Poker: Luck vs Skill

For as long as I've been playing poker, I've obviously been on the side of the game being skill based. However, after thinking about it over the past week, I think it's much more cut and dried than simply being based on skill or being majority skill. It's 100% skill. Exactly like chess. There is no luck involved. Here's why:

You'll often find poker players that try to attribute arbitrary ratios of skill and luck to games as if they are on the same gradient scale. Poker being 70/30 for example, blackjack being 40/60 etc.

• Luck: Success or failure apparently brought by chance rather than through one's own actions.
• Skill: The ability to do something well; expertise.

People will generally try to play semantic gymnastics in trying to quantify a balance of opposing definitions. I find it to be a contradiction of each definition for something to involve both skill and luck, especially when the "luck" disappears in large samples. Perhaps a more apt definition would be the term "chance" already used in the definition of luck.

• Chance: by accident or without design.

We've all heard the term "games of chance" and are quick to rightly interchange it with the term "luck." When it comes to games seemingly involving both, this term clearly does not allow for that to happen. In games of skill, every action you and your opponents make has a direct effect on everyone's expected value.

In games of chance, no action that you or your opponent can make has any effect on anyone's expected value. Skill and chance can not occupy a gradient balance with one another.In theory then, every single decision at the poker table is 100% skill based. In theory, there is only EV, there are no results. Now you're probably thinking "a ha! It doesn't work that way in practice!" and you'd be correct. In practice, our results deviate from our expected value. That deviation is called "variance."

• Variance: The fact or quality of being different, divergent, or inconsistent.

Variance is not luck.

The terms are, by definition, not interchangeable. Variance is simply the measured, quantifiable difference between EV and results. It has nothing to do with your ability or inability to affect the outcome. You shove $100 with AA and get called by KK for 80% equity and an EV of about $60. You are either going to be +$40 or -$60 on expectation for any given hand due to not luck, but rather variance. 

• Poker is 100% skill with variance in the results.

Now take the opposite type of game, lets say slots. You put $1 in and pull the lever, with absolutely no skill on your part affecting the outcome. Your EV on any given pull is -$0.05 on this particular machine. You are most definitely not going to receive exactly $0.95 back on your dollar with every pull. The difference from your EV is, again, variance. 

• Slots are 100% luck with variance in the results.

Therefore, all things where a calculable EV is available are either all skill or all luck with a measurable amount of deviation that can be used to statistically compute how much fortune appears to play a part.

• Fortune: Chance or luck as an external, arbitrary force.

Fortune is the word and concept people are looking for when they are trying to mistakenly apply a luck:skill ratio by virtue of interchanging false definitions of luck and variance in a game of skill that has deviation in the results.

The idea of fortune is the mirage that keeps recreational players entertained despite their inevitable losses. Which brings us full circle to a point where poker is indeed 100% skill, with the veneer of luck, ie. fortune, entering the equation and creating a non-existent luck:skill ratio draped over the game due to the psychological effects of variance.

February Review

February continued to work out very well for me. I'm not entirely sure anymore if it was just the super soft site I was/am playing on or something I changed in my game while simultaneously switching sites. I've put in some hours at Stars and FTP again when my fishy Euro site was down or low on traffic without any difference in winrate.

Granted I've played all of 54k hands this year due to 6 tabling the Euro site for most of it, so it's not much of a sample for winrate, but I may just start putting some more hours and hands in for FTP Rush so we'll see how it pans out. I'm definitely liking how fast I can jump back up the FTP rakeback ladder so quickly. With a few inexpensive mods, I've found I really don't mind the software at all.

Back to results, I find myself being much more appropriately aggressive after putting in some fundamental work on the math behind my actions and my opponents' ranges. For the past 2 months I've felt like I've been "in the zone" when it comes to making good decisions and hand reading like a fiend.

I've had moments of clarity like that in the past, but they'd always been fleeting, eventually leading me back to my breakeven play style. Two weeks here, three days there. I don't know if this will continue, but every few days I find myself thinking back to that basic off the table study I did at the beginning of January, sometimes running scenarios through my spreadsheets, and it continues to work for me. I think I'm a much tougher opponent to play against for it.

