Luck vs. Skill test...

[jackaaron]

Heads up match. 1.00 blinds. Million dollar stacks. Limit Hold ‘Em. No blind increases. Before I name the participants, assume that each player has equal endurance to play the entire match, and they take breaks to eat, use the restroom, etc. Both players also have the required number of days to play the entire match available to them, and on and on.

The players:

Phil Ivey

Brand new Limit Hold’em player (BNLHP) who's just been introduced to the game. He knows what beats what, and can read the board quite well. He’s aware of what constitutes a good hand, and what constitutes garbage.

Barring freak things like one of these players having a stroke during the match, I feel that you could 100% guarantee that Phil Ivey would win this match. Even though it’s only one HU match.

Do you agree? To the 100% guarantee part that is. And, if you agree, do you feel that this shows that skill dominates in this game (versus luck)?

Many times in the past, it seems that we’ve felt unsure about whether the best player could beat an average Joe in one HU match (i.e. we thought they'd mostly win, but felt that the Joe could win a few here and there). But, I think we were setting up the HU match wrong. The thing is, if someone contends that it’s just luck (or mostly luck), then it doesn’t matter how big the stacks are, nor how big the blinds are.

[Artsemis]

100%

No

[drunkencowboy]

Heres a MUCH MORE INTERESTING QUESTION.

If Phil Ivey's opponent MOVES ALL IN EVERY HAND. WHAT ARE THE ODDS HE WILL WIN THE SAME MATCHUP DeScrIbed ABOve?

[trying2learn]

Heres a MUCH MORE INTERESTING QUESTION.

If Phil Ivey's opponent MOVES ALL IN EVERY HAND. WHAT ARE THE ODDS HE WILL WIN THE SAME MATCHUP DeScrIbed ABOve?

first of all, the guy said it was limit hold em.

second, i still don't think you could 100% an ivey win. it's quite close to a sure thing, but not 100%.

[jackaaron]

It's limit hold 'em, and Ivey has a million blinds. (So does the other guy.)

[drunkencowboy]

oh when i read phil ivey i immediately assumed limit..

phil ivey isnt even that good at limit holdem...

how in the hell could anyone say he is a 100% favorite. have you lost your mind?

[Rupert]

I expect it would be very close to 100% (as in >99.99)

[magicratx]

Heres a MUCH MORE INTERESTING QUESTION.

If Phil Ivey's opponent MOVES ALL IN EVERY HAND. WHAT ARE THE ODDS HE WILL WIN THE SAME MATCHUP DeScrIbed ABOve?

I think Chris ferguson says its the novice will win 40% of teh time but thats probably assuming only 50/100 BB each

[atrainpsu]

The stack sizes would be 500,000 big bets, which would likely take over a million hands, which is clearly the long run. Against a great limit holdem player (I'm not sure Ivey is a great one), I think our newbie would have maybe a .1% chance of winning.
There is no way, the number is exactly 0% because it is possible (although infinitely small) that our newbie has the best hand almost every hand.
Also after 50-100K hands, our newbie may have grasped enough of the game to be at the level of someone like ourselves and would therefore be less of a dog.

If this headsup match was played many times, and the top pro won over 99% of them, then you could prove to a mathematically educated person that this game is a skill game, however there would still be people that don't understand and just think the pro is really lucky.

[jogger08152]

Heres a MUCH MORE INTERESTING QUESTION.

If Phil Ivey's opponent MOVES ALL IN EVERY HAND. WHAT ARE THE ODDS HE WILL WIN THE SAME MATCHUP DeScrIbed ABOve?

I don't know, but I bet they're almost exactly the same as the odds that AA holds up against whatever the new player has when Ivey finally calls. If you want an arbitrary guess, I'll go with 85.204%.

Edit: the above assumes that by "he" you meant "Phil Ivey". IE, what are the chances Ivey wins. If you want the opponent's chances, they're about the inverse.

[pete fabrizio]

The stack sizes would be 500,000 big bets, which would likely take over a million hands, which is clearly the long run. Against a great limit holdem player (I'm not sure Ivey is a great one), I think our newbie would have maybe a .1% chance of winning.
There is no way, the number is exactly 0% because it is possible (although infinitely small) that our newbie has the best hand almost every hand.
Also after 50-100K hands, our newbie may have grasped enough of the game to be at the level of someone like ourselves and would therefore be less of a dog.

If this headsup match was played many times, and the top pro won over 99% of them, then you could prove to a mathematically educated person that this game is a skill game, however there would still be people that don't understand and just think the pro is really lucky.

.1% is way way way way overestimating the novices chances of going on a **500,000** BB heater against a superior opponent. That would be about right if the person got supernaturally lucky and won the first $999,000. Assume Ivey has a 1BB/hr winrate and a standard deviation of 10BB/hr. His risk of ruin would be ((1-($2/$20))/(1+(2/20)))^(1000000/20), or about 3.09*10^-4358 (a decimal point followed by 4000+ zeroes and then a 3). Or for comparison, it's about the same likelihood of picking a random hydrogen atom out of the universe. And then randomly picking it again. And again. And again. Fifty times. So yeah, I'd pretty much say it is zero.

[jogger08152]

Can I be the rake?

[fraac]

Would be close to 50/50 against anyone of a similar character to Ivey. Ivey's poker knowledge goes out the window.

[jackaaron]

.1% is way way way way overestimating the novices chances of going on a **500,000** BB heater against a superior opponent. That would be about right if the person got supernaturally lucky and won the first $999,000. Assume Ivey has a 1BB/hr winrate and a standard deviation of 10BB/hr. His risk of ruin would be ((1-($2/$20))/(1+(2/20)))^(1000000/20), or about 3.09*10^-4358 (a decimal point followed by 4000+ zeroes and then a 3). Or for comparison, it's about the same likelihood of picking a random hydrogen atom out of the universe. And then randomly picking it again. And again. And again. Fifty times. So yeah, I'd pretty much say it is zero.

Thanks for this analysis sir. Somehow, a few of the posts have gotten off track, talking about NLHE for example, and not thinking just how many blinds each player has in my example.

I realize no one wants to say Ivey is 100% guaranteed, but it is my opinion that he is in this situation, much the same way that Dwayne Wade would dominate me in heads up basketball (actually Ivey would probably dominate his opponent even more because I'd ever so often make some of my half court shots )

[fraac]

You're all barking mad. The game as specified is pure psychology and memory, not all round poker skills. Ivey may be in the top 1% of natural game players, meaning thousands are as good as him and many will be better. Specially trained memory-men, mentalists and such would be strong favourites.