Poker bankroll management, building and strategy – online poker guide

Multi-Table or Move Up?

Thursday, April 9th, 2009 | Poker Articles, Poker Bankroll Building, Poker Strategy | 12 Comments

Submitted by Jerry, this article belongs to the Poker Bankroll Building series.

One huge advantage online poker has over live poker, aside from the valuable poker bonuses, is that online poker rooms allow you to play on more than one table at once, also known as multi-tabling.  Multi-tabling, for all intents and purposes, is why so many poker players are able to make a living playing online.  

Players typically begin multi-tabling after they have been beating their usual game for a while and want to embark on a quest to increase their win rates.  Some players who have beaten the games at one level, however, decide to just move up a level and continue playing a single table.  Why would someone multi-table to make more money rather than just move up, you ask?  After all, it seems like it would be harder to concentrate on more than one game, right?  

More Money, Less Stress

It is perfectly logical to think that if you are beating the games at a certain limit then it makes sense to move on up and start making more money at a higher limit.  For many players, this makes sense and works out great, even if there are some growing pains that come from moving up.  But with higher stakes comes greater variance – winning sessions pad your bankroll more than before and losing sessions shrink it faster.  

Therefore, the way to achieve a similar hourly win rate at lower stakes as you could at higher stakes games (let’s assume you would be a winning player if you moved up), while keeping the swings at tolerable levels is to play multiple tables.

I know I am about to oversimplify things, but, frankly, I don’t particularly feel like diving into much more than “Are You Smarter than a Fifth Grader” math right now.  Say you make five dollars per hour playing one table at your usual stakes.  If you move up to the next level, you feel that you could make ten dollars an hour.  Or, you could add another table of your usual stakes and now make five dollars an hour twice.  Add another, and you’re at fifteen dollars per hour total.  Magic!  Of course, your profitability will likely take a hit as you add tables (more difficult to process information and play optimally), so that hourly rate won’t be quite five dollars at each table, but if you play three or four tables simultaneously, chances are you can make more money per hour than you could at one table at higher stakes.  As an added bonus, your variance will not increase.  In fact, it may actually decrease, as you can offset a poor session at one table with a good session at another.

Plus, even if you feel you can make a profit if you move up, you may simply be more comfortable staying where you are.  And there is nothing wrong with that.  Poker is still a game, even if you can make a living playing it, so you might as well enjoy what you are doing.
 

Fringe Benefits

Another benefit to multi-tabling instead of moving up is the increased rakeback that you can earn.  Regardless of how well you do on any given day, rakeback will provide you with a relatively predictable stream of income.  If you play more than one table at a time, you have more than one income stream.  Again, going extremely basic on the math, if we assume that the pots, and thus the rake per hand, will double if you move up one level (obviously, we can’t assume this, but please humor me), you will earn the same rakeback at two tables of your usual level as you would at one table of a higher level.  Throw in a couple more tables, and now your rakeback is doubled.  This will help lower your variance even more, as your rakeback income can make up for a bad session.

One additional advantage to multi-tabling is that if you use poker analysis software, such as PokerTracker, you will be able to gather more data than you would be able to at a single table.  The more data you have on yourself and your opponents, the more accurate analyses you can make on your game and theirs.

Make it Interesting

For many players, playing one table is simply boring.  At least when you play live, you can talk to your table mates in between folds.  Online, you are just staring at a screen, twiddling your thumbs.  Sure, you can surf the internet, watch television, or do your taxes, but if you have that much time to concentrate on those things, you might as well not even play poker, since it sounds like it isn’t too exciting. Multi-tabling allows players to always be involved in a hand, to always have a decision to make.  It’s just more interesting for many people.  Besides, what better way to put your huge LCD monitor through its paces?

Remember, the more tables you play at once, the less you will be able to concentrate on a single game.  You won’t have as much time to process information and will have a harder time coming up with tricky plays.  You will need to constantly evaluate how multi-tabling affects your game and determine when adding another table hurts your win rate too much.  If you have to, move down a level when trying multi-tabling for the first time in order to acclimate yourself to your new way of playing.  Whatever you do, make sure you find the right balance between fun and profitability.

You could be posting your articles on the Poker Bankroll Blog. Read all about it here.

Tags: Poker Articles, Poker Bankroll Building, Poker Strategy

Online poker tournament statistics : probability of winning a poker tournament

Tuesday, April 7th, 2009 | Poker Articles, Poker Mathematics, Poker Tournament | 12 Comments

This article is a part of the Poker Mathematics series.

