Yesterday I bought this game called out park baseball. It is a baseball simulation/management game. The game has almost too much depth. I'm not a baseball expert, but I can see this game being really addictive to a true fan (and I was still getting slightly addicted). Apparently the player database has every major league player from the last 100 years. Anyways I started a fictional league because I dont' really know/care about the current players. Please post if you have tips about the game!

Yesterday I spent too much time on the game. Today I managed to get a few hours studying done, and even played a 2.5 hr session. Site is looking pretty hot. Chris is really the man when it comes to site stuff. I don't think I'll play any HU this month...I had a few bad sessions last month, and the money in 6-max is just so easy.

It is possible to attack NLHE bet sizing from a GTO perspective. A special case of this gives an interesting result. Consider another 'half street' game where the in position player has the decision to bet on the river. Clairvoyance as Chen calls it, is the situation when your opponent's hand is face up AND it is always a bluff catcher. This occurs often on the river in NLHE against poor players. You know whether your hand is good or not, and thus the only question is what size to bet (and obviously which frequency to bluff). Note that this means we never have a reason to check a hand with showdown value because villain's hand is face up.

Remember, in GTO terms, we must bet with a ratio of valuebets/bluffs such that villain has the same EV for calling versus folding (0 EV). If our range is skewed towards value hands (say 60% value and 40% air), then it is correct to bet our whole stack with our whole range. Yes, we should bet as much as possible with every hand and bluff with the appropriate frequency depending on bet size. For example, betting 2x pot means we should bluff 40% of the time.

Now some intuition to explain the result. The obvious answer seems to be for villain to call 40% of the time and negative our bluffs. This is wrong. Villain should actually fold 100% of the time. Even though we're bluffing, our range is skewed towards strong hands and thus we gain more and more for larger and larger bet sizes. To see this solution more clearly consider the case of villain calling some %, and think about our counter strategy of varying bet sizing for bluffs versus valuebets (ask me if you can't see it).

The point is that when villain's hand is face up, we should valuebet all-in with everything that beats him, and bluff accordingly. This isn't really a new concept. You may have heard the concept referred to as " the showdown tax". For example, on the river with a PSB left, bet every better hand (and some % of bluffs). Everyone is a calling station these days, so they tend to deviate from the 'always fold' case when your range is strong. Exploit that!

I wrote my first article for the private strat forum. It's an expository introduction to game theory. I'm pretty happy with it considering it was kind of a rush job. It is light on math so should be readable for everyone. Other than that I've been busy with some other leggo/poker stuff and studying for the cfa. I also have the inkling to grind a bunch of hands HU. I'm consciously avoiding omaha because it will drain too much of my time from other stuff I need to be doing. I tracked down some game theory/poker papers co-authored by Chris "Jesus" Ferguson. I'll give them a quick read and post relevant comments in a few days.

More pseudo game theory talk. Hand from a recent hu video of mine. I open 96o on button and get a flop of 766 rainbow. I bet and get called. Turn is 7, also bringing a flush draw. I checked turn: villain either has a 7/6/straight draw/A-high with occasional small PP or random float. So there's no value in betting turn. Checking lets him hit a pair or bluff river. Whereas there are almost no worse hands that can check/call turn.

Pretty standard I think. But what about the rest of our range. 96 is essentially AA-QQ here. 88 is a bit different because of the risk of free cards. So you can argue betting 88 for protection, but checking big (JJ+?). A 7 isn't too different, but maybe different enough to warrant a bet in a vacuum. The rest of our range is unpaired hands with SD value (say QT+), and hands with no SD value. No SD value hands gain from betting since villain will sometimes fold A high, and certainly straight draw type hands. SD value hands can also bet for protection. But SD hands can also check and try to pick off bluff or give up to a river bet.

