Variance vs Luck

[LinusKS]

I spent almost a year playing sngs almost exclusively, but eventually I became convinced limit play was more profitable.

But I couldn't come up with a theoretical or logical justification.

The best I could come up with was that in sng play, the variance was higher. In an sng, when you're bad beat, you lose your whole share of the prize money.

In limit play, a bad beat costs you only what you've invested in the hand.

Still, from what I've read in the forums, that shouldn't affect profitablity.

According to 2+2 received wisdom, variance shouldn't matter to the serious player. As long as your bankroll is sufficient, and you play enough hands, you should welcome variance (or at least not care about it).

But the more I thought about that reasoning, the less sense it made to me.

Consider the hypothetical: A good chess player has a an advantage at his club. He plays for money, and wins 75% of the games he plays. Then the club introduces a new variant. Let's call it Bughouse. The new game brings an element of chance to the game, and suddenly nobody wants to play anything but Bughouse. How can this development do anything but hurt the expert's win rate?

Any element of chance would necessarily hurt his win rate. Even if he somehow was able to jigger the odds, he'd still have to maintain an advantage of 3-1 on the chance element, just to maintain his old win rate.

Take a comparison to another game - hearts, for example.

There's an element of chance in hearts. But a good hearts player will beat a bad one a far greater percentage of the time than in poker. If you played tens of thousands of hands, and were still a net loser, that'd be pretty conclusive proof that you sucked at hearts. That's not necessarily the case in poker.

In chess, you wouldn't necessirily need more than one game to know what the outcome of the next 10,000 games would be.

So what's the deal?

Is variance the enemy of the professional poker player?

Or his friend?

Or is there a difference between luck and variance, and if so, what is it?

[gytten]

If the better player will win 100% of the time in a specific game, the bad player will not play. He will not enjoy it at all. Variance makes the bad player have a few winningstreaks now and then aswell.. he will enjoy the game and continue playing the game, even if he lose money in the long run.

FISH do NOT like to lose everytime they play. they like to think they are the best poker player in the world alittle now and then. Variance is what makes this come true, one out of 10 games he will be a winner, he will feel good about him self and play again... the more he wins the more he will enjoy the game and play more often. Variance is what makes poker such a popular game in my opinion /images/graemlins/cool.gif

[drewjustdrew]

Variance and luck are the same thing. Luck does not really exist, outcomes based on probabilities exist. The cumulative results of those outcomes create a variance.

Variance is not the enemy of the appropriately bankrolled player. If you can always make better decisions than your opponents, you will be pushing tiny edges that in the long run are slightly profitable, but carry high degrees of variance. There are many decisions that are highly profitable a large percentage of the time, like betting the nuts from late position, but there are many profitable decisions that people pass on in order either because they want to reduce variance or because they don't know of the profitability.

[LinusKS]

The more I think about this, the more I think you're wrong.

I think I am confusing "luck" - or randomness - with variance.

Variance only describes how far your actual results can depart from the mean.

What I'm talking about is something different.

In high-card poker, for example, skill plays no role at all. (Whoever draws the high card wins.)

You can increase (or decrease) the element of luck in any game. In Hold'em, for example, you could introduce a rule that allowed the loser to try to draw a high-card against the winner for half of (or even all of) the pot.

A rule like that would decrease a winner's edge, because there's no skill in drawing a higher card than your opponent from a random deck.

Since bringing an extra element of luck into the game decreases the winner's expectation (theoretically all the way down to zero), luck can't be the same as variance.

[k_squared]

But is it appropriate to call the element you have added to the game 'luck'? Luck seems to me to be when an unlikely outcome occurs, one that is statistically improbable. It is bad luck if it hurts you and good luck if it helps you. Luck is always a part of the game, and allows people who play poorly to win because it means sometimes bad decisions are rewarded (and conversely that good ones are not always rewarded).

What you are adding to the game isn't luck but an added element of randomness. You are turning a game that has some skill involved into one that is simply a game of chance occurences (a coin flip). Just drawing cards to see who gets a higher one is completely random and takes no skill becuase there is no further decision about what to do after you have some knowledge about the card you drew. Skill comes into play when there are right and wrong decisions about what to do in the game. Without any ability to make different decisions (or to act differently) there is no skill involved at all, but that does not mean 'luck' determines the outcome. Chance and luck are different. If you draw a king and the next person draws an ace that is bad luck, but the fact that the 2nd person was lucky has nothing directly to do with the outcome, it was merely a factor of the randomness inherent in the game. The more you increase the chance element of the game the more you decrease the gap between a skillful player and a non-skillful player (and i think this is your point). War is all chance and no skill. Blackjack is mostly chance (when played with some sense of appropriate play). Poker is a mix of chance and skill, and there-in is where the money is made! Because poker involves chance it means that bad players will win and they will enjoy themselves and keep putting money into the game. If they never won a hand the vast majority of fish would leave the game and all the skillful players would lose all their money into the house's rake!!!