Recently I have wondered if it is possible to calculate the probability of winning a poker tournament based on which strategy you use and how your all in moves are distributed. In this article I will share with you my findings. Hope you have the patience to read it all the way through:-). The table below (the culmination of way too many hours of research) is a teaser of what is ahead if you continue reading.

Check out the previous post in this series:

• Online poker tournament statistics: player exit percentage
• Online poker tournament statistics: cummulative blinds

Just to remind you, in my first post in this series I discovered an exponential relationship between the time an online freezeout tournament has been running and the percentage of players exited from the tournament. This enabled me to estimate both the time needed to reach the final table of a tournament given the number of players registered and what size tournament you should choose given the time you have available to play.

I needed this relationship to be able to estimate the number of players entering a tournament of a given duration and thus the total amount of chips in play. Once I know the total amount of chips in play is known, I can calculate the number of successive all in wins needed to win all the chips in the tournament. Finally, the last step in my calculations will  be to set up different all in probability distributions to end up with the probability of winning an online poker tournament. Confused? Don’t worry:-) I will guide you through my calculations step by step in the remainder of this article. If you don’t like math, simply scroll down to the final table where I summarize my most important findings.

The table below summarizes the total amount of chips in play for different tournament durations and the successive all ins you will need to win to win the tournament:

Again, in order to keep things simple I assumed that each all in would double the  1500 chip starting stack. According to this assumption, 2 successive all in wins will increase your stack from 1500 to 6000, 3 successive all inn wins from 1500 to 12000 and so on.

To make things a bit more realistic, let’s assume that you win half the chips you need to win the tournament by making your opponent fold (i.e no show down). In this case the number of  successive all ins needed to win is reduced by 1 for each of the tournament durations shown above.

I have chosen the following scenarios that IMO cover the typical all in situations you will experience during a tournament.

The simple reference calculation

Setting probability calculations aside and assuming all the players in the tournament (including yourself) have an equal chance of winning it, you will win a tournament with x registered players 1 out of x times. This means you will win a 100 player tournament 1 out of 100 times, a 200 player tournament 1 out of 200 times and so on. Obviously you should aim higher than this otherwise your bankroll will hit zero in no time.

1st scenario: On a roll

• You have an 80% probability of winning all your hands.
• If for example you need to win 3 successive all ins to win the tournament, the probability of winning it is 0,8*0,8*0,8 = 0,5 corresponding to 1 out of 2 tournaments.

2nd scenario: Coinflip

• You have a 50% probability of winning all your hands.

3rd scenario: Underdog

• You have a 30% probability of winning all your hands.

4th scenario: Realistic?

• 20% of your hands you are underdog (30% probability)
• 40% of your hands you have a coinflip (50% probability)
• 40% of your hands you are favorite (80% probability)

The table below summarizes the probability calculations for the 4 scenarios:

Interestingly, it turns out that in all but one scenario (the underdog) your tournament win rate is significantly larger than the simple reference calculation. In conclusion I think I have successfully managed to give a qualified estimate of the probabilities of winning online poker tournament. In my next article I will try to make some use of the numbers I have come up with. An obvious approach would be to calculate the expected return on investment (ROI) for each of the scenarios listed above.

I would greatly appreciate any comments on the math and final numbers.

You could be posting your articles on the Poker Bankroll Blog. Read all about it here.

Tags: Poker Articles, Poker Mathematics, Poker Tournament

Are You Truly Putting Your Opponent on a Hand?

Saturday, April 4th, 2009 | Poker Articles, Poker Strategy | 3 Comments

Submitted by Vic Porcelli, this article belongs to the Poker Strategy series.

We’ve all watched the great Daniel Negreanu call out an opponent’s hand.  Let’s go back to the 2008 World Series of Poker Main Event.  Daniel starts the hand with a 7-4 spades in position.  (A typical starting hand for him)  His opponent, Matt Traudt holds a K-9 clubs.  The flop comes 8 hearts-7 diamonds- 6 diamonds.  Both players check the flop.  The turn is the 10 spades.  That gives Traudt the straight.  Traudt checks.  Daniel bets 4,000 chips.  Traudt check raises all in.  Daniel immediately says.  “I had you on the flop.  You got me on the turn. That card there, (he points to the 10 spades)  that changed the leader.   You had some kind of nine right?  King nine?  Daniel folds his hand and Traudt shows his hand, the King Nine of clubs.

