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Online poker tournament statistics: cummulative blinds

Sunday, March 8th, 2009 | Poker Articles, Poker Mathematics, Poker Tools | 4 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. During the process of collecting data to solve this problem I have run into some interesting observations which I would like to share with you.

Check out the previous post in this series: Online poker tournament statistics: player exit percentage

Having discovered a relationship between player exit percentage and the time any given tournament has been running for, the next step in calculating the probability of winning a poker tournament was to estimate the cumulative amount of blinds payed for any given period of time a poker tournament has been running for.

Just to remind you, the calculations shown below are based on the blind structure of FTP (Full Tilt Poker) regular tournaments with 10 minute blind levels (I’ve only included the first 10 levels )

In order to calculate the amount of blinds payed pr. level shown in the table above, I estimated a total of 10 rounds played pr. level. Because FTP tables are 9 handed the assumption of 10 rounds pr. level means that on average a player will pay the blinds a little more than once pr. level; 1,11 times to be exact.

Summing the “Blinds pr. level” over the “Tournament duration” up to blind level 34 led to the following table:

I myself was quite amazed when I saw these numbers. 866000 chips payed in total blinds for a 6 hour tournament. That’s a lot of chips!!!!

To have some sort of reference I wanted to calculate how many successive all ins you would need to win to pay these blinds. To keep things as simple as possible I assumed that each all in would double the  1500 chip starting stack. According to this assumption, 2 successive all in wins  increase your stack from 1500 to 6000, 3 successive all inn wins from 1500 to 12000 and so on.

The rounded necessary all in wins are shown in the table above (the precice numbers in brackets). Luckily it only takes roughly 9 successive all ins to win 866000 chips….aren’t you relieved:-)

I am now ready to calculate the probability of winning an online poker tournament, but you will have to wait until my next article to find out what it is.

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

Tags: Poker Articles, Poker Mathematics, Poker Tools

Poker Team Bankroll

Thursday, March 5th, 2009 | Poker Articles, Poker Projects, Poker Tools | 6 Comments

Submitted by Matt Gai this article belongs to the Poker Project series

Free web-based service for turning your home poker game into an enterprising partnership with your friends

This article explains the history, features and strategy behind pokerteambankroll.com

The idea was spawned as my friend and I were talking during a car ride down to Atlantic City for a poker tournament over a year ago. He said to me, “We should get everyone in our home game to pool our money together so we can play in big tournaments like a World Poker Tour (WPT) Championship and the World Series of Poker (WSOP) Main Event!” That was all it took to get the wheels spinning.

The very next week I drafted up the concept on paper so all of the home game players could get on the same page. I laid it out for everyone. Our team goal was to put together enough money for one $10,000 buyin to the WSOP Main Event for one of us, plus $1,000 for 1 Main Event Satellite buyin for a second player, plus $2,000 for travel, food and lodging expenses for both. $13,000 in all.

In order to reach our goal, we were going to follow this plan…
Any profit made in our home game could be contributed to our team bankroll in exchange for an equal number of points. I would collect the money from each player and record an equal number of points on paper (e.g. $82 profit contributed = 82 points recorded). I then put the money in a savings account that I set up just for this. We did this every week – and we still do. Anyway, every week, profits are contributed and points are given. And it adds up quickly!

The idea is, when we reach our goal, whoever has the most points will take $11,000 from the bankroll and use it to travel to Las Vegas to play in in the World Series of Poker Main Event, poker’s most prestigious tournament. Our team member with the 2nd most number of points will take $2,000 from the bankroll, travel to Las Vegas and play in a satellite tournament to try to win a seat in the Main Event. If that player wins a seat, then the team will have 2 players in the Main Event, thereby doubling our chances of cashing.

Here’s the best part, and you may have guessed it already, but, if either player cashes any money in the Main Event, everyone who contributed to the team bankroll will be paid out according to their percentage of contributions. For example, if the point leader, who contributed $3,500 in profits to the team bankroll, which is 27% of $13,000, cashes $100,000 in the tournament, he or she wins $27,000. The rest is paid out accordingly.

What this means is that everyone has a shot to win big money, regardless of how much you contribute. Take this hypothetical example: Player B has the least amount of points contributed (130), which translates to a 1% share in the bankroll. If the point leader wins the WSOP Main Event and cashes $10 million, player B wins $100,000. Not bad for a $130 investment!

So here’s where the web site comes in. I got tired of recording everything on paper, and so, being a webmaster, I decided that the best way to keep track of all of our activity would be online. That way, everything got recorded safe and sound, anyone on the team could easily check their statistics at any time, and everyone would always know where they stood with respect to the goal. We started recording and tracking every single buyin, cashout and contribution for every weekly home game on the website.

From there I starting adding features like a message board, photos, avatars, event selection, goal management, team management, emailing and more. It became so useful and so integral to our team that I decided to put it out there for the entire world to use.

Now anyone can create a private team on pokerteambankroll.com and use it to turn their home game into a big tournament team effort – and transform their home game players into poker super stars – all for free. Good luck!

Post by Matt.

