There are two definitions of variance.  The first is the statistical definition of how far a set of numbers is from their mean.  For example, if you were a conservative player(tending to play less hands) winning $100 an hour playing poker, your variance would be lower than someone who was a more aggressive player (tending to play more hands and be involved in more pots).  The reason is that there are more opportunities for your stack to go up and down as you are involved in more pots.  The other definition of variance used in the poker world is the idea that all situations will even out in the end, so that being on the wrong end of a bad situation is just “variance,” or a statistical anomaly taking focus away from what is really important aka. your winrate.  So when you have KK and the other person has AA, you can usually chalk it up to “bad variance” meaning that it was unlucky and that if the situation was reversed, the outcome would be the same.

In theory, if your winrate was high enough and your variance low enough, you would never(or at least very, very rarely lose).  For example, if your standard deviation(the square root of variance) was $20 an hour, your winrate was $100 and your results were normally distributed, you would only lose when you had a result that was 5 standard deviations away from the mean(which is about 1 in 1.7 million).  The reality is no one has a high enough winrate and low enough variance to never lose(or come close to it)  and that results are not normally distributed.  I was one of the most successful players in midstakes no limit and my winrate was approximately 5.5 big blinds per hundred hands and my standard deviation was approximately 65 big blinds per hundred hands.  Although I frequently lost during an individual hour, I won approximately 70% of the days that I played and 100% of the weeks.

When I hear other players talking about going through a prolonged losing streak(aka a “downswing”) they are often focused on the second kind of variance, instead of the first kind.   They often fail to realize that the main culprit for their losing money is not having a high enough winrate(or too high a variance).  For example, if two players have the same standard deviation (the square root of variance), say $70 an hour, and one wins at $100 an hour and one wins at $30 an hour.  When they both experience a rough patch and are one standard deviation away from their results, the player winning at $30 per hour loses $40 an hour during this period and experiences a “downswing,” while the the player winning $100 wins only $30 an hour during this period.  However, they are both the same dollar amount and standard deviation from their true results!

Why should I care about all of these statistics and numbers you ask?  The answer is simple, poker is an emotional, thought driven game and results and emotions can affect the way you make decisions .  I assure you that the player who has undergone a “losing streak” takes it much harder mentally and emotionally than the player who is still winning, albeit at a lower rate.  If you feel like you have been losing and that the plays you have been making have not been working, you are less likely to make the optimal play when the opportunity arises.

It has been proven that losses hurt twice as much as wins thrill.  This idea is very important when comparing more conservative and aggressive playing styles.  As a looser player it is much tougher to maintain your winrate because when you are losing it is tougher to play your A game AND you are involved in more situations.  Not only does losing cause you to play your B or even C game, where your decision making is worse, as a looser player, you are now making more of those bad decisions.

When playing poker in person, you get the opportunity to observe people for large amounts of time and you can see there are many players(often of the loose aggressive variety) who do very well when winning, but who, when losing, play the same way despite the fact that their edge is no longer there.  For example, let’s say it is profitable to open T3s on the button when everyone has folded.  Doing so requires that you value bet 2nd pair well, fold when someone has a bigger flush, call at the right time with draws and a host of other things.  When a loose aggressive player is playing well and winning, he might be able to do all of these things and to turn a profit.  However when he is not playing well, playing this hand might get him into situations where his errors compound and he is no longer able to make all of the correct decisions necessary to make this hand profitable.  If he continues to lose, his winrate will drop, he will win less frequently and play less than his A game more frequently, all of which will contribute to less winning and more frustration.

There are many reasons that it might be beneficial to play tighter, but I believe that the most important one is the reduction of your variance.  Since many players do not have an adequate bankroll to play in the stakes they normally play, increasing variance and lowering their winrate increases the risk of ruin if they happen to encounter a run of bad variance.  This will prevent otherwise winning players from being able to play(and therefore win) assuming they could always play their A game, which is a near impossibility when they are losing and low on funds.  Playing more conservatively will allow you to play your A game longer, since you will be winning more instead of losing.  In addition, playing tighter has the huge benefit of helping you to avoid situations that are close that will tend to become unprofitable if you are not playing your A game.

