Posts Tagged ‘theory’

I’ve played more tournaments than usual in the past few months, and while I certainly can’t complain about how they’ve gone for me this year, I nonetheless find myself feeling frustrated at the end of virtually every Sunday. Last week, I started thinking about how a few years ago you rarely saw antes in tournaments. I can’t say that I put a lot of thought into this, but I felt like the larger pre-flop pots turned things into a shove fest, with every hand ending pre-flop and skill being minimized. Then I read this blog post by Daniel Negreanu:

Lower antes increase your M, which allows you to go into survival mode on a short stack for a longer period of time without feeling the pressure of going all in. Average big blinds per player in the tournament is what you’d look at to see how much “play” there is in a tournament. The higher the average big blinds per player is, the more streets will be bet, and the more maneuvering will occur post flop. A tournament that boasts a higher bb per player average is one that is clearly more skillful because more intricate decisions will be necessary. Deep stacked poker is just harder, plain and simple. That’s not debatable.  Read the complete post...

Thanks for all your help so far in generating this list. Now that I’ve got a revised version of it, let me try to explain a bit more about what I’m going for here.

I believe that a bet or raise should always have an objective (or objectives), and that you should know your objective(s) before betting. This is crucial both to decide whether to bet at all and to size your bets appropriately. In theory, one ought to be able to write an equation for the value of a bet as a function of some combination of factors on this list.

For example, if I make a pot-sized shove with As Qd on an Qh Ts 5s flop in a heads up pot, I believe the value of that bet would be equal to

Value + Protection + Deception

Some of these can be calculated more precisely than others. For Value, I can make an educated guess about how often he will call with worse hands and what my equity is against that calling range. Likewise I can determine how much equity his folding range has. Deception is much less precise, since we are talking about the extent to which shoving AQ here increases the profitablity of a shove with a hand like AJ in some similar future situation.  Read the complete post...

Even though I’m too sloppy/lazy/uneducated to work out the details of complicated problems, I’m quite interested in the mathematics of poker. I feel like I do have a broad grasp of the game theory that underlies many situations and can use that to aid in my decision-making. Recently, I’ve been curious about how to quantify exactly the value of seemingly abstract concepts like position and implied odds. I think I may have come upon a sketch of how to work some of it out, though I doubt I’ll ever follow up on it.

We start with the “exploitability”, the idea that there is something about how you play that an opponent could potentially take advantage of. Conversely, “unexploitable” means that there is nothing an opponent could do to take advantage of how you play. Importantly, unexploitably is not always the most profitable way to play. Often, you will do something exploitable in order to exploit something exploitable an opponent is doing.

Suppose that you hold AQ in the big blind in a $1/$2 NLHE game. The action folds to the SB, who open shoves for $20. If you know that this opponent will only shove JJ+ and AK, you can fold your AQ. Though itself exploitable, this fold exploits your opponent’s excessively tight shoving range.  Read the complete post...

I was sitting at two decent HSNL tables yesterday with the same very good player, and happened to stack him at both tables. At 25/50, he cold 4-bet TT and called my 5-bet shove. I had AA. At 10/20, he 3-bet 98s, I flatted with KK, we got it in on a 876 flop, and I won the flip.

He sounded like he’d had a rough week and was pretty tilted, started telling me I was terrible and trying to get me to play him heads up. As much as I complain about how nobody at 5/10 will play me, the truth is that I am also pretty nitty about only playing heads up against people I think I hae an edge on. I don’t have a ton of experience with this particular player, but he sits waiting for action at 25/50 and seems solid enough, so it’s a good bet that he’s better than I am.

Long story short, he offered me a 5% return on losses to play him. When I declined, he offered 7%. Now, there were some reasons I didn’t want to play him anyway. We didn’t get into terms, but he discussed it with another player, and wanted to play at least 3 tables of 25/50 for at least 1 hour. Although I will take shots when the games are good, I don’t actually have enough money on stars to play those stakes habitually. Plus, in order to focus, I’d probably have to quit most or all of the other games I was playing, some of which were reasonably good.  Read the complete post...

On my recent post, “Defining His Range Into Oblivion“, tce left a comment that I felt warranted a new post:

This is a tantalizing post with some really interesting ideas that need more meat. Can you say more? In my experience, trying to blow someone off an Ax hand is just too disruptive to my bankroll. Many players are just too stubborn and will chk-call all three streets. I finally learned that my best counter-strategy is to simply bet the hell out of my hand when I can beat Ax. Turning 2nd pair into a bluff in the hopes of blowing someone off Ax? I dunno, I need to hear more.