So, is Daniel Negreanu a magician?  Make no mistake, he puts people on a hand better than anyone on the planet.  But how does he do it?
Believe it or not part of the answer is Daniel’s own table image.  He is the master of  “small ball” poker.  Raising virtually any two cards with expectation of a continuation bet regardless of the whether the flop hits his hand or not.  If he faces a re-raise, he’s out.  Due to the fact of his relentless exposure, other players know this style.  Mike Traudt knows it.  Which is why he would be in the hand with a K-9 to begin with.  Traudt did not re-raise Daniel pre-flop, so Daniel can be safe to believe that Traudt does not hold a premium hand like AA or KK.
On the flop, both players check.  If Traudt had any over pair, he would fire at that pot to make Daniel pay to draw either a straight or flush with two streets yet to come.  Then 4th street tells the story.  The 10 puts the straight draw on the board and Traudt checks!  That’s the key component to the story Daniel was trying to put together. Daniel puts in a bet, and Traudt check raises all in.  He clearly hit the straight.

But Daniel Negreanu always has to go a step further doesn’t he?  He calls out Traudt’s two cards exactly!  But why did he guess a K-9?  Why not A-9?  Had Traudt held A-9, he more than likely would have re-raised Daniel pre-flop.  But he didn’t.  So a K-9 made all the sense in the world to Daniel and Norman Chad suggests maybe we should send him to find Osama Bin-Laden.

Let’s put this into practice for you.  You can start to develop a story right from the pre-flop betting.  If you raise a A-Q from middle position, and you get re-raised from the big blind, you immediately must put that player on a hand better than yours.  The big blind knows he will be horribly out of position after the flop.  Would you want to be out of position with anything less than AA, KK, or AK?
Conversely if the button re-raises, you can expect he is using position after the flop as a weapon against you.  If you miss your flop and check to him, he will fire at the pot, guaranteed.  If you fire a continuation bet after missing the flop, he will more than likely raise you just to see where is.  If you missed the flop you will have to fold.

Let’s say you hold Q clubs-Q spades.  You raise and the cutoff seat just calls.  Your first piece of the puzzle is in place.  He more than likely does not hold AA or KK.  You know you are ahead pre-flop. The turn comes 6 diamonds-10 diamonds – J hearts.  You throw out a bet of about half the pot.  Your opponent calls.  Without a raise you have to assume he is on the flush draw.  If he hit a set he would re-raise you in a heartbeat.  The turn is a deuce diamonds.  You bet half the pot, he comes over the top and re-raised you all in.  You are beat. Throw away your Queens.  That’s a tough lay down to make with two over cards to the board, but you have to know that your opponent hit his flush. Throw it away.

You started with a great hand two Queens.  The board betrayed you and you had to fold the third best starting hand in No Limit Texas Hold ‘Em.  But one of the most basic rules you must follow to be successful is that hand strengths change with each street and sometimes you have lay down a premium starting hand, which will be the topic of my next column.  “Don’t get married to a hand.”

You could be posting your articles on the Poker Bankroll Blog. Read all about it here.

Tags: Poker Articles, Poker Strategy

Tableside Manner

Friday, April 3rd, 2009 | Poker Articles, Poker Rules | 2 Comments

Submitted by Vic Porcelli, this article belongs to the Poker Rules series.

So what is your reaction to a bad beat?  Is it standing up and yelling at someone for putting all their chips at risk on a draw after he hit his flush to beat your top pair, top kicker?   Or maybe you just tap the felt and say, “nice hand.”    The latter of course is the choice I hope you’ll make.  If your choice is to yell at an opponent, I’ll bet the next thing you do is to find that ear to tell your bad beat story to.   The reason someone yells at an opponent is the exact same reason why we tell our bad beat stories.  It makes us feel like we are better players and the other person is inferior and just got lucky. 
Poker is a very emotional game.  We can go from the euphoria of winning a large pot after outplaying an opponent, to the sorrow of putting all your chips in with a nut flush only to lose to a runner runner full house.  It’s how we handle those emotions that make the difference. 

The irony of verbal attacks is hypocrisy.  Players attack opponents for doing the same thing they would do.  When you play a suited connector in early position, hit your straight, and collect a nice sized pot, you just play an aggressive style of poker.  When someone else does it to you, he is a donkey. 
My favorite example is a bluff gone bad turned good.   Player A, bluffs at a pot.  Player B folds.  A few hands later, Player B bluffs back at Player A.  Player A calls.  By the time the river card hits, Player B’s hand improves and his bet on the river is no longer a bluff but a value bet.  Player A calls and loses the hand.  Player A then berates Player B for playing a 7 6 off suit then sucking out a straight, when player A’s bluff a few hands before was a lesser starting hand than Player B’s 7 6.

