douglas Zare, Sept 2000) 
Are luck and skill related?  (Eskimo+, Feb 2003) 
Does backgammon need less luck?  (Raccoon, Jan 2008)  [GammOnLine forum]
How much of backgammon is luck?  (Wai Mun Yoon, Jan 1998) 
How much skill versus luck?  (Alexandre Sierra, Nov 2000) 
How much skill versus luck?  (JP White+, Aug 2000) 
How often to win with perfect play?  (Robert-Jan Veldhuizen, Nov 2000) 
Is backgammon gambling?  (Luc Palmans+, Oct 2010) 
Is backgammon gambling?  (Kevin D. McLeaster, Sept 1997) 
Is there really luck in backgammon?  (benf+, Jan 2012) 
Recognizing luck  (Walter Trice, Dec 2004) 
Strange result  (az-willie+, Mar 2003) 
The Bower Luck-O-Meter  (Gary Wong, Aug 1998) 
Why are stronger players luckier?  (Bob Sweeney+, Oct 2002) 

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