What I'm definitely most proud of so far this year is my play from the blinds. It's easy to win on the button, but I think the loss rate from the blinds really shows who feels on top of their hand reading game. Having loss rates of -2 in the SB and -26 in the BB is a huge factor in my overall winrate so far. I have historically run at about -20 and -45, respectively.

It's taken me a very long time and I've done similar work before, but I'm finally fully accepting that the math does not lie, no matter how counter-intuitive it may be at times. For me, the battle between ego and theoretical strategy is a big one at the table. I need to keep that in check. All of your study amounts to nothing if you're going to be making spite calls and spewy shoves.

March has started where February left off. I'm going to have a conservative goal of 40k hands. The game plan for site selection is going to be FTP/Stars and primarily Rush/Zoom due to the increased traffic while my winrate sustains.

Jan.  34 buyins |  16k hands   |    21 bb/100*
Feb.  44 buyins |  32k hands   |   14 bb/100
* modified from last review, forgot to include Stars results.

HH Review: Min 3-Bet Pot Mistake

February continues to go fairly well after 18k hands. I had a mini implosion weekend before last and ended up trying to force a lot of plays that were just not going to work and getting crushed by weird 2 pair after weird backdoor gutshot. That was an 18 buyin downswing over 4k hands. I've since recovered that and then some. I'm sitting at an overall winrate of 17.5 bb/100 on the month,  a third of that small stakes and the rest micros.

Something I never did on Stars was mix stakes. I just found it too confusing. With the lack of traffic on my new site, I'm finding it's much better for my winrate if I do mix in three or even four stakes for the highest fish ratio. It's interesting how I've started thinking more in terms of SPR than in $ or even in bb.

HAND HISTORY

Villain in this hand is 32/14 with a 6% 3bet over 180 hands. All of his 3bets have been from the blinds.

$0.10/$0.25 No Limit Hold'em - 5 players

BTN: $15.66
Hero (SB): $25.16
BB: $15.16
UTG: $40.07
CO: $20.30

Pre Flop: ($0.35) Hero is SB with 7 J
3 folds, Hero raises to $0.50, BB raises to $1.10, Hero calls $0.60

My min-steal is a bit marginal with J7o as he's a bit more aggressive than average postflop, but he does fold to 50% of flop cbets and 40% on the turn. He's also shown himself to be a bit spazzy a significant portion of the time. I spite call the near min-raise, but I think the math generally has me covered at potentially $16 profit for a $0.60 call giving me 27:1 stack odds. I'm going to hit 2 pair or better about 6% of the time and draws add a few points as well.

Flop: ($2.55) 7 7 4 (2 players)
Hero checks, BB bets $1.65, Hero raises to $3.90, BB raises to $6.15, Hero raises to $17.85, BB folds

Jackpot flop. My concern now is how to best get my money in. He's a bit fishy so 6% is probably going to be top heavy with a range like 88+, AQ+. That means I have 95% equity trying to dodge the fullhouse spike. 55% of his range is overpairs, 45% is Ace high.

I was torn between getting all the money in on the flop fearing that calling could bring an action killing overcard like an Ace or King and would shut down 88-JJ. But at the same time, I'd prefer to let him spazz or hit with his Ace high hands. I picked a size slightly larger than a min-raise to give him room to play back with $12+ effective and an $8 pot to get me to fold a hand like 33 or 55 with his unpaired hands, with his overpairs obviously raising as well.

Once he clicks it back, he has almost $8 left. He has 71 combos, so lets break down each group of hands in his range:

• 88-JJ (21): These likely shut down if an Ace or King hits the turn. They maybe shut down half the time if a Queen hits. Given that weighting and the likelihood of those cards hitting, I miss $8 on 20% of turn cards. There is a small chance he checks back a hand like 88 or 99, so lets say a conservative 25% when an Ace rolls off by the river.
• QQ-AA (18): These will probably not shut down at all given a $15 pot with $8 left.
• AQ-AK (32): These will generally fold to the flop shove. I'd say there's a 20% chance he spazzes out with them if checked to on the turn. He's going to hit a pair and stack off 24% of the time by either hitting the turn and shoving or checking back and hitting the river.

