luck vs. skill -- a statistical analysis

[akishore 0]

all this talk about pot odds and coin flips and luck, etc. have made me nostalgic about some statistics i learned in high school. not too complex, but interesting.basically, the jist of a statistics way of thinking is that anything is possible. probability theory doesn't say that in 10 million coin flips, you will get half heads and half tails, it just says that a coin is as likely to fall heads as it is tails. it is completely possible that each of those 10 million flips will be tails. thus, nothing is truly certain.so how do we define certainty? we say, if something is very unlikely, we will discount it as truly possible because it's very improbable that such an event will happen. e.g. if i tell you i have an 80% basket rate when i shoot hoops, you tell me to shoot 100 shots, and i only make 2, was i lying? you don't know--it's possible i just got very unlucky--but you say "the chance of you getting SO unlucky is almost zero, so i don't believe you!"to define it mathematically, we say something is certain or possible if the chance of it occuring is greater than some probability alpha--usually this probability is 0.05 or 0.01 (5% of 1% respectively). so in a series of 7 coin flips, the probability of each of the 7 flips landing tails is (1/2)^7, less than 1%, so we say it's very unlikely.of course, this applies to poker because luck plays a part in every game. how do you know how much of your winnings/losses are because of luck? here is a great section from poker for dummies that gives an example of short-term luck vs. long-term skill (paraphrased):a computer was used to simulate 60,000 hands of $20/40 hold'em. that's one year of play with eight hours a day, 40 hours a week, if you get in 30 hands per hour--about right at a live game.ten people in the game had IDENTICAL player profiles, so the long-term expectation was that everyone would break even (everyone is getting the same cards in the long run and they are playing them the same in the long run). nevertheless, there were four losers and five winners. the big loser lost $3.18 per hour ($6,360) while the big winner won $1.99 per hour ($3,980). that's a lot of money to lose and win in the short run, even compared to the big bet of $40!then, the computer was asked to play the same game, same people, for 3,000,000 hands (30 hands per hour, 2000 hours per year, 50 years--about a lifetime of professional poker, as long a run as is humanly possible).now, the big winner was ahead $60,214 ($0.60 per hour) while the big loser was stuck $35,953 ($0.35 per hour). although you can see this is still a lot of money, the rate per hour has shot down dramatically to an almost negligent amount compared to the big bet (both about 1% of a big bet).based on this, you can safely say that in the long run of poker, you can attribute about 1% - 1.5% of your winnings/losses to luck. it also says that a year is probably not enough to get into the true "long run".another interesting but unrelated (at least to this thread) simulation they did was introduce two poorer players while the other eight remained identical. one was too tight and the other was too passive, and after 50 years of poker, both were down $3 million and $4 million respectively, and everyone else in the game was a winner.the big winner was up $1.2 million ($12 per hour, a huge increase from the $0.60 per hour he made in the previous simulation) and the smallest winner was up $800,000 ($8 per hour, still a big amount compared to the neutral long-term).that goes to show the importance of choosing the right game. a game where there's one fish is better than a game without fish, and a game with 3 fish is better than that even. of course, a low limit table full of fish is the best of all--yes, toogood, even $0.50/1.00.hope this helps,aseem

[AvoidReality 0]

Interesting read, many thanks

[KStrom 0]

Good read

[TheMathProf 0]

Indeed, your statement of the year not quite being long enough to be considered the long run is somewhat supported by the Law of Large Numbers, which states that when the number of trials n is large enough, that (actual results)/(possible results) is approximately equal to the probability of that event happening.60,000 hands seems like a lot, until you consider the multitude of different types of poker hands that come up, especially post-flop. Did my flush draw with overcards hit against his top pair? Did my pocket deuces make trips the expected amount of the time. In poker, with the Law of Large Numbers, the number of hands has to be large enough to actually allow each of these situations to occur a Large number of times.It was an interesting read. Thanks for the post.

[MrConceit 0]

Good post. And it would be pretty scary to me if I hadn't thought about this a lot before. Luck can play such a huge roll over what SEEMS a long term to us.Like say 1 month (online). That seems like such a long time in terms of playing cards day in and day out. But it really isn't. Some of my friends still don't believe you can run bad for like 3 weeks straight. I hope they can continue to believe that, but sadly it's unlikely.The other opposite problem some people have is they had 1 good session or good week, and now think they have a certain skill that might not be totally accurate. So if they start losing a lot, they keep talking about downswings and bad luck because they've read or heard about such things. But the easiest answer if you're losing money (for a few weeks or few months straight) is you aren't as good as you think you are. Not that it has to be the only or most true answer. But ya know....

