How consistently should the better player win a game?

The fact that the better player nearly always wins in chess is described as both its best and worst feature.

Few like it when a clearly inferior player can just lucksack into a win. On the other hand, everyone is a beginner at any game at some point, and chess is notoriously hard to get good at for the above reason — not to mention the fact that it’s easy to get discouraged when you’re clearly behind with no chance of catching up.

Where do you like the line drawn?

I think it depends on what your “goal” is. The reason for the popularity of No Limit Hold 'Em is that the better player’s advantage only emerges after thousands of hands played. The randomness and luck factor are so strong that everyone views him/herself as an excellent player.

Since you mentioned chess as an example, and since chess has various ratings systems, It may make better sense if you substitute “more highly rated” for “better.” If you do then the statistics hinted at in the rating system will give you a rough idea of how “consistently” the higher rated player will win.

The main issue with any rating system is that it is always in flux. Players’ ratings are dynamic so that the momentary rating difference between two players may have changed when they meet again some time in the future. Provisional ratings try to take this into account.

If you want more depth to your answer, start with Chess rating system - Wikipedia.

This question is going to be exponentially complicated by the follow-up question: “How much better?”

Typically, team sports have a much higher rate of “worse team has a decent shot” than individual sports. Also, games with lots of scoring generally make it harder for the worse team to win.

An interesting exercise may be to rate the major sports in their likelihood of an upset on a 1-10 scale. My ratings:

Soccer: 9
Football: 5
Basketball: 3
Baseball: 7
Hockey: 8

Individual sports/games:
Tennis: 2
Golf: ? (this one is interesting, because it goes by score instead of player vs. player. If it were normally done by 1v1 match play, you’d probably see a fairly low chance of an upset)
Swimming: 3
Sprinting: 2
Distance running: 1
Chess: 1
Poker: 10

I play around with designing board games in my spare time.

My rule of thumb is that a better player should win about twice as often as his weaker opponent.

According to typical rating systems (used for chess and table tennis, and who knows what else…) if a player is ranked 50 points higher, they should win 2 out of 3 matches. At 100 points higher, they should win 4 out of 5 matches against their opponent. If they are 200 points higher, they should win 39/40 matches against their opponent. So it changes a lot depending on “how much better”.

The answer is, it depends. The balance between luck and skill is a huge part of what differentiates various games and part of what draws or pushes away fans. The obvious extreme examples are chess and poker, and I quite love both games and both involve an enormous amount of strategy, but they’re still fundamentally different. So we really need to consider what makes them different.

Chess is an example of a complete information game. Both players have exactly the same information about the state of the game and there’s no randomness involved. Theoretically, either player could compute all the possible future states from the current state and there’s an ideal way to play it. Checkers, Go, Othello, and a few others are also good examples. IMO, this sort of game should heavily favor the better player because it’s just all about who can do the most with the same information. Thus, in Chess, or any complete information game, the better player should win considerably more often than the worse player, otherwise the game is “solved”, like Tic-Tac-Toe.

There’s another class of game that’s partial information. There’s no luck involved, but each player has only some of the information available. Some good examples of this would be Battleship, Guess Who, Mafia/Werewolf, etc. In general, I think the better should still have a considerable advantage, but less of one, because a better player ought to be able to have a good way of estimating or putting limits on what he doesn’t know and minimizing that factor, but there’s a chance he is wrong. If the better player doesn’t win a lot more often, it just means that the game is either too simple, and thus it’s really easy for low skill players to figure out what they don’t know, or it’s too complex, and skilled players can’t put any effective boundaries on their lack of knowledge. But ultimately, a large part of what makes the skill in these types of games IS the ability to estimate that information you don’t know, not simply calculating future states from what you do.

There’s also luck based games. A lot of board games fall in here, Monopoly is probably the best example, and most other board games fall here. Every player knows all the same information, but you can’t “solve” the game because you still have to have luck with dice rolls and where you do or don’t land and on what turns. I’d say that the better player ought to win reasonably often, but because of the luck, and that that luck is based on a binomial distribution, you ought to be able to model how likely they are to win with overlapping those distributions with the means separated by the difference in skill. You do have some of these types of games that, while technically having information, don’t actually require any skill on the part of the player, like Chutes and Ladders requires no decision on the part of the player, just rolling the die and moving the piece, so there’s no measurable difference in skill.

Finally, you have the luck-based, partial information games, and Poker is the obvious example here. If the better player wins too much, it downplays the luck part of the game, and if he doesn’t win enough, it downplays the information based part. Obviously, because of both the partial information and the luck based part, the better player ought to win less in this type than any other type of game.

So, we have four sub-types of games, and I think we can use that as a baseline for judging how often the better player ought to win and we can generalize this to sports too. Take soccer, for instance, the games are generally very low scoring, so luck will play a larger role and it’s no surprise that upsets happen often. Contrast it with Basketball or Tennis, and there’s WAY more scoring, so it’s more likely to converge on the difference in skill in the game, so the better ought to win more often. But when you compare all of that to, say, racing, there’s no randomness there and we consistently see the best runners, drivers, swimmers, or cyclists performing at the top there.

Poker is an interesting example, in that it is clearly a skill based game, or else you wouldn’t see famous people consistently making a living at it. I try very hard at it and break even at mild limits.

However, on several occasions, flat-out amateurs have won the game’s highest honor, the World Series of Poker main event. Chris Moneymaker famously won it after qualifying online, and since has won little else. It’s completely inconceivable that an amateur could win, say Wimbledon, or the Masters.