So my dilemma then is making the correct decision between:

• Winning $8 that I would not have won 25% of the time x 30% of range (88-JJ). EV difference = +$0.60.
• Winning $8 that I would not have won 38% of the time x 45% of range (AQ-AK). EV difference = +$1.37.

Clearly then, shoving the flop is a mistake.

HH Review: Folding Out Equity

As promised, I'd like to review an interesting hand every week or two. This was one of the more interesting hands of today. Note that I'm using Flopzilla to compute hand range values and weightings.

STATS:

• UTG:  44/27 - cbetting every hand and barreling a good deal, too. Not positionally aware at all and raising 45% of unopened pots.
• CO: 24/18 - likes to cold call a ton to nut peddle post-flop, folds to most cbets.
• Hero (BB): 30/25 and running hot on this table - raising cbets 25% and calling cbets 30%.

$0.50/$1 No Limit Hold'em - 6 players

UTG: $101.50
MP: $127.52
CO: $172.08
BTN: $187.20
SB: $46.69
Hero (BB): $333.37

Pre Flop: ($1.50) Hero is BB with 9 T
UTG raises to $2.62, 1 fold, CO calls $2.62, 2 folds, Hero calls $1.62

Not an ideal hand to call out of position, I'd have a lot more postflop playability if it was suited. However I am getting 4.2:1 and UTG flops a lot of nothing. My plan is to let him hang himself if I hit and steal it when I miss given that CO doesn't get too involved past most flops.

Flop: ($8.36) 6 T Q (3 players)
Hero checks, UTG bets $6.27, CO folds, Hero raises to $24.17, UTG calls $17.90

I flop 2nd pair. The plan is to check/raise if CO folds to the auto-cbet and check/fold if CO continues. The reason I want to go for a raise here is because there are tons of hands that I am currently ahead of that have equity and I either want them to fold or get value from them. These would include hands like AK, AJ, KJ, J9, 98, 87, 99, 88 and 77. Only 15% of his range consists of top pair or better, while 28% consists of Ace-High and 30% of pure nothing.

Either having villain fold or call with worse is fine with me given my mid strength hand that can't stand much heat on most turn cards without initiative, which means my options are to either give up now or try to steal like in my preflop plan. I also have a few backdoor straight draws as backup for future aggression opportunities.

Flopzilla tells me that I have 62% equity against his cbet range and 35% equity against his continuance range. I'm expecting a fold about 65% of the time. My Excel equity calculator tells me with 35% equity, I need a fold only 14% of the time to breakeven.

This is precisely the scenario that Baluga Whale talks about in the newest edition of Easy Game where he kills off collection of dead money as a reason to bet, simply combining it with a new definition of bluffing where getting your opponent to incorrectly fold their equity and/or preventing them from making the bluff they should make go hand in hand. ie. Fundamental Theorem of Poker: if he knew I had 2nd pair, he would shove his entire range and therefore he makes the mistake of not re-bluffing.

Turn: ($56.70) 9 (2 players)
Hero bets $306.58, UTG calls $74.71 all in

At this point his range consists of 40% top pair or overpairs which I now beat, and 25% 2pair or better that beat me. The remaining 35% consists of draws. I have 57% equity against this range, so while I am ahead 75% of the time, it's by a slim margin. I'm flipping with his range if he folds all of his draws.

Given the amount of money in the pot compensating for my thinness in equity, folding is not an option. My choices are to either bet/call and pray for a blank river if he just calls, or shove right now.

I'd prefer not to flip for it if possible if he decides to shove over a smaller bet or call and show me one of 20 gross river cards. Therefore I'm using the same reason for overbet shoving here as I did for raising on the flop in trying to get him to fold significant chunks of equity rather than giving him the opportunity to try to bluff or thin valuetown himself with that equity.

River: ($206.12) Q (2 players - 1 is all in)

Final Pot: $206.12
UTG shows J 9
Hero shows 9 T
Hero wins $203.12

January Review

I'd like to do monthly reviews this year to try to boost my content on this blog back up a little bit. I'm hoping I can possibly do a few Hand History reviews throughout the month as well.