[chuckf410 0]

I think it was Douglas Adams who wrote in HHGttG something to the effect of:We live in an infinate universe of infinate possiblities.And then of course there is the Schrodenger's(sp?) Cat theory.Both of the above theories are why I am comfotable playing three card poker blind.

[princeof56k 0]

One important factor the simulations you mentioned might of missed: the rake.I believe in the game you descibed of 10 players who play exactly the same, the rake would make all of them long term losers. Think about it. If the house just collected $1 from every pot, over 60,000 hands that would be $60,000 right down the drain.I think the real interesting question is how many fish are needed at the table to overcome the rake and make the good players long term winners? Are there any simulations that account for the rake?

[DeadMoney6545 0]

Good Post... and the lil jab at the end too was nice as well :twisted:

[swami 0]

NICE :shock: :shock: Thanks

[KidKanuck 0]

excellent post. Outstanding food for thought and discussion.IMO...I think that there is one thing that makes this very impractical to reference while being totally mathematically accurate when judging ones ability as a poker player.If you could simplify a players skill level as a a rating on a scale of 1-100 and it happens to be exactly 50....what is the likelihood that that player is to view his or her skilll as exactly 50...particularly after a run of good or bad cards. While some players are more rational than others...pure rational behaviour just plain does not exist in activities where psychology, emotion, and confidence is so present.this is why I truly believe in the saying "you create your own luck".KK

[jayistheman 0]

that takes me back to the old AP stat class... nice post

[akishore 0]

One important factor the simulations you mentioned might of missed: the rake.I believe in the game you descibed of 10 players who play exactly the same, the rake would make all of them long term losers. Think about it. If the house just collected $1 from every pot, over 60,000 hands that would be $60,000 right down the drain.I think the real interesting question is how many fish are needed at the table to overcome the rake and make the good players long term winners? Are there any simulations that account for the rake?

rake was not included on purpose to make the experiment focus more on short-term luck vs. long-term skill. and if you play in home games, there will of course be no rake, unless you are a fascist "friend" to your poker buddies. :-) but yes, rake has a huge draining effect in the long run. if you look at poker tracker or any program like that will show you that you've already lost a huge amount of profits through rake.i don't think you can figure out so easily how many fish are needed to negate the rake effect, since it all varies based on how you play and how they play, etc. introducing two worse players (who weren't even that much worse) was to show the massive magnified effect bad play has on a good player's bankroll.aseem

[jogsxyz 0]

.The other opposite problem some people have is they had 1 good session or good week, and now think they have a certain skill that might not be totally accurate. ....

After one good week, many newbies are starting silly threads like 'should I turn pro?. Yeah, sure.

[allinbluff35 0]

After one good week, many newbies are starting silly threads like 'should I turn pro?. Yeah, sure. yup, and a lot of people like to rain down on certain peoples parades because they don't think it is possible for anyone to do it because they can't do it themselves.

[LeeDanger 0]

.The other opposite problem some people have is they had 1 good session or good week, and now think they have a certain skill that might not be totally accurate. ....

After one good week, many newbies are starting silly threads like 'should I turn pro?. Yeah, sure.

Hey, I was the one that started that thread, and it wasn't one week it was one session!!! :evil:

[offmandh 0]

awesome post!!!

[MrConceit 0]

After one good week, many newbies are starting silly threads like 'should I turn pro?. Yeah, sure. yup, and a lot of people like to rain down on certain peoples parades because they don't think it is possible for anyone to do it because they can't do it themselves.

Ouch, sorry guys. I didn't mean to start any old fights over. I was more thinking of some personal friends of mine. :)It's usually only kids (though not always of course) who try to jump into the trying-to-be-pro-thing too quickly. Most people have too many responsibilities to jump in really fast and quit their job."Yeah, so honey, I quit my job yesterday, and I'll be playing poker for a living, you can cover our mortage until I hit my stride right?"

[akishore 0]

excellent post. Outstanding food for thought and discussion.IMO...I think that there is one thing that makes this very impractical to reference while being totally mathematically accurate when judging ones ability as a poker player.If you could simplify a players skill level as a a rating on a scale of 1-100 and it happens to be exactly 50....what is the likelihood that that player is to view his or her skilll as exactly 50...particularly after a run of good or bad cards. While some players are more rational than others...pure rational behaviour just plain does not exist in activities where psychology, emotion, and confidence is so present.this is why I truly believe in the saying "you create your own luck".KK

that's a good point. the simulation could not take those intangibles into account, but even if it had, assuming every player was identical, the results would be similar, no? if anything, maybe the short-term fluctuation would have been bigger, e.g. when on a losing streak the person goes on tilt and plays worse for an x number of hands, when on a rush, a person gets more aggressive and wins more pots, etc.in reality, things are never so black and white, of course. it's an interesting point you bring up about creating your own luck. i'm not sure i totally understand or agree with the basis of that idea, but i certainly see where you're coming from. that just goes to reiterate that poker is about everything BUT the cards. that's why all 8 good players were winners in the game when two bad players were introduced--the cards remained the same, didn't they?good post.aseem

[allinbluff35 0]

After one good week, many newbies are starting silly threads like 'should I turn pro?. Yeah, sure. yup, and a lot of people like to rain down on certain peoples parades because they don't think it is possible for anyone to do it because they can't do it themselves.