In summary, the no SD value hands and occasional 7 gain the most from bets (44 and such). The medium strength hands like 88 A9 are strong enough to check down or pick off a bluff. The strong non-7 hands do fine by checking and betting or calling river unimproved. Should be even be betting here? Our range for betting will be really polarized, and I can't see a way to effectively merge our range (e.g. it's not like he c/c with K high vs our A high).

How do we gain more from bluffs without skewing balance? Solution is to check monsters and raise a proper proportion of our checked air hands as well as monsters. But the problem is that we rarely have a monster. Thus we can't bluff raise river too often.

The hard part is choosing correction action for hands like QJ (marginal SD value vs a river bet and some vs a check). How often do we pick off river bets with these? How often do we bet river when checked to? Playing rivers correctly is pretty tough. But with position it shouldn't be that hard. Does this balance even matter in this spot? This is a pretty rare board texture, but the ideas probably extend to similar spots. What do you think?

In Chapter 11 of MOP Chen analyzes some half street games. Half street games are poker games with one street of betting, in which only one player can do the betting. This situation comes up enough in practice to be useful to analyze. When at the river in position and the pot is big relative to stacks, the oop player often checks and his only choice is call or fold (effectively a half street game).

In these situations the in position player's optimal strategy is usually +EV. That is a powerful idea. It means that this player is +EV regardless (with the same EV) regardless of what the oop player does. Position is goot! Exploitive strategies need to be better than optimal to deviate. This is an obvious statement, but it illustrates that even players using exploitive strategies should understand some game theory in order to "know" when to deviate.

The key result of the chapter is the calculation of the optimal ratio of bluffs/valubets and the related optimal ratio of calls/folds for the ip and oop players. In the special case of NLHE with PSBs, this reduces to bluffing 1/3 often and calling 1/2 often.

There are a few ways to come up with the 1/3 and 1/2 frequencies. One way is to randomize your frequency with individual hands (call 1/2, fold 1/2 etc). That is the mixed strategy. Mixed strategies seem to occur when hand ranges are small. With large hand ranges, it's probably simpler to use absolute hand values to determine frequencies. For example, say you have 2 hands - tptk and two pair, both of which are the "same" against villain's range. The optimal strategy may have you call with two pair and fold tptk. Of course you could fold two pair and call tptk but that increases probability of bluffs with better hands. For most examples it appears that Chen models the range of hands with the interval [0,1] of real numbers. This makes calculations simpler.

Implementing optimal betting frequencies in practice requires an awareness of your own hand ranges. Obviously you need to know what your range is before choosing the 1/3 to bluff with. The final thought I want to mention is the inverse relation between payoffs and frequency. In optimal play, choices with high payoffs should be chosen with less frequently. The rowshambo example from chapter 10 is a good example. If you change the payoffs so that rocks has a higher payoff, the optimal solution requires that you choose rocks less frequently than in the equal payoff version. The intuitive reason is that you choose an optimal strategy vs the maximal exploitive strategy of villain. Since villain will also try to exploit the higher payoff, you have to do it less often to avoid exploitation. In real poker, you should bluff less often for $100 into $200 than you do when bluffing $200 into $200.

I will flush out my thoughts here on the subject. First, some definitions. An exploitive strategy is a strategy against a specific fixed strategy. For example, villain always bets $100 on the river as a bluff, so you call with all bluff catchers (the latter is the exploitive strategy, the former is an exploitable strategy). What we're familiar with is finding the maximally exploitive strategy (MES) (i.e. choosing the strategy to maximize EV against a particular strategy).

Optimal strategy is then derived from the idea of MES. We are hero, and suppose villain plays the MES against us. In other words, he adapts his strategy to maximize EV against our strategy. Hero's optimal strategy is the strategy with the highest EV against villain's MES. Equivalently, the optimal strategy makes villain indifferent between their various exploitive strategies (I'll leave it as an exercise. It is fairly simple to verify using the definition of optimal). This second definition (the exercise) is most useful in actually finding solutions to particular game theory problems.

