In gambling, as in the stock market, you must consider two things when determining whether a game or portfolio is worthwhile: volatility and expected return. In gambling, these things are usually measured in hourly rate. Most gamblers underestimate the former and overestimate the latter. In fact, most gamblers I know probably have little concept of what volatility even is. According to Malmuth in Gambling Theory and Other Topics, an expert player may have to play over 4000 hours before he can be voer 99.8% sure to be above even (based on a standard devation of $650 and a win rate of $30). That's two full years of full-time playing before you can be assured of being in the black! How many pros would have the bankroll, patience, and psychological fortitude to play that long before throwing in the towel?
Volatility is a measure of the riskiness inherent in a game. The most common and useful measure is the standard deviation. If my standard deviation in a game were $300/hour and my expected return were $0/hour, then 68% I can expect to be within one standard deviation (-$300 to $300) after one hour of play. 95% of the time I can expect to be within 2 standard deviations (-$600 to $600).
Keeping these number in mind, I've found, is very useful for two reasons. First, it keeps me humble and prevents me from putting my bankroll at great risk. Usually, doubling stakes means more than doubling standard deviation, because competition tends to be better. Also expected return will be less than double for the same reason. Thus, if I were to move up from my usual $2-5NL game to the $5-10NL game, as I planned to do in January, I would have to accept a doubling of my standard deviation, while less than doubling my expected return.
Second, knowing about these standard deviation helps keep losses in perspective. A common question gamblers ask themselves (and others) when they are running badly is "Am I playing badly or am I just unlucky recently?" If you know your standard deviation, you can at least give yourself some idea by answering the question: "If I were playing as well as I normally do, what is the likelihood that I would have lost as much as I have over the past X hours?" Usually the number will be higher than you would have expected. This doesn't quite give you the answer you were looking for ("Bad or unlucky?"), but it does give you some perspective on how much luck really does play into results. For me, this can help me to regain my confidence during a losing streak.
Most people tend to attribute their good results to skill and their bad results to bad luck. I am just the opposite. In fact this post was inspired by a statistically unlikely session I had last night, where I came out almost 4 standard devation ABOVE my mean over the course of 7 hours. Boy, was I ever lucky!
By the way, the Rio games got good again and I'm going to qualify for the WSOP freeroll tournament. I sure hope volatility is on my side again that day.
Friday, February 24, 2006
Tuesday, February 21, 2006
Commerce Casino
I was in LA with Brigid this weekend, and on our way back to Vegas we stopped to check out the Commerce Casino. There's a chance I'll move to LA at some point, so I wanted to see what the poker options there are. I've read quite a bit about the differences between Vegas and LA for poker (most recentlyin Malmuth's Gambling Theory and Other Topics), but I wanted to see first hand. I've heard the Commerce has the largest poker room in the world (by number of tables). Actually, it's two rooms - one high limit and one low limit. Both are bigger than any room in Vegas, with the low limit room somewhat larger.
Since I stopped playing at the Bellagio, seeing the big name poker stars isn't as routine for me as before, so it was fun to see all the recognizable faces at the Commerce. The first star I noticed was Gus Hansen, Brigid's favorite player for obvious reasons. At his table were Phil Ivey, David Benyamine, Lyle Berman, Eli Elezra, and a couple others I don't remember now. Todd Brunson at David Williams were playing nearby, too. Unlike at the Bellagio, where there is a semi-private room for the "big game," the big games at the Commerce are right on the floor with all the other tables, which is pretty cool.
Except for some inconvenience getting to the Commerce (lots of traffic in LA), it seems like a viable poker option. Next time I go I'll check out the Bicycle. Any other good poker rooms in LA?
Since I stopped playing at the Bellagio, seeing the big name poker stars isn't as routine for me as before, so it was fun to see all the recognizable faces at the Commerce. The first star I noticed was Gus Hansen, Brigid's favorite player for obvious reasons. At his table were Phil Ivey, David Benyamine, Lyle Berman, Eli Elezra, and a couple others I don't remember now. Todd Brunson at David Williams were playing nearby, too. Unlike at the Bellagio, where there is a semi-private room for the "big game," the big games at the Commerce are right on the floor with all the other tables, which is pretty cool.
Except for some inconvenience getting to the Commerce (lots of traffic in LA), it seems like a viable poker option. Next time I go I'll check out the Bicycle. Any other good poker rooms in LA?