And yet that element of skill does win out in the long run. Realistically, I will continue to break even or win a tiny bit this year playing low limit poker, while Daniel Negreanu will make money playing high stakes poker.

I’d argue that the intent of the game plays a big part. Your average Milton Bradley family entertainment game is going to want something closer to luck than skill, because kids will likely be playing with adults. Even among adults, you want some luck to take part.

That said, sometimes you can have wildly imbalanced competitive games that are really only imbalanced at certain levels. A lot of fighting games fall into this category, where at the really low skill levels usually some skills are hilariously broken, at intermediate levels everything is (roughly) fair, and then at pro levels only one or two people are used because theoretically they’re the best. These games can be fun as long as you’re playing within your skill level, and as long as you can house rule out the gamebreakers.

I don’t design anything, but I like playing a lot of card games and board games and that’s where I put a good fun skill-luck ratio, too, about 67%-33%. Too much a gulf, and it’s hard to keep less skillful players in the game or even wanting to play the game. I feel games like backgammon and cribbage fall into this range (although the win %age fluctuates depending on how wide the gulf between skill levels are. A master vs beginner might get closer to an 80% win rate. But a “good” player vs an average or casual player would settle in at around 67% or so, I would guess.)

That’s a pretty reasonable ratio for most games. I think the range between 2:1 and 3:1 is pretty good. If it’s lower (i.e. skill plays less role), it becomes a game of luck. If it’s higher, it becomes too challenging to enter the game. Chess is practically a profession beyond the casual level, and I’m simply not interested enough to go there. Similarly, my wife won’t play some games with be because I consistently beat her and she doesn’t feel she has a chance.

I think Blaster Master has a pretty good discussion of perfect knowledge vs partial knowledge vs luck.

I think perfect or near perfect knowledge games with multiple players are a special case. This is games like Puerto Rico or Hansa Teutonica. A skilled player can easily be foiled by one player either looking to spoil another or an unskilled player making bad plays. For example, in Puerto Rico, if it’s obvious that the current player should take a specific action to prevent the next (skilled) player from getting it (assuming they don’t give up too much in the process), but an unskilled player may not see that move. If the unskilled player picks before the skilled player every time, the skilled player will have even better options than he otherwise would.

To a lesser extent, I’ve seen this in non-perfect knowledge games like Hearts. My sister hates it when I’m passing cards to her because I’m very aggressive about what I pass.

That’s kind of an odd reaction. What is an “agressive” pass in hearts? You’re always trying to maximize the chances for your hand. Is it like passing the Ace and King of Spades? What else would you do? (And, yes, there are times when you might want to keep those cards, and passing the queen of spades is often enough not the optimal play.) Of course, it gets a little more complicated when you’re trying to target specific opponents, but, in general, aren’t all passes in hearts “aggressive”? Surely, you’re not passing low and medium value cards unless you’re trying to shoot the moon or voiding a suit or something like that.

By aggressive, I mean that I frequently play to have points start coming out early, even if it means taking one or two myself.

I tend to pass with the intention of playing to what I pass. If I don’t get dealt the Queen of Spades, I will surely dump the Ace and King, then lead to them to draw out the Queen. I’ll do similar in other suits, passing high to protect medium cards which I can lead to draw out points, knowing there are cards out there I can lead to when I want to lose the lead.

I’d say about 70% or so. Enough so that the worse player wins a significant fraction, but that the superiority of the better player is also established.

Interesting. Most of that is fairly normal strategy, in my experience. And, yes, you want to dump the AK Spades most of the time, and generally keep the Q spades if you have three spades behind her.

AK spades is an automatic pass unless you have the queen, so that’s not the aggressive part. That’s just normal. It’s the breaking hearts early that I think drives her nuts.

And we play that the queen of spades cannot be passed. Nor can the two of clubs.

Ah. I see. I don’t mind early fishing for hearts. I don’t like limiting what cards can be passed–to me, it breaks some of the strategic depth of the game. I’ve played “no pass 2 of clubs” before, but never “no pass queen of spades.” That kind of ruins the game for me.

I don’t pass the AK of spades unless I have little to back them up. I prefer having a few high cards in my hand because they allow me to get on the lead when I need to be. And with the frequency spades get led, it’s usually not to difficult to find yourself the last play in the trick anyway, so you can dump the A/K on it. Plus, it’s extra protection in case someone passes you the Queen. And once the Queen’s come out, they are no more harmless than the A/K of diamonds. (Or clubs, but the A/K of clubs are usually played by the time the QS comes out.) I usually find it better to cut myself from a suit then to pass the A/K.

And passing the queen is not only often times not the optimal play, it’s typically the sub-optimal play, even moreso if you’re passing left. I also rarely pass hearts, and if I do, I always make sure I pass a low or middle one with any high ones to keep someone from shooting the moon with hearts. (Much easier to shoot the moon with spades and diamonds then hearts, anyway. If I pass you nothing but hearts, expect that I’m either planning on taking no points or all of them. Because having hearts in your hand helps you stop others from shooting.)

And I’ve never played in games that limit what can be passed. Most of the time I don’t even play with the “first trick safe” rule. Never really got the point of it. It’s rare the person taking the first trick will wind up with more than one heart anyway, and I’ll happily take a heart to dump off high clubs, which just suck at the end-hand.

AK of spades is not an automatic pass without the queen.

Just sayin’

Yeah, I should amend where I say “you want to dump the AK Spades most of the time.” It’s usually not the best move to pass spades of any sort.