The end result is that reducing your variance and keeping your winrate high has important additional benefits like keeping your mind sharp and being in the positive frame of mind that will allow you to win even more money.

Unfortunately for most amateurs, they do not use this strategy and amount to “doing what they feel” which makes it relatively easy for a professional to figure out why the amateur takes the actions he takes.  For example if an amateur checks a strong hand on the river when a flush card comes in, it is generally because he is worried about being beaten.  Thus, in the future, when a flush card comes in, a professional will deduce that it is much more likely that the amateur has a flush when he bets.  If the amateur threw a wrench into the professionals hand reading, for example, bluffing when the flush possibility was in spades, the professional would almost never figure it out and would be folding more often than he should.

This idea became clear to me when watching a hand played by an excellent live player who I will call Don.  The game was $5/10 no limit with $4000 effective stacks.  He raised preflop to $40 with 6d5d and was reraised by a bad amateur player to $150 which Don elected to call, knowing that the amateur almost surely had a big hand, either QQ, KK or AA.

The flop came Ts6c2d and the amateur bet $300(almost the size of the pot) after Don checked.  This almost certainly meant that the amateur had a big pair and Don knew it.  Don elected to checkraise to $800 hoping that the amateur wouldn’t want to put in so much money with his big pair, in addition to having a pair and a backdoor straight and flush draw in case he amateur called him.  The amateur elects to call.

The turn is a 7d, and Don elects to bet $1900.  Sitting at the table, I knew that Don just had one pair and was hoping the amateur would fold to this big bet.  The reason I knew this was because Don was a good player and almost certainly would have bet less if he wanted to be called, because that would make it more likely he would be, then make it more likely he would be called on the river.   For example, a much better bet sizing on the turn with about $3000 left would be $1200 on the turn and $1800 on the river and I knew that Don knew it.  So why would he bet so much unless he was trying to induce more folds from the amateur?  As it turned out, the amateur thought a long time, and eventually went allin with QQ and Don called, missed his flush draw and his two pair draw and lost.  I realized after that Don actually should have shoved the turn to induce the maximum amount of fold equity from the amateur.

Knowing that the Don would make the optimal play against an unknown opponent allowed me (and possibly his opponent) to decide that he did not have QQ beat and went allin instead of folding. In these situations professionals can be somewhat restrained by knowing what the optimal way to play the hand is and not wanting to veer too far away from that.  This leaves most of them playing relatively formulaic and makes it easier for good opponents to figure out what they are holding.   Adding a bit of randomness or doing things a bit oddly can make it much more difficult for your opponents to read your hand and can entirely change your image at the table.  So, randomly open to $100 on the button instead of $35 the first time your are on the button and the new dealer just sat and include whatever other randomness you can in your game.

Firstly, live play is usually significantly deeper than on the internet.  This means that the river bet is going to be more significant amount live and you often will have had to announce your strength to your opponents earlier in order to be betting that amount.  The combination of these two effects means that your opponent will more often fold when a lot of money goes into the pot.  While this was not always the way people reacted in the past, I believe it is the way that the games are trending.

Secondly, on the internet the pot size is right in front of you, whereas in live play, you must make an effort to count it.  This means that while people have a general idea of the pot size being small, medium or large, they don’t know it exactly and thus a 2/3 pot size bet to them means less than it would online.  In addition, live opponents (especially the poorer playing ones) are more influenced by the amount you bet (also being small, medium or large) then the amount relative to the pot.  So, if the pot is “big” to them you will be called with roughly the same range for anything they perceive to be “big” bet.

So how should this affect your strategy?  I think that when value betting, you should be betting the most your opponent will call and that in live poker, the amount is inelastic once it has become “big.”  When value betting against certain opponents, you will have to be content with not getting their entire stack.  For an extreme example, if your opponent will not call more than $500 on the turn or river, then you are often best off betting $500 on both streets, instead of trying to set him up for a 2/3 pot size bet on the river(which he won’t call if it is more than $500).