Monday, February 13, 2006
Rio WSOP Freeroll Update
As I described in my last post, I'm considering trying to qualify for the freeroll WSOP satellite tournament at the Rio by playing 80 hours in February. The qualifiers from January played their tournament Sunday night. There were 18 qualifiers, 16 of whom showed up for the freeroll. I recognized about half of them, and they were all decent players, as expected.
There are a few new important factors for me to consider. First is that 2nd-10th place were also paid, a total of just under $3000. So the total value of the tournament is now about $12,000. Unfortunately, word has gotten out about this promotion, and a lot more players will probably be qualifying in February. In my previous post, I had guessed that there would be 24 players - now I think there will be over 35. I'll guess 40. Qualification is now worth only about $400 to me (previously approximated at $560).
Another problem is that the influx of new players who are serious about poker has made the Rio games much, much tougher than usual. About 80% of my opponents the past few days have been competent professional players. I'm used to maybe 40%. Aside from the promotion, continuing to play in these games would be an example of terrible game selection, .
On the other hand, I have already racked up about 43 hours this month, so I only have 37 more to go in the span of 15 days. If it weren't for this promotion, I would probably play at the Rio 0-10 more hours this month, so I would have to play about 32 extra hours there to qualify. Since qualifying is worth $400 to me, this amounts to $12.50 an hour.
Would my win rate at the Mirage (or some other casino) be at least $12.50/hour more than what I expect to win in the very tough games at the Rio? This seems very likely. If that's the case, it no longer makes much sense for me to pursue the goal of playing 80 hours. On the other hand... my girlfriend is coming to town this weekend and I could play 4-8 limit with her at the Rio and avoid the sharks. The 4-8 Rio game is certainly not $12.50/hour worse than any other 4-8 game in town. I don't know what to do.
There are a few new important factors for me to consider. First is that 2nd-10th place were also paid, a total of just under $3000. So the total value of the tournament is now about $12,000. Unfortunately, word has gotten out about this promotion, and a lot more players will probably be qualifying in February. In my previous post, I had guessed that there would be 24 players - now I think there will be over 35. I'll guess 40. Qualification is now worth only about $400 to me (previously approximated at $560).
Another problem is that the influx of new players who are serious about poker has made the Rio games much, much tougher than usual. About 80% of my opponents the past few days have been competent professional players. I'm used to maybe 40%. Aside from the promotion, continuing to play in these games would be an example of terrible game selection, .
On the other hand, I have already racked up about 43 hours this month, so I only have 37 more to go in the span of 15 days. If it weren't for this promotion, I would probably play at the Rio 0-10 more hours this month, so I would have to play about 32 extra hours there to qualify. Since qualifying is worth $400 to me, this amounts to $12.50 an hour.
Would my win rate at the Mirage (or some other casino) be at least $12.50/hour more than what I expect to win in the very tough games at the Rio? This seems very likely. If that's the case, it no longer makes much sense for me to pursue the goal of playing 80 hours. On the other hand... my girlfriend is coming to town this weekend and I could play 4-8 limit with her at the Rio and avoid the sharks. The 4-8 Rio game is certainly not $12.50/hour worse than any other 4-8 game in town. I don't know what to do.
Tuesday, February 07, 2006
80 hours at the Rio
This week I found out the Rio has been running a promotion where you get to play in a freeroll satellite tournament for the main event of the WSOP. All you have to do is play 80 hours in a calendar month, or win two of their daily tournaments in a month. I had heard rumors about this for a while, but nobody seemed to know quite what was going on, even the dealers and floorment. Despite this, there were supposedly 17 people who qualified back in December, and they played their freeroll on January. I don't see how this is possible, since in mid-January, the poker room staff still couldn't give me any information about what the promotion was, and their rewards card swipers weren't even working, meaning they must have kept hand records of everyone's hours. Never did the rumors include mention of the WSOP, only that there might be some sort of freeroll for players who log a lot of hours. Suffice it to say that there was a lot of confusion and hearsay surrounding the situation until last week.
Now, the situation is much clearer. They have the rules posted on the wall, and the comp card swipers are working again. I play a lot at the Rio, but also a lot at other places, so I'm trying to determine whether it's worth trying to reach 80 hours. Here are some factors that will weigh in the decision.