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

Tags: Poker Articles, Poker Projects, Poker Tools

Basic poker tournament strategy

Tuesday, March 3rd, 2009 | Poker Articles, Poker Strategy, Poker Tournament | 4 Comments

Submitted by Cody Kirshner this article belongs to the Poker Tournament series

Have you been playing tournaments that you wish you could do better in, or you are doing well and then all of a sudden have a “blow up”?  We all feel that way from time to time, and even the best of us will make a misread and loose all of our chips, but that is the nature of tournament poker.  Every decision that you make in tournament poker could be the hand that can cost you the tournament.  So I decided to come up with a strategy that I use all the time when I play my tournaments.  I am not saying any of this strategy will either, guarantee success, or will win you a tournament right off the bat, but it should help you become a better tournament player.

The early stage of a poker tournament

Before we get into the strategy let me break down what you should be looking for in the early stages tournament.  In the beginning of any tournament it may be very difficult to get reads on players, especially if you have no past experience playing with them before.  You should proceed with caution against these types of players, until you can get a better read on them.  There will be other players at a table that you may think are playing solid, but when they come to the show down you see they were limping in early position with a hand such as Q9, something very marginal, and they called the whole way with the board being 10 6 7 2 5  trying to hit a gut shot for half of their stack.  Against these “calling stations” you want to play solid hands and make the most of them.  Calling stations can help you greatly in the early stages of a tournament because they can give you a few hundred to help build up your stack.  Then finally there is the wild and crazy “donks” that will play any single hand, make outrageous bets that don’t even make sense, and they have absolutely no idea what they are doing.  These are the players that you only want to play really premium hands against because they are willing to give you chips if you have the patience to take them. 

Now comes the strategy in the tournament, the hands you should be playing.  In the early stages of any tournament I usually sit back and only play premium cards (AA, KK, QQ, any good pocket pair…AK AQ and sometimes AJ, A10 in later position) because I look at the table and try and scout my opponents. I add and preach please don’t play KJ, Q10, K10 when people make a good size raise to you early on. It simply isn’t worth busting with hands like these.  Because if someone raises you early on and the board comes 4 9 K, and the person pushes all in after a good size raise pre flop, and you have K10 you will probably call and if they flip over AK you are practically drawing dead.   I just suggest not playing these types of hands early on because it isn’t worth busting on marginal hands such as these.  Which brings me to my next point, don’t be raising either with these types of hands early in a tournament because you will more often end up losing more chips than you will be gaining.  The early portion of a tournament should be the time when you just sit back and try and pick your spots with good hands and allow yourself to build up a good chip stack, while not putting anything at risk with marginal hands.  It may seem hard at first but if you show good patients at the beginning it will really pay off for you.

The middle and late stages of a poker tournament

Now that you have made it through the early stage of the tournament ( I think the first hour is the early stage until first break.)  it is time to reflect on your chip stack. If the tournament started with 1500 and you have 3500 that allows you to be a little more open.  You can raise with KJ, Q10s, J10s, these types of hands in middle to late position, but still don’t be raising in early position with these types of hands, it is still too early.  On the other side of the spectrum if you are low stack with 1000 when you started with 1500 be looking for premium cards, and be willing to fold marginal hands until you find a good spot to put all your chips in with.  With 1000 chips you are still not dead in the tournament especially if the blinds are around 40/80.  I have seen too many people give up in these stages of the tournament because they think they don’t have a chance and just shove with QJ off and someone calls with AJ and they bust you.  So remain patient because you still aren’t in trouble just yet.  Also at this stage of the tournament you know how 1 or 2 people are playing as well because you have been playing with them for the past hour.  So if they are conservative make sure you are using that to your advantage ( if you raise pre flop don’t be afraid to put a continuation bet on the flop when you miss completely cause you might just take it down there.)  In the same sense if someone is playing very tight and you know they only bet when they have something don’t be afraid to fold to him if your AK misses because you don’t need to be a hero and make a amazing bluff when they have top pair, it just isn’t going to work.

When you have made it through 2 hours of play, this is where things become interesting.  You are getting real close to the money and people will start tightening up their games, or the big stacks will bully the short stacks because they know that they are just trying to get in the money.  This is when, if you have a big stack don’t be afraid to try and take a few stabs at certain pots if the short stacks keep checking to you, and if the big stacks are bullying you, don’t be afraid to reraise them because they just might be trying to push you around.  Also this is the time when if you just have an average stack don’t be afraid to try and steal a few pots because the blinds are starting to get higher and higher.  Your selection of hands can change to a lot of different types of suited connectors and if nobody puts a raise into the pot, don’t hesitate to make a raise of your own.  But be careful, because you don’t want to become too aggressive and lose a bunch of chips just because you’re trying to steal the blinds from other people.  So I just suggest only raising with suited connectors in middle to late position.  If you manage to make it past the money bubble then the tournament turns to having a new objective, the grind down to the final table.  What you will see is right after the money bubble concludes and everyone that is remaining makes the money, the game will start to loosen up again.  People will get back to playing normal poker, and as should you.  At this point in the tournament you will become very familiar with certain players and the certain styles that they play, so once again use that to your advantage.  If people are hyper aggressive, don’t be afraid to check a monster and let them bet into you.  At the same point, retorting early that if a person is conservative don’t be afraid to take the pot from them, but just be careful.  Another big thing here is when you know the player, watch out for random plays they might make, especially if you have a good hand…MAKE SURE YOU DON’T GET TRAPPED.  If a real aggressive player that always bets continues to check watch out because they might just be slow playing something very big. So if they check and you bet and they reraise you, be careful that they don’t have a monster and bust you out. 