There is an important property of optimal solutions worth stating. In practice, optimal strategies tend to be mixed. Mixed meaning that you choose action A X%, action B Y% instead of always choosing A or B. The key property is that the EV from any choice from a mixed strategy is the SAME. Say we're on the river and are deciding whether to bluff. If villain was exploitable we'd either bluff 100% or bluff 0%. If we don't know villain's tendencies we choose an optimal solution (against his MES). Something like bluff 30%. The key is that our EV is the same whether or not we bluff.

Thus, in the game theoretic approach to poker there is no value in choosing inferior strategies (i.e. -EV type plays for 'image'). Choosing inferior plays for future EV is a purely exploitive approach! Put more bluntly, game theory advocates believe that metagame is irrelevant.

I hope all that is correct. More to come.

I used to be a pretty passionate blogger, but things have gone down hill lately. Anyways, I am back now. The trip was great. I was in Dubai for over 3 weeks. We stayed at my wife's parent's place. Dubai is great for many things - shopping, food, and service is ridiculously better than in Canada. Most people there have maids and cooks... It is quite awesome not having to worry about the next meal. I don't have any good pictures. It's not the type of place where you can go around sight seeing (it was 45-50 celsius during the day). We stayed at a ridiculously baller hotel called Emirates Palace for my wife's birthday (each suite had 3 butlers lol).

While there, I had an interview with a banker at Citibank. They want me to pass the CFA exam (level 1) before bringing me on. I am aiming for a trading position in their forex division in Singapore (Singapore is their main trading center for currency). Thus I've been extremely busy studying for this exam. I apologize for the late replies to PMs. I am finally available for coaching!

That's all for now. I'm off to make a Party video (1/2 or 2/4)

I'm traveling to Dubai tomorrow for 3 weeks. My wife's parents live there. We are also going to Mauritius (Africa, near Madagascar) for a few days to celebrate my wife and her mom's birthday (it's on the same day). I'm going to mostly relax and eat tons of great food.

I made a sweet $100 NL video today on Party. It is 4-tabling the bad beat jackpot tables which are pretty sick loose right now. I won about 6 buyins and talked about the adjustments related to merging your ranges against loose players. There is more bluffing at $100 NL than I expected.

Leggo is really moving forward. Sauce and Unknown Soldier are great additions to the team, and more great things are coming in the future. It really annoys me when people on 2+2 give DeucesCracked and CardRunners so much love. I think pound for pound we have the best videos. Leggo almost never produces a subpar video. We are easily the best site for small-mid stakes grinders. Enough of the mini rant.

That is all for now. I will post trip pics when I get back. Be good.

So I did well on some of my May goals (reading books, some NLHE) but failed miserably at others (PLO 0 hands played, no poker reading). But that is OK I guess. I've been watching a lot of basketball and cricket which increases my life EV.

The coaching section is up and running now, and it is pretty cool. So I have been coaching a bit more lately. I also made a 2 part video series on the OnGame network. These should be up within a week. It was 2 tabling 1/2 5-max. I won about 5 buyins and the games were really good. But the software is life-tilt inducing so I probably won't make one on there for a while. Next video will probably be ipoker or HU SNG on Stars (the deep stack no blind increase ones).

I am no longer going to Vegas. I have to travel with my wife to visit her parents this summer, and I don't feel like going for just a week like last year. The up side is that I get to visit Dubai again, which is a really cool place. We will be celebrating my wife's and her mom's birthday (same day). Anyways, that is all for now. I will get around to reading Mathematics of Poker sometime, and will post a review when I do.

So I got my chair today. I absolutely LOVE this chair. It is so comfortable that I decided to just read/browse today instead of putting in hands. I'm going for a little live poker trip to Niagara Falls today. Spur of the moment thing...Maybe I am putting off putting in hands haha. I'll be going for 2 nights. I've heard there are juicy 5/5, 5/10, and 10/20 games there. Like poker trip report to come.