PokerStars 100 billion hands

I ducked out of work a bit early to witness history and take a shot at the Stars 100 billionth hand. It was quite a spectacle. This was the lobby in PLO very close to when it dropped.

Wow! Nearly 400,000 players. Over 50,000 tables. nine tables of $10 FR limit Omaha. over 150 FR $10 Omaha and over 400 $10 6max Omaha. There were over 1000 tables of $25 NL.

To try to get some extra shots as the big hand neared I attempted to join a $0.02/$0.04 limit hold'em game. New tables were insta-filling and I couldn't get on. I clicked the Seat Me button and it timed out and couldn't get me a seat. Luckily it offered me the option to start a brand new table. I agreed and instantly the new table filled. I actually won a couple of the LHE hands for a tiny profit yay. It was fun.

It was exciting this whole road to 100. It's a bit sad now that it's finally over after these years. The finale was great and really well done. Thanks PokerStars.

Omaha variance and convergence

I got thinking about profit and variance in Texas hold'em and pot-limit Omaha.

In hold'em I recorded results using hold'em manager. What I noticed, and others have reported this, is that all of the profit in hold'em was from Aces and Kings. I broke even on the rest of the hands combined.

I don't have HEM for Omaha so I have to speculate some. Suppose that for a winning player all of your Omaha profit comes from AA hands.

Now the AA hands don't win as often as they do in Omaha as hold'em. But there's a positive side. You'll be dealt AA again soon enough so you'll get more frequent shots to make your profit.

In hold'em you are dealt Aces 1 time in 221. Same for Kings. So you grind and expect to break even on 219/221 hands (99.1%) and all your profit is on 2/221 (0.9%). Losing with AA-KK is a disaster as they are so infrequent. It would seem then that hold'em results in a way could take longer to converge, as the profit hands are so infrequent.

In Omaha you get AA 1 time in 40 (2.5%). So you may break even on 97.5% of Omaha hands and get ahead on 2.5%. Losing with AA isn't so bad as you only have to expect to wait 39 hands for your next shot, instead of 99 hands in hold'em. So in that sense although there may be more deviations and swings along the way, results should in a way converge sooner in Omaha than in hold'em.

The Smart Money by Michael Konik

I recently read The Smart Money: How the World's Best Sports Bettors Beat the Bookies Out of Millions by Michael Konik. It was very good. I'd heard about it here and there on the 2+2 forums.

Konik is a freelance writer for men's magazines like GQ, Maxim, and Outside writing about destination golf and other stereotype mens lifestyle pursuits. While doing a story on big time sports betting he meets Rick Matthews from a syndicate known as the Brain Trust. During a round of golf together Rick proposes a plan for the author (who is from L.A.) to pose as a new money high roller sports gambler in Las Vegas.

Konik's job in the Brain Trust is to find a Vegas sportsbook who will take large sports wagers in the tens of thousands a game and to bet the games Matthews picks. The Brain Trust needs to use "beards" to get their bets down as Vegas and other bookies will not take "sharp" action from professional sports bettors like Matthews who are betting with an edge on the house.

Konik settles in at Caesars Palace and gets RFB (room, food, beverage) while posing as a player, a sports high roller with money but no clue. From there the author and his girlfriend enjoy high roller casino life while trying to stay a step ahead of suspicious bookies who come to suspect he may be fronting sharp action.

Along the way Konik makes lots of money and learns a lot about sports betting. Indirectly we can deduce some details of betting strategy. The Brain Trust in general sees value in underdogs, as "squares", the regular folks, will overvalue favourites.

One thing I hadn't thought of is that underdogs and the under in over/under aka "totals" tend to go together. Which makes sense after I thought about it for a bit. If a football favourite loses the game or wins and fails to cover it can be largely caused by failures in offensive execution. Red zone stalls and turnovers, missed field goals, big plays called back. All of these factors which help the underdogs also drive down scoring.

It was an entertaining and educational book and a good read. I recommend it. I had the honour of being the first to read it from my library as they ordered it in for me from the request a book on their website.

I'd like to get into sports betting. Back in high school I used to do some imaginary 11-10 football plays for a few weeks each NFL season before falling into the red and giving up. It's a new world today thanks to the Internet. If I wanted to I could chuck say $110 into a bank account for sports, then make a small deposit somewhere, then make $1.10 plays.

If the picks break even (a pure random algorithm will be lucky half the time) then over say 100 plays I'd win 50 times for $50 and lose 50 times for -$55. So for only $5 of expectation I could make 100 small plays just to get started. Alas for now sports betting and options trading (the third side of the triangle) will stay on the sideline. Still working on poker and hopefully some interesting developments at the tables to report in the coming months.