It’s a good question. This concept isn’t just a neat way to bluff. The point is that when you have position and a good sense of your opponent’s range, you have a generous edge because of your ability to make better decisions on the river. You want to have a big pot and also enough money behind for a big river bet, ideally with nothing left over in the effective stacks, to maximize that edge. Then, it’s just a matter of actually making that river decision.

Against this opponent, I’m confident that in a 4-bet pot, a bluff in that spot would be very profitable. Against a looser opponent who will not fold Ax, then you will value shove more hands and bluff less.  Read the complete post...

Full Tilt Poker, $5/$10 NL Hold’em Cash Game, 2 Players
LeggoPoker.com – Hand History Converter

Hero (SB): $2,434.50
BB: $3,954.50

Pre-Flop: T K dealt to Hero (SB)
Hero raises to $30, BB raises to $100, Hero raises to $255, BB calls $155

Flop: ($510) 3 A 2 (2 Players)
BB checks, Hero bets $199, BB calls $199

Turn: ($908) K (2 Players)
BB checks, Hero bets $480, BB folds

Results: $908 Pot ($0.50 Rake)
Hero mucked T K and WON $907.50 (+$453.50 NET)

If he called the turn, I was shoving the river. Position, deep stacks, and judiciously employed small bets are a lethal combination. It’s exceedingly difficult for him to show up with enough big hands to prevent me from exploiting him with river shoves.

If both players employ game theoretically optimal strategy, the advantage will obviously go to the player in position. His EV in the game will be a function of the pot size and the number of betting rounds, meaning that it behooves him to structure the betting so that there is roughly a pot-sized bet remaining on the river. He can then maximize his edge by making better decisions than his opponent about when he wants that last bet to go into the pot.  Read the complete post...

This was an odd format. If you lost all 5000 of your starting chips in the first two hours, you got a free T5000 rebuy. However, if you reached the end of those two hours with chips, even if you had less than 5000, you got nothing. Essentially, it was a use-it-or-lose-it insurance policy.

I entered the tournament with the expectation that I would play mostly normally for the first hour but push hard with draws or in spots that I thought were very slightly -EV and not make any big folds. I also reminded myself not to make any big bluffs, since theoretically others should be more willing to call down as a result of the Second Chance.

As the end of the two hours approached, if I was still in the neighborhood of 5000 chips, then I’d start getting crazier, eventually just open shoving in the hopes of either doubling up or using the free rebuy that was about to disappear.

With about half an hour left to go, I had over 8000 chips when I ran into this psychopath:

Full Tilt Poker, NL Hold’em Tournament, 60/120 Blinds, 8 Players
LeggoPoker.com – Hand History Converter

SB: 6,390
Hero (BB): 8,690
UTG: 9,080
UTG+1: 14,775
MP1: 5,756
MP2: 11,176
CO: 9,055
BTN: 6,018

Pre-Flop: (180) A 2 dealt to Hero (BB)
6 folds, SB raises to 480, Hero calls 360  Read the complete post...

Weeks ago, I got a comment that I promised to answer in greater depth. Well, I’ve finally gotten around to it. Here was the question:

I read with interest the blog in which you say that you use AQ as a four / five bet semi bluff.

With what hands are you getting called with?

I ask, because in analyzing how to play against Harringbots, I discovered that there are some unusual hands that do well against standard Harrington hand ranges. For example, KJs is almost as good against AQ+/77+ as AQo. The benefit of playing KJs is that opponents will automatically add KQ and AJ to your range which will presumably make the AA/KK hands even more profitable. Of course, KJs does not occur as often as AQo but playing AQo 2/3 of the time and KJs 100% of the time would give you the same semi-bluff frequency.

I think this is an interesting idea, particularly because of the deception it creates. As the commenter points out, people may assume that if you showed up with KJs you will also be shoving hands like AJ and KQ. I was frankly a little surprised when I ran the numbers and saw that the equity difference between AQo and KJs vs a range of TT+ and AK (in answer to the first question, it depends on the spot, but in general my 4-bets aren’t getting called by 77-99) was less than 1%.  Read the complete post...