I think some of my lack of strategy and results posting had to do with playing on Stars and some of the regs knowing who I was. However, about a week ago I decided to try out a new site given how tough and reg infested the games are on Stars and my lack of volume for a decent rakeback percentage between Stars or FTP. Not that my new site's rakeback is anything decent either, but I just want to go back to the days of soft games and steamrolling people -- although this time instead of being the standard nut-peddler, I'm quite enjoying valuebetting light at every turn.

The biggest issue I've found with most other sites has been having terrible software and customer support. I've since realized that "terrible software" to me means cards that are not easy on the eyes and unworkable button layouts. If I can't lean back in my chair and enjoy myself rather than get a headache from squinting at my cards and figuring out which buttons are which on a 24" monitor, you have bad software.

The site I'm on now (and no I won't reveal it for the sake of what I stated above) has a great waffle style deck and decent layout, along with the action being easy to follow. I typically played on Stars with Table Ninja with my sound muted, but I have found adding sound to sites with less than stellar software helps a lot for following action.

Without further ado...

JANUARY RESULTS

Yes this is a brag. Yes this is only 7500 hands. Yes that is 30 buyins. And yes that comes out to 40 bb/100.

I have actually put in a lot more hourly volume than I was on Stars, but I am only playing 4-6 tables for about 450 hands/hour on an 6max MT-ratio of 4.2 given the reduced traffic on this site. I think that's mostly to do with having this huge amount of confidence that every time I sit down, I feel like a 15 bb/100 session is running bad.

I'll keep this running monthly tally in big blinds rather than dollars as per usual. It is all about the decisions and learning after all. I'll be pretty happy with 25k-30k hands per month at this rate.

Jan. - Micros | 34 buyins | 8200 hands | 41 bb/100

Guess Who? Beginnger Strategy Analysis

My daughter has recently taken a liking to hauling out all of my old board games. The favourite so far is Guess Who? Due to my consistently being demolished the majority of the time and having victory snatched away from me with one remaining piece by 1/8 Hail Mary chances many more than 1 out of 8 times, I decided to look at the numbers to try to gain an edge.

I'm choosing to ignore all of the potential meta-game, question combining and deceptive game play strategies available. She is not yet 5 years old after all. But I thought there must be some statistical edge to gain through the simple, common questions.

The Setup

• 24 Characters.
• 9 Common traits: Bald, Bearded, Eye Colour, Gender, Glasses, Hair Colour ,Hats, Moustachioed, and Nose Size.
• Traits are split relatively evenly at 19:5: 5 with glasses, 19 without glasses, 5 females, 19 males, 5 with large noses, 19 with small noses.
• There are two exceptions: Only 4 bearded characters and 4 with brown hair.
• Traits are split unevenly between characters, ranging from 1 to 4 uncommon traits each.
• Each player chooses one character at random out of a deck of cards.
• *Note I am also ignoring the fact that, according to 4 year olds "Oh, I/you already had this one! That's silly! [draws a new card]." Also, some hair is distinctly yellow, not blonde.
• The game proceeds by a process of elimination.

The result of inputting all of this data into a spreadsheet cross-referenced by character quickly shows that there is a sum of 63 uncommon traits among the group: (5 each among 7 of the non-hair groups (35), 4 of one (4), 4 hair colours of 5 each (20) and one hair colour of 4(4). Thus we can already determine that the first guess (assuming we always get a 'no') will yield 5 eliminations for every guess except questions about beards and brown hair which will result in 4 eliminations.

Keep in mind that your character will skew the results, essentially acting as blockers. Therefore we should avoid guessing character traits that our character possesses. For example, if our character has black hair and we ask if our opponent has black hair, we are only eliminating 4 characters in practice (again, ignoring the meta-game of optimal elimination vs bluffing strategies employed by experienced players).

However -- and this is where the true genius of Milton Bradley's board game creation ability shines by balancing luck and skill -- there are small, yet distinct statistical advantages to gain in the combination of your first two guesses.

Top 10 Ranked Questions:

Worst 10 Ranked Questions:

It becomes immediately obvious that it's not a good idea to ask first questions about beards or brown hair or the traits our character has blocked as they are all under represented, as well as second questions where the first eliminated some of those traits already, such as gender and hats, as a 'no' to female already eliminates two hats (Maria and Claire).