How much of a commitment would this be? I didn't start playing at the Rio this month until Friday, Feb 3 because I didn't know about this promotion and I'd been playing at the Mirage insted. Since Friday I have 18 hours logged at the Rio. February is 1/4 over, so my 18 hours are behind pace - I need 62 more in 3 weeks. Without trying, I would probably play 20-35 more hours there this month anyway. So the opportunity cost is about 35 hours during which I would be doing something else. For instance, I recently found out that the Mirage gives a $15 food comp just for playing. The 2-5 Mirage games are pretty good, but not quite as good as the Rio. The Mirage also has good 10-20 and 20-40 limit games, and a lower rake than the Rio.
How many players would I be going up against? Supposedly there are about 18 qualifiers from January, and they'll be playing on Sunday. So far this month, the Rio has been much more crowded than in January. Although I suspect this is mostly because of the Super Bowl, it's also possible that now that the rules are posted, more people are attempting to qualify for the tournament. The shortness of the month compensates for this somewhat. I approximate 24 other qualifiers for February.
How tough would my competition be? There are two players at the Rio who are probably better than I am, but they don't play there every day, so I doubt they'll qualify. The regulars at the Rio are decent, but not great. The real problem here is that there will be no fish - against a normal tournament field, at least 20% of the players are terrible. This won't be the case. I have relatively solid tournament skills, so I'd say that against a field of 24 solid players, I have about a 1/16 chance to win. If I knew the tournament structure, I could make a better approximation.
How much is the prize worth to me? Well, the prize is entry into the $10,000 WSOP main event. Although I could afford it, I would not put up the $10K entry fee on my own, so clearly it is worth less than that to me. How much would I be willing to pay to enter the tournament? $9000? Probably. Close enough.
What is my equity? $9000/16 = $562.50. So, I'm spending about 35 extra hours at the Rio over the course of 3 weeks for an expected extra $560, or about $16 an hour (neglecting the length of the freeroll tournament itself). Is that worth it? Probably - $16 is still a significant boost to my win rate.
I'll try to keep myself on pace, and then check out the freeroll on Sunday to see who shows up, what the structure is, and how many players there are.
Now, the situation is much clearer. They have the rules posted on the wall, and the comp card swipers are working again. I play a lot at the Rio, but also a lot at other places, so I'm trying to determine whether it's worth trying to reach 80 hours. Here are some factors that will weigh in the decision.
How much of a commitment would this be? I didn't start playing at the Rio this month until Friday, Feb 3 because I didn't know about this promotion and I'd been playing at the Mirage insted. Since Friday I have 18 hours logged at the Rio. February is 1/4 over, so my 18 hours are behind pace - I need 62 more in 3 weeks. Without trying, I would probably play 20-35 more hours there this month anyway. So the opportunity cost is about 35 hours during which I would be doing something else. For instance, I recently found out that the Mirage gives a $15 food comp just for playing. The 2-5 Mirage games are pretty good, but not quite as good as the Rio. The Mirage also has good 10-20 and 20-40 limit games, and a lower rake than the Rio.
How many players would I be going up against? Supposedly there are about 18 qualifiers from January, and they'll be playing on Sunday. So far this month, the Rio has been much more crowded than in January. Although I suspect this is mostly because of the Super Bowl, it's also possible that now that the rules are posted, more people are attempting to qualify for the tournament. The shortness of the month compensates for this somewhat. I approximate 24 other qualifiers for February.
How tough would my competition be? There are two players at the Rio who are probably better than I am, but they don't play there every day, so I doubt they'll qualify. The regulars at the Rio are decent, but not great. The real problem here is that there will be no fish - against a normal tournament field, at least 20% of the players are terrible. This won't be the case. I have relatively solid tournament skills, so I'd say that against a field of 24 solid players, I have about a 1/16 chance to win. If I knew the tournament structure, I could make a better approximation.
How much is the prize worth to me? Well, the prize is entry into the $10,000 WSOP main event. Although I could afford it, I would not put up the $10K entry fee on my own, so clearly it is worth less than that to me. How much would I be willing to pay to enter the tournament? $9000? Probably. Close enough.
What is my equity? $9000/16 = $562.50. So, I'm spending about 35 extra hours at the Rio over the course of 3 weeks for an expected extra $560, or about $16 an hour (neglecting the length of the freeroll tournament itself). Is that worth it? Probably - $16 is still a significant boost to my win rate.
I'll try to keep myself on pace, and then check out the freeroll on Sunday to see who shows up, what the structure is, and how many players there are.
Wednesday, February 01, 2006
Caesars
As I mentioned before, Caesars has a new poker room. It opened mid-December. The room is very large and has state of the art technology. It's located in its own alcove right between the sportsbook and Pure (supposedly the most popular nightclub in the world right now). I've played there several times and the games are reasonably good. However, I don't plan on going back anytime soon for the following reasons...
