What percentage is luck involved in a games outcome?

[OutsideLime]

@froodster:

Two EQUAL F***ING players. EQUAL. Neither makes a mistake, or they both make equal amounts of mistakes. So they are EQUAL. Neither one gets ahead because they are EQUAL. unless you bring in another factor in which they are NOT EQUAL. Then that factor constitutes 100% of the difference that exists between them, because in other respects they are EQUAL.

EQUAL. as in NOT DIFFERENT. They play THE SAME with EQUALLY good strategy.

Nothing about the game is equal.  Imbalanced forces, imbalanced distribution, imbalanced resources, necessary imbalance of strategy.  One player gets to go first and set the stage for coming turns based on what he does.  The game state changes completely from round to round.

Lots of inequalities besides the luck of the dice in A&A that can determine the difference between two players of equal skill.

It’s a silly argument, of course.

~Josh

[Mork Far]

if there is an equality of skill, then all that is left is the luck of the roll.

[jsp4563]

Good/Bad dice early on magnifies the “Luck” effect.

[OutsideLime]

Let me pose this hypothetical related to the discussion.

Let’s say you could clone yourself perfectly, an exact double of you with all the same memories, experiences, behaviour, intelligence, everything.

Now sit down to play games of chess with your clone.

Do you think that every game will result in a draw?

Not rhetorical, honestly asking the question.

~Josh

[frood]

I don’t think every game would result in a draw. First, white has a slight advantage because it moves first. Secondly, you might not be as good at playing one side or the other. Thirdly, I believe there are random elements in our decisions - you might be distracted by something that the other you isn’t, and sometimes you just happen to see the right move and sometimes you don’t.

When the computer plays chess against itself, does it always win? Most chess programs probably also contain some randomness by design, to keep things interesting.

I have posed in the other thread on this topic, what would happen if the TripleA AI played a game against itself? Would it always be even? Well, no, because eventually the dice would favour one side or the other. But if it played No Luck, with hits determined purely by punch, maybe it would tie, unless the AI is more adapted to playing one side or the game isn’t perfectly balanced.

Interesting to think about…

[squirecam]

@froodster:

I don’t think every game would result in a draw. First, white has a slight advantage because it moves first. Secondly, you might not be as good at playing one side or the other. Thirdly, I believe there are random elements in our decisions - you might be distracted by something that the other you isn’t, and sometimes you just happen to see the right move and sometimes you don’t.

Which are things I mentioned that result in the “other you” losing, and NOT luck. The other you simply made more mistakes than the “real” you did.

Equal skill does not mean perfection. One of “you” is bound to screw up sooner or later.

Squirecam

[frood]

But then, is the other “you” equally skilled as you on that day? If it’s not luck, it must be skill, or does “making a mistake” mean some third category? I say that the player who makes a mistake is, in that particular game, playing with less skill (perhaps they are usually better but are not playing their best, but the fact is the outcome is a less skillfully played game.

So once you define one player as making more/earlier mistakes, you are no longer discussing equally skilled opponents. I am talking in THEORY about what would happen if you had equally skilled players - whether those could really exist is irrelevant. These players are an abstraction created for the purpose of a thought experiment. If you want to talk about a different theoretical situation that’s fine, but if your imagination can’t fathom the concept of equal players then we simply won’t be able to discuss the implications of equally skilled opponents for this skill v. luck debate, mr. squigglygams.

But I also think there is an element of luck in whether your opponent will make a mistake. There is a randomness in our decision making. I think the rate at which you make mistakes is a measure of your skill, while simple luck determines when you make those mistakes. Ie. if you tend to make a dumb move once every six moves, it won’t be every sixth move that you screw up on - it is randomly distributed.

[squirecam]

@froodster:

But then, is the other “you” equally skilled as you on that day? If it’s not luck, it must be skill, or does “making a mistake” mean some third category? I say that the player who makes a mistake is, in that particular game, playing with less skill (perhaps they are usually better but are not playing their best, but the fact is the outcome is a less skillfully played game.

The Colts won the superbowl, and are a “skilled” team. Yet they lost to teams of equal or less skill, when they played bad (i.e. made mistakes). If you want to say they were “less skillful” on that day, so be it. Then under your scenario the “more skilled player” won.

But I’d just say it was more the mistake/less skill aspect that caused a loss, vs pure luck.

But to just say “equal skill” is leaving out an important fact. These players are equally skilled, BUT NOT PERFECT. So they will still screw up.

Luck should ONLY be the sole determining factor if/when God plays himself. Since his moves are perfect, it is only the dice which determines the outcome. (Or, perhaps Dice + inherent game balance, as the allies have an advantage in the game)

As for a AI which is “perfect” which could test the theory, like I said earlier, I’d reserve judgment until I saw one. Which wont happen in my lifetime, if ever.