Ouch, sorry guys. I didn't mean to start any old fights over. I was more thinking of some personal friends of mine. :)It's usually only kids (though not always of course) who try to jump into the trying-to-be-pro-thing too quickly. Most people have too many responsibilities to jump in really fast and quit their job."Yeah, so honey, I quit my job yesterday, and I'll be playing poker for a living, you can cover our mortage until I hit my stride right?"

you didn't, I am just a sarcastic prick when it comes to my personality and you probably won't find more than 10 useful posts of mine on this forum.

[JistTheFist 0]

That was an excellent post to start things off man... but I agree with what the other guys is saying about it not being too accurate.... and here's why....I recently read about something called "Caro's Law of Loose Wiring".... It was written by Mike Caro, the same guy who wrote "caro's book of tells."basically what it talks about is that most poker players make their decisions on a whim..... they may play a hand for almost no reason at all except that they wanted to. well... I don't really know how he puts it exactly... I can't remember but it's in the book of tells in the intro... or I'm sure you can find something about it on google.... It's a very short and interesting read.... however... I guess you could make the arguement that if they are identical players they will make the same plays just cuz "they feel like it" the same number of times over time.

[justblaze 0]

That was an excellent post to start things off man... but I agree with what the other guys is saying about it not being too accurate.... and here's why....I recently read about something called "Caro's Law of Loose Wiring".... It was written by Mike Caro, the same guy who wrote "caro's book of tells."basically what it talks about is that most poker players make their decisions on a whim..... they may play a hand for almost no reason at all except that they wanted to. well... I don't really know how he puts it exactly... I can't remember but it's in the book of tells in the intro... or I'm sure you can find something about it on google.... It's a very short and interesting read.... however... I guess you could make the arguement that if they are identical players they will make the same plays just cuz "they feel like it" the same number of times over time.

lol really? caros law of loose wiring is by mike caro? solve any more brainbusters today? sarcasm aside, though, this is assuming most poker players are terrible players. the simulation assumes you are playing in a game with 10 moderately skilled players. moderately skilled players to not make decisions on a whim, with the possible exceptions of decisions which they know are even money either way. but even then, the EV in the long run is the same so it has no effect on the simulation. PS the book of tells is useless, way to waste your money.

[UglyJimStudly 0]

sarcasm aside, though, this is assuming most poker players are terrible players.

Yeah, but I don't think that's an unreasonable assumption overall. You find specific situations where this is incorrect, but probably the majority of poker players aren't very good.

the simulation assumes you are playing in a game with 10 moderately skilled players. moderately skilled players to not make decisions on a whim, with the possible exceptions of decisions which they know are even money either way.

Perhaps, but OTOH I don't think the simulation was supposed to be representative of any real poker career, either. It's more an experiment that shows what sort of results those ten players can expect if they all play together, and the results show them why they shouldn't play together and why they also shouldn't be too surprised at having a bad week, month, or even occasionally year. In the real world, 10 poker pros will never sit down and play each other for a whole career (or even a non-tournament session), they'll leave some seats for the fish.

[justblaze 0]

sarcasm aside, though, this is assuming most poker players are terrible players.

Yeah, but I don't think that's an unreasonable assumption overall. You find specific situations where this is incorrect, but probably the majority of poker players aren't very good.

the simulation assumes you are playing in a game with 10 moderately skilled players. moderately skilled players to not make decisions on a whim, with the possible exceptions of decisions which they know are even money either way.

Perhaps, but OTOH I don't think the simulation was supposed to be representative of any real poker career, either. It's more an experiment that shows what sort of results those ten players can expect if they all play together, and the results show them why they shouldn't play together and why they also shouldn't be too surprised at having a bad week, month, or even occasionally year. In the real world, 10 poker pros will never sit down and play each other for a whole career (or even a non-tournament session), they'll leave some seats for the fish.

i think were agreeing with each other?

[TRYING2GTEVEN 0]

63% of statistics are made up on the spot :wink:

[Fira 0]

I believe that this wouldn't apply to no limit poker... one hand can mean your entire chipstack, and a bit of luck can mean a lot more than 1% of your winnings or losings. Am I correct?