Poker and Statistics – Like Beer and Pizza!

Like Dr Fro, I have also been keeping records of my poker results. I got lazy for a while and didn’t keep track of anything for more than a year, but I started up again in July and I’m beginning to accumulate enough data to start making observations. I’ve made some graphs that are quite interesting (click on the graphs to open larger versions).

First off – I’m taking time out from tournaments, too.

The first thing you’ll see from this graph is that I’m down $465 since July. The next thing you’ll notice is my bad day in Vegas earlier this month (more on that below), and the third thing you will see is probably that $435 of my total losses is from playing in big tournaments with large buyins ($100+) and forty or more players. While the poker “revolution” has been great both for the attention that the game is getting and the increase in action from bad players, a lot of newer players are naturally drawn to wanting to repeat what they see on television and thus are wanting to play in tournaments. Granted, as I have extolled in this space many times before, these tournaments can be very lucrative opportunities against (usually) poor competition, but the tournament structure itself limits the extent to which that poor competition can be exploited. Tournaments require one to be lucky (or at least to avoid being un-lucky) for a long period of time before any positive return can be realized, while it only takes one big hand for a cash game to become profitable.

Another way to look at this: Even if my skill and experience were to increase my chances in a 50 player tourment by a factor of 10, that would still just improve my chances from 1 in 50 (pure luck) to 1 in 20 – only 5%! Assuming that the entry fee in every tournament I play is $100 (which is on the low side), that means I could end up dropping $2000 (or likely more) in entry fees before I could expect to start seeing the benefits of this “lucrative” opportunity. Granted, this reasoning is slightly simplistic because I could at least finish “in the money” in a couple of tournaments and at least get some money back, but that money still probably wouldn’t be enough to cover my losses in all of the other tournaments where I win nothing.

So if tournaments are bad bets for me and I’m so sure that I have a positive expectation from just grinding away in cash games, then just exactly how much should I expect to win in a cash game? That’s the next graph:

This is a graph of a normalized distribution of my hourly results in cardroom (casino style) games since July. There are 56 hours of data there. If you’re not familiar with a normal distribution, it can best be explained as a chart that shows the the forecasted results of a series of trials (events) on the x-axis, and on the y-axis, the percentage of trials that achieve each particular result. In this case, the chart is showing my expected results in big bets won or lost for each hour of poker played. For example, if you look at the dashed pink line, I should expect to win just over 4.5 big bets per hour 20% of the time I am playing cards in a cardroom. This chart was created by taking a weighted average of the results of my hours of play and then finding a standard deviation per hour, then applying those two pieces of data to a normal distribution (this is Freshman Statistics 101 – just trust me if you don’t understand it).

There are actually two distributions on this graph because of those 56 hours, 3.5 were played in a daytime mid-limit game in Las Vegas (Bellagio 8/16). I lost 10 big bets an hour and slightly went on tilt enough to where I think that time was indicative neither of my normal game nl results – the players were much better, the stakes were higher, and the game was much tougher than my usual 3/6/12 action at the FSC. For all of these reasons, I debated whether to include these hours at all and compromised by making two curves – one that includes these hours and one that doesn’t. Quite clearly, those 3.5 hours had a significant effect on my analysis because dropping them out increased my average result by almost one full bet (and from positive to negative) and it reduced my standard deviation (the variability of results and “spread” of the curve), too.

So what does this graph tell me? For one thing, it says that, at least based on the 53 hours I have played since July, I have a positive expectation per hour of slightly more than half a big bet, and, for all of you stats literate readers, 95% of the time I should expect my results to be within a range of -7.7 and +8.8 bets per hour. This is still a fairly large spread and my mean earnings number is still less than the 1 big bet per hour that all of the expert writers claim should be the goal of most players. I will continue to update this analysis as I keep playing – I would expect that my mean results will slowly increase and the standard deviation will slowly decrease. More later.

Where have I heard this before?

Tuesday night at the Friendship Club.

Dealer: “There’s the last card. Johnny Mac is first to act.”

Johnny Mac: “I bet $6″

Dealer: “Mr. Singletary, $6 to you.”

Mr. Singletary: “I call.”

Dealer: “OK, show ‘em… Looks like Mr. Singletary has the nut flush… and… full house down here for Johnny Mac, fours full of aces.”

Dumbass #1: “Why didn’t you bet the full $12?”

Dumbass #2 (The “Hat Man”): “I’ll tell you why! He didn’t know what he had! He misread his hand! HAR HAR!”

Johnny Mac: “HA HA – you got it! I’m a freakin’ idiot! You guys caught me! Duuuuuuh! ”

Mr. Singletary: (very thoughtfully and slowly) “No, no, no. He knew what he was doing. If he had bet $12 I would have folded.”

Dumbass #1: Really? An ace-high flush is a pretty good hand!”

Mr. Singletary: “It doesn’t beat a full house! I thought he was just betting a smaller flush!”

Honestly, I still don’t think those guys understood my reason for the $6 bet, even after Mr. Singletary explained it himself.