Squirecam

[frood]

So is it luck or skill that determines which of two equally skilled players will screw up first?

It can’t be skill, since skill is equal, as defined in the question. That leaves luck. Not the luck of the dice, but the luck of who was daydreaming about Pamela Anderson and who was focused on the game.

[rjclayton]

Frood, I think you are splitting hairs at this point.  In any case I reword the question as “equally matched” rather than “equally skilled” just to be sure.  Regardless of how it is worded, sounds like most posters are defining it as going into the game, the odds-makers in vegas give either player a 50-50 chance of winning.  Hence equally matched.  Anyone can look at a game after the fact and pick the winner (hindsight is 20-20).  And for example I can confidently state that the Colts were always the superior team and were more skilled than the Bears.  However, I had picked the Bears to win the superbowl so what does that mean?  I had a favourite quote from my university rugby coach who said “On any given day, any one team can beat any other team”.

If the odds makers were undecided going into the superbowl (ie. 50-50), then would we all be sitting here saying the Colts won only because they were luckier?  No, we’d still be saying they won because they out played the bears and were a much better team on the day.  Maybe if they play 99 more Superbowls against the Bears then the Bears win 50 of them, but on that day the Colts were better and it has nothing to do with luck.

[Guest]

Good analogy.

[frood]

Well maybe I am talking about something else entirely. Perhaps my big mistake has been using the term “skill” rather than “skillful play” or even simply “strategy”

Basically I am saying that the question of “How big a factor is luck” cannot be answered that simply. The degree of importance of luck is relative depending on other factors, the only other one I can actually think of being “skillful play” - maybe that’s better than an abstract attribute of general “skill”.

Luck is a significant, probably game-deciding factor when two players play equally skillfully. When one player plays like a total moron and the other plays like the Kasparov of A&A, then luck will not be a significant factor in the outcome of the game, unless of course the difference in luck between the two players is as vast as the difference in skillful play.

However, luck tends to average out over the game, and skillful play will compensate for and minimize the effect of luck. There is an infinite range of degrees of skill, but you can only be so lucky or unlucky. So on the whole, I would say that skillful play is by far the more important factor. But when there is no meaningful difference in skillfulness, then luck becomes a factor.

Maybe think of this analogy: compare the significance of the presidential vote in Florida, and in the rest of the country. Generally,
the vote in the rest of the country is much more important than the vote in florida. But you need both factors to determine who won the election. If the rest of the country has resulted in a tie, then suddenly the Florida result becomes much more important.

That’s the concept I have failed miserably to communicate: that the importance of one factor will vary depending on the closeness of other factors. When other factors cancel each other out, the factors that are not equalled out will determine the outcome.

Finally, I’ll just say this: in any event, percentage is the wrong unit with which to measure the significance of a factor. Instead, I think you have to use descriptions like “success will vary directly in proportion to the degree of luck, and in a squared proportion to the degree of skillfulness of play.”

[dezrtfish]

21.5%

[Wazzup]

Luck only involves the outcomes of battles.

Decision and strategy of units involved to increase probability of favorable or unfavorable results in battle outcomes.  Do you attack a territory with 1 inf, 1 ftr v. 1 inf, or 2 inf, 1 ftr v. 1 inf?  Or do you use your bomber to SBR instead of support ground troops?  The outcomes of the battles heavily depend on whether you approach the game conservatively or agressively.  Agressive tendencies will usually result in a wider range of possibilities, and increase the probability that expected results occur farther away from the average.  Conservative tendencies will usually narrow the possibilities and decrease the probability that expected results are further from the average.

Both approaches work, and two people evenly matched and skilled players can have totally different philosophies.

Giving up territories to secure board position is another.  Or giving up territories to increase your counterstrike could be another.  With AAR, there is almost no one game’s outcome that mirrors another with an exact board setup.  In chess, probability of battle outcomes does not exist, and a board setup could be the exact as the previous match.

[rjclayton]

Pagan, good thoughts.  Just wondering if you voted in this poll and if so what % you believe luck plays.

Welcome aboard.

[Guest]

Hail and well met, Pagan!

[axis_roll]

I’ve tallied up the votes from three A&A sites (http://aamc.net/bunker/forumsql/forum/forum_posts.asp?TID=149&PID=772#772, http://www.axisandallies.org/forums/index.php?topic=8840.0, and http://www.axisandalliesworldclub.com/cgi-bin/ultimatebb.cgi?ubb=get_topic;f=1;t=004346).