The final table of a poker tournament

Finally you have made it, you outlasted the field, and only 9 remain…you made it to the final table.   This is why you play poker, to have a chance at final tables.  There will probably be big money pay outs in all spots, but  the top 3 will pay the most…depending what site you are playing on.  I have learned to play final tables from the great Phil Hellmuth.  He said “you can’t win the tournament 9 handed, let the bad players make their mistakes, take some pots, and win the tournament 4 or 5 handed.”  This is the smartest strategy I can give you.  At the beginning of the final table be conservative let the other players lose their money, but you play tight and conservative.  My suggestion on hands would be to stick to an early tournament strategy.  As the players start to get knocked out that is when you are able to change your strategy and start mixing in different types of hands again.  Now if you are the short stack at the final table try and wait for a good hand if you can. If this is not an option look to take a stand with the best hand that you think you will get while being at the table before the blinds will eat you alive.  If your stack is about 10X the big blind yoiur move should be a push and only a push. 

I hope that my strategy has given you some insight on what you should be doing with tournament play.  Patience will allow you to have a deep run, and well timed plays.  If you are smart and are able to catch a few breaks you will be able to make a final table.  Remember don’t be playing KJ QJ Q10…etc. in early position, early in the tournament.  These types of hands will get you busted in a tournament.  Stick with good solid premium hands early to help build your chip stack as much as you can.  This is a very basic strategy for tournament play, it can get more difficult, but for beginners this is a good formula to follow to allow you to have success.  Good luck. And see you at the tables.

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

Tags: Poker Articles, Poker Strategy, Poker Tournament

Online poker tournament statistics: player exit percentage

Sunday, March 1st, 2009 | Poker Articles, Poker Mathematics, Poker Tools | 7 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. During the process of collecting data to solve this problem I have run into some interesting observations which I would like to share with you (warning: math content ahead). First a little teaser….my findings indicate that it is possible to make good mathematical estimations on how many hours it will take before the final table in a tournament is reached based on the number of players registered for the tournament:

In the table below you will get a feel for how many hours you will have to play to reach the final table based on the number of players registered.

In the following table you will get a feel for the size of tournament you should choose given the time you have available.

Here’s a recollection of how I calculated the numbers above:

My tournament statistics project is based on online poker tournaments at Fulltilt poker and more precisely freezeout tournaments (i.e no rebuys and add ons). First of all, I came to realize that I would need to be able to estimate the number of players in an MTT given the time it takes for the tournament to finish. For example if a tournament lasts 3 hours, how many players were registered to play in it from the beginning?

What I did was to note down the following information for 25 online poker freezeout tournament on Fulltilt poker:

• The time the tournament had been running
• The number of players registered
• The number of players remaining

From this data set I was able to calculate the exit percentages, that is the relative number in percent of player exits, and plot them against the time the tournaments had been running. For example, in one tournament running for 3 hours and 28 minutes, 611 players registered and of them 25 remained yielding an exit percentage 95,9%.

Player exit percentage raw data

I was quite surprised to see the raw data plot shown above because it indicates an exponential mathematical relationship between the exit percentage and the time an online freezeout tournament has been running for. This relationship seems to be independent of the buyin of the tournament and the number of players entering.

I transferred the raw data to Origin and did a peak fit analysis to determine the mathematical relationship between the exit percentage (EP) and the hours played (x). Based on my original data set I imposed the following boundary conditions:

• EP(x=0)=0% : No players exit the tournament before it starts
• EP(x=6 hours) = 100% : All the freezeout tournaments I sampled had ended within 6 hours

Player exit percentage fitted data

Turned out the relationship was exponential as expected:

• EP(x) = A(1-exp(-Bx)), in this case A was 99,5 and B was 0,96

Now here comes Now here comes the interesting part. Given the equation above, relating the exit percentage with the number of hours played, it is now possible to estimate both the hours it takes a tournament to finish and the inverse, namely the number of players entering into a tournament given the hours it takes to finish.

Since I’m not able to paste Excel formulas into WordPress blog posts, I have made some tables with some sample data just to give you an idea of how you can use the formula.

In the table below you will get a feel for how many hours you will have to play to reach the final table based on the number of players registered.

In the following table you will get a feel for the size of tournament you should choose given the time you have available.

Hope you found the information in this article useful. If you have any comments or want a copy of the Excel spreadsheet I used to calculate the data in the tables, please let me know.

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

Tags: Poker Articles, Poker Mathematics, Poker Tools