Now let’s look at tableside manner as a strategy.  The player who berates other players for making moves, or making loose calls immediately puts himself in the spotlight.  “Look at me I’m a loud mouth.  If I lose a pot to you it’s not because you’re a good player. It’s because you got lucky.”   Trust me, with that attitude people will come after you.  They will make more loose calls and re-raise you just to knock you out of a tournament so they don’t have to hear your big mouth anymore. 

Good solid poker players look at loudmouths as inferior players anyway.  “He’s not that good, so he shoots his mouth off to compensate.”  That good solid player will trap a loudmouth with a set and come over the top of your big bet with your top pair and top kicker and send you to the rail.  On the other hand, a quiet player who nobody notices is even there.  A player who never raises his voice, always says good hand, having fun and being very conversational.    That’s the player no one cares about.  No one is coming after him. 

Two easy examples of players with these two opposing characteristics are Phil Hellmuth and Daniel Negreanu.   Does everyone love to be the one that knocks Phil out of a tournament?  Yes!!  Do people willingly lay down their hands down to Daniel?  Yes!!  (of course in the case of Daniel Negreanu, he has more than likely just freaked you out because he called out the exact two cards you are holding)   I’m sure Daniel has taken a bad beat or two in his career.  I’ve never seen him yell at the opponent who knocked him out.
So, before you start attacking other poker players because they knocked you out of a tournament.  Look at yourself and be honest with your self by asking “how could I have played that better?”  “Why did I lose that hand?”  Because in most cases you may have made a mistake, a bad read.  Or did you even put your opponent on a hand at all?  Which is the subject of my next column.  “Are You Truly Putting Your Opponent on a Hand?” 

You could be posting your articles on the Poker Bankroll Blog. Read all about it here.

Tags: Poker Articles, Poker Rules

Calculating Bankroll Requirements

Wednesday, April 1st, 2009 | Poker Articles, Poker Bankroll Management, Poker Mathematics, Poker Tools | 2 Comments

Submitted by Scott McIntosh, this article belongs to the Poker Bankroll Management series

In gambling games such as poker, blackjack or video poker where the player is trying to make money not only is it important to be playing with a positive expectation but also much care must be taken not to lose all of one’s money. As the saying goes – “It takes money to make money”. This requires winning players to maintain a certain amount of money in reserve to handle losing streaks and is commonly known as the player’s “bankroll”. This article will explore how to estimate the amount of money that is required to be kept as a poker bankroll in order to play so as reduce the probability of going broke to an acceptable level.

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Risk of Ruin Formula (warning serious math content ahead)

The risk of ruin formula is given below. The formula is based on a random walk with upwards drift and has some assumptions that although not exactly correct are good enough that it still gives a good approximation of a poker player’s risk of ruin. These assumptions include: a) normal distribution of results b) constant win rate and standard deviation. If the actual parameters vary too far from these assumptions care must be taken as the formula is likely to underestimate the actual risk of ruin.

Risk of Ruin = e ^ (-2WB / (S ^ 2))

e = Constant (2.718281828)
W = Win Rate, measured in $ pr. hour
S = Variance (has a unit that doesn’t really make any logical sense)
B = Bankroll, measured in $
^ = Power symbol (e.g. 3^2 = 9; 3^4 = 81)
/ = Division Symbol (e.g. 24/6 = 4; 56/7 = 8 )

Reference : D. Schlesinger, Blackjack Attack, RGE publ., Oakland 1997 (2nd ed. 2000)

Note: A player’s win rate and standard deviation is usually obtained from a Poker Database program such as “Poker Tracker”.

Example

Given a winning poker player with win rate of $30/hour, standard deviation of $600 and bankroll of $15000:

Risk of ruin = e ^ (-2*30*15000/(600^2))
Risk of ruin = 8.208500%

Although this is a precise answer given to 6 decimal places it is only an approximation and probably would be rounded up to give a 10% risk of ruin in practice.

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What Risk of Ruin should you accept?

One can never eliminate the risk of going broke, that is reducing the risk of ruin to 0%. Whilst 5% might be acceptable to a part time player, a professional whose only source of income is from poker should use something like a conservative 1% risk of ruin. Also given the error likely in measuring the win rate and standard deviation and also changing table conditions one should maintain a higher bankroll than calculated.

This article was written by Scott McIntosh of ReviewPoker Rooms which has a Bankroll Calculator based on the formula given above.

You could be posting your articles on the Poker Bankroll Blog. Read all about it here.

Tags: Poker Articles, Poker Bankroll Management, Poker Mathematics, Poker Tools