Luck is not equivalent to randomness, although the apperance of luck occurs because of randomness (or chance).

-k_squared

[cardcounter0]

I don't think that rule would change anything. When the more skilled player got beat, he would also have a chance to draw the extra card for half the pot.

SO it would still boil down to the person with the most skill winning the most pots, you have just made the long run a little harder to obtain.

[pzhon]

[ QUOTE ]
According to 2+2 received wisdom, variance shouldn't matter to the serious player. As long as your bankroll is sufficient, and you play enough hands, you should welcome variance (or at least not care about it)...

Consider the hypothetical: A good chess player has a an advantage at his club. He plays for money, and wins 75% of the games he plays. Then the club introduces a new variant. Let's call it Bughouse. The new game brings an element of chance to the game, and suddenly nobody wants to play anything but Bughouse. How can this development do anything but hurt the expert's win rate?

[/ QUOTE ]
The correct comparison would be that the player wins 75% of the time at $1/game in blitz chess (no draws), but 55% of the time at $5/game at bughouse. In each case, the payer wins $0.50/game on average. If the bughouse is played for more than $5/game, the player should prefer bughouse.

People are willing to lose much more per hour playing poker (or bughouse) than they are willing to lose to obviously superior opponents at chess.

[Pepsquad]

[ QUOTE ]
[ QUOTE ]
According to 2+2 received wisdom, variance shouldn't matter to the serious player. As long as your bankroll is sufficient, and you play enough hands, you should welcome variance (or at least not care about it)...

Consider the hypothetical: A good chess player has a an advantage at his club. He plays for money, and wins 75% of the games he plays. Then the club introduces a new variant. Let's call it Bughouse. The new game brings an element of chance to the game, and suddenly nobody wants to play anything but Bughouse. How can this development do anything but hurt the expert's win rate?

[/ QUOTE ]
The correct comparison would be that the player wins 75% of the time at $1/game in blitz chess (no draws), but 55% of the time at $5/game at bughouse. In each case, the payer wins $0.50/game on average. If the bughouse is played for more than $5/game, the player should prefer bughouse.

People are willing to lose much more per hour playing poker (or bughouse) than they are willing to lose to obviously superior opponents at chess.

[/ QUOTE ]

BINGO.

[dogmeat]

Variance is a mathematical term relating the standard probability of an outcome and the expected variance from that expectation for a given number of chances. Variance is not luck. Luck is a term used to explain good or bad (as applied to what an individual wants) events. From a mathematical standpoint, the idea of "good luck" of course does not exist, but could be (poorly) applied to situations that fell beyond expected returns, or simply had a smaller percentage chance of happening. In this way it does not mean it should not have happened, only that "good luck" would be the term applied when a "long-shot" happened.

Dogmeat /images/graemlins/spade.gif

[LinusKS]

You're right, randomness is a better word to use than luck.

And it's true bad players play because they can win despite bad play.

All things being equal, though, a player who thinks he has a skill advantage would rather play where skill counts more than luck, since randomness pushes the expected outcome toward zero.

[einbert]

You aren't concerned with the variance of the game, you are concerned with the skill factor of the game. The skill factor in flipping a coin is 0%, and the skill factor in chess is upwards of 90%.

The reason these NL SnGs are less profitable is the skill factor is very low because of the quickly increasing blinds. If the blinds started at 1%-2% (of the starting stack) and increased every 30 minutes according to a slow, smooth structure, the skill factor would be very high. But typically, the blinds in these events start at around 1%-2% and the blinds double (or nearly double) every ten minutes. This creates more action and keeps nonthinking players happy by allowing very simple strategies (all-in or fold) profitable. In a deep stack, slowly increasing blind structure this strategy would not be nearly as efffective, and would be near-suicide early in the tournament. The skill factor in a hand of limit holdem is much, much higher--one reason is that decisions must be made on EVERY street, rather than a simple all-in negating the need for that tough decision-making.

Lower skill factor leads to more decisions being closer to 0 EV--it lessens the amplitude of each decision. A greater skill factor would mean that every decision made by the player is very crucial, and a single mistake could have a huge -EV rather than a small one. The extreme example of this is if you and I decide to bet on a coin flip. How much we bet and whether we choose heads or tails, both of our EV is 0 as long as we both put up the same amount of money. If I challenged a master chess player to a $100 match, if he is a 95% favorite to beat me, his EV to play the match would be +90$EV (95% of the total prize pool).

That's my opinion on what you are trying to say.