Calculating variance at $1/$2 live

I've been playing $1/$2 live at my local casino since the summer of 2009. During that time I've recorded my results. When I come back home I record the number of hours played and the amount won or lost. The results are just recorded in an Excel spreadsheet.

At this point I have over 100 sessions and over 400 hours played. Results are ok. around break even, maybe down tree fiddy or so. Estimating 25 hands an hour live that's a sample size of around 10k hands.

While I have the totals and per hour can be readily calculated I was thinking of things like determining if my sample looks like a normal distribution, calculating my variance, and how confident I can be in the results to this point.

I looked at sessions first, since that is the form of the raw data. Now with sessions there's an immediate observation they are not the same size. Often I play 2 or 3 hours. More infrequently 4+ hours. Nonetheless that's where I started.

With sessions the variance came out at $117 per session over the data set. In Excel it can generate histograms with a bit of setup. Using the interval size of $10 I could convince myself that the graph has a semblance of a normal curve.


Over to hours. For live players I believe per hour is the way most of us usually think about cumulative results. People don't say "I lose $10 a session on average". They may say or calculate "I lose around $3 an hour playing."

Unfortunately the per hour data isn't great quality. The problem is results are recorded per session, not per hour. The result of this is that outliers are not accurately recorded and true variance is underreported.

For example suppose I play 3 hours and lose $30. Hourly, that would expand as {-$10, -$10, -$10}. In reality it would be something like {lost $50 the first hour, broke even the second, won back $20 the third, went home}. In this example the average hourly deviation is $0 in the averaged out session, and $27 an hour in reality. Alas the actual hourly data just isn't recorded so I can't know for sure true hourly variance.

Using the "expanded" way of assigning the session hourly result evenly over the number of hours played. It comes to a variance of $32 an hour. The histograms actually aren't that bad, especially the $10 intervals graph looks fairly not terrible.

Alas as noted the true hourly variance has to be higher, perhaps $60 an hour? I can't be sure.


There is a way using the central limit theorem to somewhat overcome the loss of hourly accuracy due to the results being recorded as sessions. If I put the sessions together into 10 hour buckets then I can overcome at least some of the lost accuracy. For example suppose I play 5 of 4 hour sessions for 20 hours. If I put them into 10 hour buckets then there's no loss of accuracy in sessions 1, 2, 4, or 5. in session 3 half of its result is assigned the first 10 hour bucket and half is assigned the second.

By using the per session results to "fill" consecutive 10 hour buckets and averaging sessions across boundaries, it came out to a variance of $176 per 10 hour block. Which is fairly good considering there are only around 40 data points. The histograms are a bit sparse but not bad looking using $25 and $50 interval sizes. I found using the 10 hour buckets scheme produced the highest sigma value when determining confidence levels. It was around 7% higher confidence than variance based on individual sessions which had about a 100 data point size.


So that's not bad. I'm glad I went through this exercise. It took a little bit to think it through, around as long as I expected. Plus I have the spreadsheets and Python helper scripts up so they can be reused. CSV file format can be your friend.

It was a bit humbling I was a bit surprised by how high the standard deviation is and how low the sigmas are in the confidence levels of the results. A fat tail can be good. Basically 10k hands isn't really a good sample size. I'd say based on my direct observations here 10k hands is a bare minimum to get some rough numbers. Basically I should come back by doubling the sample size to 1000 hours and I suspect that would fill in and smooth out a lot of the graphs.


There's a reason I'm more systemically interested in $1/$2 results at this time and I hope to have something to post in the nearer future.

Winning Strategies for No-Limit Hold'em by Nick Christenson and Russell Fox

I finished another poker book recently Winning Strategies for No-Limit Hold'em. It was ok. I had heard of it from the 2+2 magazine and I decided to add another no limit book.

The authors talk about bet sizing quite a bit. It's an interesting topic and I got some ideas from it. Also some stuff about bluffs was pretty good. There's a quiz with sample hands at the end which is now pretty standard in poker books and that was good.

That should be good for now for new strategy reading. There may be a strategy or meta type book or two still on the radar screen. For now my plan is to absorb what I've already read and some rereading may be beneficial.

busted Full Tilt roll

I managed to turn my $20 stake at Full Tilt into $0. Started out ok at $10 PLO. Then hit some bad luck. Donked off the last 50bb with TT 3bet all in on QT8 flop. I knew that was bad as it's always QQ or J9 in this case. It was J9 and I was 28% when the last of my money went in. I was frustrated and just shoved it in.

So back to Stars to grind $10 PLO and try to get back to even.

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There's a remarkably good bonus scheme for people with linked PokerStars and Full Tilt accounts. Put in $100 on Stars and get a $27 TCOOP ticket. Then transfer the money to Full Tilt and get credit for a deposit and $20 straight up bonus. That's basically a 47% bonus on depositing.