100…9
…90…4
…80…3.5
…70…5.5
…60…9
…50…11
…40…9
…30…8
…20…8
…10…1
…0…1

69 votes.  One site only offer 5 poll choices, so categories were in units of 20 (hence the .5 votes)

Typical bell-type curve right around 50%, but several votes(9=13%) for 100% luck.  I think these people totally bought into the concept of two exactly equal players, hence everything is determined by luck.

Thanks all for voting and/or discussing.

[frood]

Just for clarity (as I was one of the main “Equal skill” proponents) I do not believe the game is 100% luck. My view is that luck is only the deciding factor when the players are close enough in skill to allow it to play a role.

As an example, I lost my round 2 tournament game as a result of very poor strategy on my part. By the end of round 3 no amount of luck would have saved me, so luck was not a significant factor. If I were to play myself however luck would play a much bigger role, assuming both of “me” played with pretty equal skill.

Maybe that puts me in the luck=10% category, but fundamentally I just don’t think that the importance of a factor can be measured as a percentage. Rather, you can only look at it in terms of its role in an equation.

Example: the area of a circle equals pi times the radius of the circle. What “percentage” of the area of a circle can be attributed to the radius? Or to bring in two factors, In the case of an ellipse, what percentage of the area of an ellipse can be attributed to its length and what percentage to its width?

If we define game outcome as the result of two factors: difference in skillfulness of play and difference in luck, how can you attribute a percentage to either one? What fraction do you divide to measure this?

If people thought all along that I was arguing for 100% luck then either people aren’t reading my posts or I just am not able to communicate very well.

[mateooo]

Luck is always there. Anyone who has ever lost that battle with a <1% likely outcome, knows that. Hopefully, that bad outcome occurred on a battle that was not crucial, but sometimes it does. To say that luck is 100% of a game, is wrong. Even if players are equally skilled, there are different ways to play, different openings, many different choices to make,and many different ways to respond to the small fluctuations in luck that occur (one extra INF here, one less there, that battle went great, but that battle sucked…)

There are definitely games that are completely determined by the luck of the rolls, but those games tend not to last long. Personally my favorite games are the ones where luck is pretty average, or when one side gets really lucky in one area and really unluck in another, resulting in a complete change in the game.

[DarthMaximus]

My argument against luck (I put it at about 20%) was because I’m looking at it long term.  Of course in any given game you can have just terrible dice and lose b/c of it, but if you start losing 5, 10, 15 games and say you get terrible dice you might want to start looking at the attacks you are making.

For example, say you have a trading scenerio with Russia where you can attack both Kar and Ukr with 75% to win each battle OR just attack Ukr with a 95% to win.

Hey great, I’ll take the 75% chance to win each, not too bad.  But in reality you only have ~55-60% to win both.  It is not luck that may cost you here it is your decision to do two 75% battles vs. one 95%.  Given the game circumstances that may be worth the risk but you should start to see where this becomes problematic.

Take 3 battles where you have 80% to win each.
( .8 *.8 *.8 ), now you are down to only about a 50% to win all 3.  It is not necessarily luck if you lose a 20% battle here.  It was 50/50 that you’d win all 3 to begin with.

Even 3 battles of 90% (.9*.9*.9) = ~72%.
Add in a 4th battle at 90% and you are down to about 65% to win all 4.  Odds are still on your side but I think 65% success rate starts to near the threashold of whether you want to be that risky (depending on game circumstances of course).

There is also the question of “What do you consider lucky?”
For instance, I may not consider losing a 70-30 battle to be unlucky, heck 1 out of 3 times I’ll lose that battle.  But someone else might.  Of course I’ll be mad that I lost, but should I do the exact same battle everytime I’ll end up on the 70% side waaay more often then the 30% side.

I think a key is seperating the really bad luck from whether a move was bad or really good luck from a good move.

That’s why I have the 20% stance.  I basically think that 1/6, say a trn hits your bom in an attack can be classified as luck.  That’s 16%, so I just round up to 20-25% and flat out tell myself that 20-25% of the games I play I’m not going to win no matter what, I still try to win but… 
Somewhere along the line I’ll lose a key battle where I had a 80%+ chance to win, and poof I’ll lose.

So what I try and do is to try and maximize the 70-80% of games where I do get the middle of road dice (or close to it) for the first 2 rds.  Then leverage any advantage I gained into a long term adv where the number of multiple attacking rds or “risky” battles decreases.

Over the long term you’re probably going to win as many “lucky” games as you lose “unlucky” games, so you have to take the gift wins when you get them but really concentrate on the games where you do get the middle of the road dice early and try to put yourself in a postion to not have to worry about luck later, or limits its impact as much as possible.  Say only do 1-2 major attack (90%+) vs. 3-4 minor (70-80%+) where the odds of success on all diminish.