No Limit Tournament Primer

Good advice, but I don’t think I’ll be using it anytime soon. I am going to take a bit of a break from NL tournaments. I like them, but daddy only gets x number of hours to play poker and I’d rather use up my free passes playing cash games, where I can win much more often than I do at tournaments and get a better rate per hour.

The Greene Friday night crowd stats.

I keep track of every penny won and lost gambling. I decided to look at my results and see what conclusions can be drawn about playing with the Greene Friday night crowd.

I have played 16 times and won $1,170. I have 15 winning sessions that average $84.60 with one loss for $99. The overall average is $73.13. Sounds like easy money, right? I don’t think so. Let’s look further:

My six biggest scores occurred in 2000 and 2001, with an average score of $162.80. Yet my three worst outings occurred this year (-$99, +$12, +14).

My running average has decreased 13 straight games, with one 50 cent exception.

Clearly this is a trend, but what does it mean? I can think of several possible explanations:

1) The competition has gotten better; or they have improved at a greater rate than I have.

2) I have gotten worse.

3) The games called are different and give me less of an advantage.

4) Bad luck

5) They are on to me.

I will throw out number 2 because I don’t think it is common for ANYONE to actually get worse at poker if they play regularly. Perhaps someone can get rusty after a long break, but I don’t think I am worse. I will also throw out number 4 because the trend is so overwhelming. Last, I will throw out number 5. One day, we were “on” to Glazer and learned to just call his aggressive bets. But I don’t think there is anything about me that everyone is “on” to. I don’t think I have a bad tell or a glaring weakness that is being taken advantage of.

So it is a combination of 1 and 3, and I think that 1 is the answer.

With 3, I have to say that this definitely is a factor. We used to play games where I had a massive advantage like Hold’em or Anaconda. But now there is a lot of 7-27 where I don’t think I have any advantage at all. I would say my EV on Hold’em could be as much as $20 per hour, but at 7-27 it is $0.

But the biggest factor is people have gotten better. The two guys I used to win the most from were Romberger (sp?) and Nichol. Rom is gone and Nichol has improved by leaps and bounds. So while the average player is by no means ready for the WSOP, there is clearly a lack of people making massively wrong decisions.

This shouldn’t be any great surprise – there is a real survival of the fittest thing in poker games. If you don’t improve, you eventually lose too much and stop playing.

Since the primary reason I play in the game is for fun, I welcome the improved play. It adds to the fun for sure. However, I am going to need a new game on the side to replace the lost income. Anybody know Ted’s phone number?

We played at John’s on Friday, usual stakes of 25c-$3, dealer’s choice. Biggest hand of the night was 7-27 for $170. I got half with 27 for $85, but I put $55 in, so I only cleared $30. Big hands defined the night, and I ended up +$12. Big winner took home about $140.

One person committed one of my pet peeves, which inspired me to post all of my pet peeves. This is not a bitch list, because I always have fun. Yet, I would have more fun, if people stopped doing the following:

Not paying attention. It’s your turn, its only 50 cents. Just fold, call or raise. Don’t tell me a story about work. It’s annoying. Play poker.

Arguing about rules when you are clearly wrong. It is ok to argue the rules in the exotic games because in all likelihood, the dealer did not spell them all out. But if we are playing for instance Texas Holdem, there is no need to argue about the rules. There is only one way to play. Same with Omaha, stud, and draw. If you think differently, then you are wrong.

Getting pissed at others for not doing what you want them to do. For instance you and the hero are going low and a third person is going high. You raise and the hero doesn’t like it because he knows that he is putting in a third for a shot at a half. He lectures you. He is wrong to do that for two reasons. One, you may have a perfect low and therefore correct in raising. But also, his lecturing is constructively table talk which is strictly against the rules for good reason. It is collusion against the third player.

Cutting to the left. You cut to the right. There is a reason for this.

Buring and turning early. Wait until all the betting is done, then burn then turn. Again, there is a reason for this. Surely you are bright enough to understand it.

Dealing and THEN calling the game. Especially ater there are up cards. God this is annoying.

Acting as if a question is unreasonable. If we play chase the bitch, I want to know what happens when the last up card is a Queen at the onset of the game. So, when I ask, don’t give me that look of “oh shut up” just answer the bloody question.

Always throwing in the low denomination chips. OK, if you have a mountain of quarters, you can throw them in the pot, but please don’t count out $3 worth of quarters to call every single time. It slows down the game when you call, when we split the pot and again when the winners stack their chips.

Thinking for 2 minutes to call a game. Look, you have had an hour to think of a game, and now that its showtime, you have stagefright? Lets just cut the deck for high card, highest card gets to punch you in the face, and then the deal passes to your left.

Some of my favorite things are: gracious winners, nice guys, good players, a decent mix of whacky games with real games and pizza, all of which were present on Friday.

cf

People are playing cards in illegal games in Dallas? Scandalous! I can’t believe this is going on! Goodness! What are we going to do? I mean, we all know that drug laws work really well, so why don’t laws against illicit gambling? Someone call the police!