1. Unreasonable rules. The MGM room had this same problem when they opened up. The people in charge want to make strict rules to try to eliminate any gray area when disputes arise. This is understandable - advisable even. The problem is that players and dealers are used to a certain set of rules, written and unwritten, that are used in all the other poker rooms in town. When you make new rules and tell neither the players nor the dealers, it is unreasonable, and will only cause more disputes. The solution is probably to have strict rules that conform to the current customs of play in poker rooms around Vegas. A good example of this is "cutting your stack" when betting. If you want to bet $70 and you bring out a stack of sixteen $5 chips, most casinos allow you to count out these chips and then bring two back, as long as you leave your hand on them. At Caesars, this is an $80 bet unless you verbally declare "$70". This rule alone makes me very unlikely to want to play at Caesars again, unless they change it.
2. Poor service. I wanted to get some food and another player told me they will bring food to the table, and all I had to do was ask for a menu. This is a nice feature that some, but not all, casinos offer. I got my menu and the floorperson asked me for my ID so I could get a comp card. All I had to do was give the waitress my card when I ordered. Well, four hours, $17, and one cheeseburger later, I still didn't have my comp card or any discount, and I was out of my seat asking the floorperson where I could get my card. She said I should go to the front desk. The front desk told me I had to go out into the casino, past the deli to the rewards center to get it. So I searched the casino for a few minutes, found the rewards center, got my card, and went home. The next time I went to Caesars I had been playing for about 6 hours when I decided to order some food. Suffice it to say that an hour and a half later, after they had finally gotten around to asking me for my order, I was ready to leave. And not come back. Now, I realize getting food brought to me at the table is a luxury, but expecting the casino to follow through on their offer of it should not be to much to ask.
3. Inadaquate restrooms. The restroom has just a few urinals and is located just outside the poker room, to be shared with sportsbook patrons and nightclub goers. This means lines are common, especially when the nightclub is hopping. On the plus side, it makes for an amusing social scene as the world of the drunken nightclub people collides with the world of the poker players.
All of these problems, particularly the first two, can be fixed rather easily. In fact, I expect them to be fixed within a month or two. Until then, Las Vegas has plenty of other more worthy options.
1. Unreasonable rules. The MGM room had this same problem when they opened up. The people in charge want to make strict rules to try to eliminate any gray area when disputes arise. This is understandable - advisable even. The problem is that players and dealers are used to a certain set of rules, written and unwritten, that are used in all the other poker rooms in town. When you make new rules and tell neither the players nor the dealers, it is unreasonable, and will only cause more disputes. The solution is probably to have strict rules that conform to the current customs of play in poker rooms around Vegas. A good example of this is "cutting your stack" when betting. If you want to bet $70 and you bring out a stack of sixteen $5 chips, most casinos allow you to count out these chips and then bring two back, as long as you leave your hand on them. At Caesars, this is an $80 bet unless you verbally declare "$70". This rule alone makes me very unlikely to want to play at Caesars again, unless they change it.
2. Poor service. I wanted to get some food and another player told me they will bring food to the table, and all I had to do was ask for a menu. This is a nice feature that some, but not all, casinos offer. I got my menu and the floorperson asked me for my ID so I could get a comp card. All I had to do was give the waitress my card when I ordered. Well, four hours, $17, and one cheeseburger later, I still didn't have my comp card or any discount, and I was out of my seat asking the floorperson where I could get my card. She said I should go to the front desk. The front desk told me I had to go out into the casino, past the deli to the rewards center to get it. So I searched the casino for a few minutes, found the rewards center, got my card, and went home. The next time I went to Caesars I had been playing for about 6 hours when I decided to order some food. Suffice it to say that an hour and a half later, after they had finally gotten around to asking me for my order, I was ready to leave. And not come back. Now, I realize getting food brought to me at the table is a luxury, but expecting the casino to follow through on their offer of it should not be to much to ask.
3. Inadaquate restrooms. The restroom has just a few urinals and is located just outside the poker room, to be shared with sportsbook patrons and nightclub goers. This means lines are common, especially when the nightclub is hopping. On the plus side, it makes for an amusing social scene as the world of the drunken nightclub people collides with the world of the poker players.
All of these problems, particularly the first two, can be fixed rather easily. In fact, I expect them to be fixed within a month or two. Until then, Las Vegas has plenty of other more worthy options.
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