For the sake of being meticulous, lets look at an in practice example. You draw George with uncommon traits of white hair and a hat. Theoretically, if all cards were in the deck, asking about hats and white hair would yield a 24/9 result. However, in practice you have already eliminated 2 traits and 1 character from the group as blockers and have a true result of 22/8. This makes asking other 24/9 questions such as glasses and black hair superior to the question involving traits you own. Likewise, this drops starting questions about baldness and hats off the top of the starting list.

Understanding the best starting questions is a little more difficult as it's hard to know at a glance which combination of traits applies to the largest group of characters, especially as the game progresses into the 3rd and 4th turns. Therefore the best thought process seems to be thinking through and eliminating your worst options while memorizing the top five or ten theoretical guesses until you have a better understanding of the top starting guesses versus your character blockers.

I'm hoping this analysis will give me and all of the readers out there with unscrupulous pre-school opponents the edge we need to win. Good luck.

My take on the gun control debate

I infrequently dive into the political spectrum, and I know a lot of Americans still read my blog when I do post. Given this debate is so extreme and has even taken over the national news in Canada, I thought I'd offer up my thoughts.

In the latter half of last year, with the increased mass violence in the US, especially with the Sandy Hook shooting, I found myself thinking more and more "What the hell is going on down there?"

Since then, and despite being fed copious amounts of gun control debate, I've come to a conclusion. And surprisingly, my conclusion doesn't let me pick one side of the fence or the other.

That's because this entire debate is absolutely pointless.

As of right now, the debate is focusing on mass shootings and assault weapons and 100 round clips as a direct, knee jerk result of the spike in rampages in 2012. This is expected as the media and politicians thrive on shock value. Despite the tragedy that they are, preventing mass murders is nothing more than a drop in the bucket.

With 14,000 homicides annually and 10 - 12,000 of those estimated to be gun related, you could have a 30 victim rampage every month and it would only amount to 2.5% of all murders. If you could then wave a magic wand and remove every last assault weapon and all 30+ round clips from the country and prevent 100% of mass shootings, you would still have 13,640 people dead by the end of the year. And there isn't even a rampage every month now. Dollar for dollar, you're by far better off ignoring the mass shooting problem and throwing tens if not hundreds of millions of dollars more at trying to prevent drunk driving and diabetes.

The narrative in the US is way off mark. 14,000 homicides per year is 38 people violently killed every single day. That's the equivalent of 3 Aurora incidents. Every day. But everyday news doesn't make the news. The narrative would be on the right track if the major news networks had a "Homicides Today: ___" ticker fed by affiliate updates running in the bottom corner of the screen 24 hours per day.

There's something very wrong when a Western, developed nation is a huge outlier at 3-4 times the homicide rate of other Western, developed nations. I'm not entirely convinced it's the guns alone. There are stark socio-economic differences between the US and Europe that may cause this statistical rift, but Canada should be a much closer comparison by a significant degree:

• 80%+ of Canadians live within a few hundred miles of the American border.
• We consume massive amounts of American media.
• I assume obtaining guns illegally isn't that much more difficult for people that want to commit crimes.
• Even with the recent increase in minimum sentences for violent crime, we have extremely lax punishment for all types of felonies compared to the US.

So we're basically America-light of the North without the big prison stick, yet have a homicide rate 1/3 that of the United States. Granted, US rates have dropped by 50% since the ludicrously high rates in the 70s, 80s and 90s. There are only three obvious, significant differences I can think of between our countries:

• Adequate access to mental healthcare.
• A ridiculous difference in the number of legal guns.
• The 2nd Amendment.

There may be some additional cultural factors that come into play that I can't really speak to living on the outside. Perpetually being at war, the alleged gun culture, the laughable "video games / music made me do it" arguments... I find there's a big missing link between any of those or other social dynamics and the willingness to actually pull the trigger on someone. I also think the US Constitution is one of the best social contracts ever written, and would never want changes made to it lightly or as the result of knee jerk, emotional responses if I were American.

But as long as everyone's focused on this smallest, niche part of the overall problem instead of honestly figuring out what that missing link is between factor and action, Americans are never going to solve this issue.