Also, I think that you can push your opponents off hands by betting amounts that push them out of their comfort zones.  For example, in a limped 4 way pot, if the flop comes 922 and I lead out from the big blind and get called by one player.  I check the turn 4 and he checks too.  I can make a “big” bet on the river and win the pot most of the time, since when my opponent does not bet the turn, he doesn’t have a “big” hand and thus won’t call a “big bet” with it.

I hope this stirred up some thoughts on bet sizing, and I would love to hear what others think about the differences between live and online.

My name is Jason Schlachter and I used to have the greatest job in the world until I was fired by the government 2 years ago.  I was an internet poker player.  Playing poker on the internet challenged me and pushed my limits.  Each day I woke up excited at the prospect of being the best I could be and through my hard work, I was one of the most successful internet players.  Not only was I successful in my job, but I took pride in the fact that I could provide for my family, and I loved the flexibility that allowed me to never miss spending time with them.  It has been 2 years since the government has prevented me, as well as my colleagues and other aficionados from playing poker on the internet.  Now, despite the fact that the law that was passed in 2006 making internet poker illegal has since been ruled NOT to apply to games of skill (like poker), and the proliferation of casinos everyplace in the US (including lottery and horse racing on the internet)the government continues to prevent internet poker sites from operating in the US and no longer allows me to pursue my chosen profession.

It took me a very long time to be able to admit to people that I played internet poker professionally, because some people did not understand the skill involved and therefore looked down on me, asked me when I was going to do something real with my life and called it gambling.  In reality, playing poker professionally is actually a bit like being a professional chess player and a bit like being a stock trader.  Like playing chess, it requires  thousands of hours of study to determine what the best moves are in different situations and when to use them.  You must be able to consider what your opponents are thinking and their thought processes as well as to remain in complete control of your emotions at all times.  As in stock trading, it is necessary to analyze situations in real time and to have the ability to make quick, calculated and rational decisions, often for a lot of money.  Despite what many people believe, it is in fact nothing like playing craps or the lottery.  You are competing against other players, not the casino, and your skill has a large effect on the outcome.  In fact, as someone who has played nearly 8 million hands in his lifetime, an amount which would take more than 300,000 hours in the casino, I can assure you, there is little gambling involved.

I began to take poker more seriously in 2003, when I was senior at the University of Pennsylvania.  I had played poker with friends on occasion and realized that there was a lot of skill and that I could get better by studying the mathematics of the game.  As a former runner and tennis player, I enjoyed the competition inherent in poker, was looking to improve and was willing to work at it.  I went to Atlantic City once or twice, but between taking 5 classes and writing my thesis, I did not have time to make the trip, so I decided to deposit a few dollars in an online poker site.  I began playing for pennies and soon I was trying to learn the best way to beat my online opponents too.  Often this required working out solutions away from the table and my geeky, math loving, solution based self loved it.  When I graduated, I moved back home and was looking for jobs during the day, and playing poker at night.  Before too long, I was making far more money playing poker then I could if I had gotten the jobs I was seeking, so I decided to continue.

In September of 2006, on the last day before Congress would break for the election, Bill Frist and John Kyl, two extremely conservative Republicans tacked on the Unlawful Internet Gaming Enforcement Act(UIGEA) to The SAFE Port Act.  This bill made it a crime to process payments to online poker sites according to the 1961 Wire Act.  Despite the fact that no one on the Senate-House Committee had seen the final language in the UIGEA, it did not matter, because it was attached to The SAFE Port Act, which had to pass.  After this bill was passed, the European Union and Antigua filed lawsuits and won damages against the United States as a result of this law violating free trade agreements.

In 2009, New York and Illinois requested clarification of the UIGEA from the Department of Justice(DOJ).  In April of 2011, the DOJ took action to shut down the sites that were still operating in the US, ignoring the request for clarification over whether operating a site was actually illegal.  It was not until December 2011 when the DOJ finally admitted that the 1961 Wire Act did not apply to poker, which made their attempts to close the internet poker market in 2006 and 2011 wrong.

In fact, before the UIGEA, the internet poker market in the US was operating well and in the open.  Since 2006, poker has moved into a grey market and players who want to play have been forced to deal with disreputable companies, delays in payment and even the possibility of not getting paid.  When the US government shut down the poker sites in 2011, the reputable site that I played on, paid me, as well as everyone else immediately, but the players on Full Tilt Poker and Absolute Poker were not so lucky.  The government has sold the company and has said that they will pay the players the money that is owed but to date has not done so and has shown no plans to.  This is very unfortunate for many people who needed these funds for living and working expenses, who were not only fired by the government, but have also had their money trapped by them.

Since 2011, I have been forced to travel to Atlantic City and Pennsylvania in order to support myself and my family.  Not only has my income been reduced substantially but my expenses have also risen. In addition, since I live in New York City, nearly a 2.5 hour drive from there, I cannot commute and must stay over and be away from my wife for extended periods of time.  While many of my colleagues opted to move out of the country to work playing internet poker, I did not feel as though this was a reasonable option for me.

The government has admitted that they have erred in this matter and have lost in the WTO regarding internet gambling.  I believe they are hypocrites for continuing to push the lottery, horse racing and for allowing casinos to be built everyplace, while denying people the ability to gamble in their own homes.  I am asking that the government finally do what is right and just and to restore internet poker to people who want to play.

Sincerely,

Jason Schlachter

It’s amazing how well players can play when they are playing well and winning versus how poorly they play when they are not.  I have a lot more to say on this in another, but for now, its off to work!

There is usually a fine line between costing yourself too much expected value in the present term in order to expand your range to gain yourself more expected value in the long term.  I see far too many players against whom it is difficult to narrow down their range, but because their range is so wide, solid play defeats them.  For example, if someone pushed all in every hand, they would be unreadable and their hand range would be wide, but it would be very easy to beat an opponent who plays like that.

Let me show you two examples where narrow hand ranges played a role in allowing me to win a pot I would not have ordinarily won.

Playing $5/$10 No limit with $2500 effective stacks.

There are 5 limpers and I call out of the small blind with 98o.  The flop comes Jh7s5s giving me an open ended straight draw.  I check, the big blind, who is a solid regular bets $50.  3 players call and I call as well.  The turn is the Tc.  I lead out $175 and the big blind makes it $675.  Everyone else folds and I am 100% sure that he has the straight here.  Because he is limited to only having the nut straight here (he wouldn’t raise 2 pair with so many people to act behind him, and wouldn’t bet the flop with 43 into so many people) we are currently splitting the pot.  However, I can make it look like I have something else so that if a scary card comes on the river, I can bet and hopefully win the pot.  Note how his limited range should allow me to play perfectly against him, while he has a more difficult time playing against me.

I elect to call and the best card comes on the river, the Js, bringing in the flush draw and pairing the board.  I elect to shove all in and he grumbles about it being the worst card for the straight and folds.  If he had a wider range then just the nuts on the turn(or if I thought he might have a wider range), then I would not have been able to play optimally against him and would have just shoved all in on the turn to with the hopes that he would call with a worse hand, or fold his equity in the pot.

Another example comes from pot limit omaha(in this game you MUST play 2 cards from your hand).  Effective stacks are $700.

There are 2 limpers and I complete the small blind with 8c7c7s6s. The flop comes Jc9d7d.  I bet $20 and only the big blind calls.  I have played with him a bunch and know that he will only put a lot of money in with the nuts and will not be tricky.

The turn is a 4c giving me a flush draw along with bottom set.  I bet $60 and the big blind calls.  My plan is to bet a river that does not pair the board or complete a flush just in case he has a bigger set.  Since I am representing T8 for the straight(and can easily have it), and I know he will never call the turn with the nuts or call the river without it, my bet is what I call a freeroll.  I am rarely beat by a better hand, but just in case I am, I will win the pot anyways.

The river is the 2s, completing no draws.  I bet the pot and the villain throws up his hands in disgust, shows me JJQT which had me in very bad shape, and folds it.  If my opponent was tricky in this situation and could have just called with the nuts on the turn so that HE could win the pot if the board changed, then I would have had a lot more concern about betting the river(and the turn too).  In this case, my opponents straightforward play caused him to lose a pot that another opponent might have won.