Shabbir's Diary

I continue to improve against Sparbot

At my coach's urging, I have been playing heads up battles against University of Alberta poker bot, Sparbot.  It's the dumbest of their algorithms, playing a heads up hold'em game that's perfectly balanced without taking into account any opponent tendencies.  I'm playing it with it's configurable parameter set to "passive".

When I say "balanced", I mean it's bluffing bad cards enough, and slowplaying good card enough, that in theory you don't ever know what it has.  However if you play a conservative game and don't bluff a lot, and get a decent set of hands, I find that the balancing it does to it's game is a money loser.  Countless times I've called it down with a decent hand to find that it was bluffing and congratulations, you've confused me a little.  Now let me get back to stacking your (virtual) chips.

The same is true for slowplaying good hands, where you want to extract value but it doesn't for "balance" reasons.  When I get to draw for free against a better hand to a potentially better hand, and then make my hand, it's costing itself money, both in expected and real value.

Though my 16 sessions so far probably aren't statistically significant, there's a clear trend to them which I'm going to let my cognitive bias tell me means I'm getting better at playing this opponent. 

As a refresher, I'm playing 300 hand sessions against Sparbot.  At the end of each session I record my results, which gives a positive or negative "small bets per hand" for the session, either positive or negative, depending on if I made or lost money from my original buyin.  I'm not taking a rake out of the pot, since it's very hard to make a profit against the rake.  (I'd never make money, just lose less)

The blue line is a running average.  My opponent's algorithm has a slider setting for "passive" to "aggressive".  Sparbot is set to passive for this experiment.

Combinatorics in Texas Hold'em Limit Poker

Combinatorics is the mathematical technique of enumerating and analyzing combinations of objects.  If you've ever had a pair of pocket Aces preflop and had an opponent bet his whole stack against you, you did a form of this analysis in your head.  Presumably your reasoning went something like this:
"I have the best hand.  Any two unpaired cards or any other pair is an underdog to me.  On the rare chance that my opponent has Aces, we're at best dead even in probability to win this hand.  Over all those hands, I'm an overall favorite, I shove."

Combinatorics are not necessary in that situation since the math is obvious.  But what about later in the hand, when you've got something less than the nuts and you've got to examine the range of hands that intersect with the common cards on the board?

When you don't have the nuts, knowing where you stand is important.  When you're a solid favorite, without the nuts, you should still raise when you're a favorite versus the likely range of your opponents hands.  Here's an example from a recent Limit Texas Hold'em $.50/$1 heads up game I played at Pokerstars.   If you want to practice your heads up Texas Hold'em, I recommend you pick an online poker site from this list.  If you're going to play at Pokerstars, use this Pokerstars marketing code.

Ok, onto the hand.  I'm the Hero, my opponent is the Villain, obviously.

Preflop: Hero is Button with , 
Hero raises, Villain 3-bets, Hero calls

I'm not going to do too much preflop analysis here, but suffice to say that my hand is in the top 15% of all hands, so not only should I raise it, but I can call three bets.  (One might argue that I missed a chance to cap it. I would not disagree)

Let's see how the rest of the hand went down.

Flop: (6 SB) , ,  (2 players)
Villain bets, Hero calls

Turn: (4 BB)  (2 players)
Villain bets, Hero calls

River: (6 BB)  (2 players)
Villain bets, Hero raises, Villain 3-bets, Hero calls

Total pot: $12 (12 BB) | Rake: $0.50

Results:
Hero had K, 10 (two pair, Kings and tens).
Villain had K, A (two pair, Kings and eights).
Outcome: Hero won $11.50

Our villain's line is Bet-Bet-Bet/Raise.  (That means "Bet on the flop, Bet on the turn, and bet and re-raise on the river).  What possible hands fit that line and also put in 3 bets preflop?

• Some combinations of 8x would play that way.  The preflop 3 bet implies A8s, A8o and K8s.  I could also add 98s.
• A number of pairs would play this way, including 66, 88, TT, JJ, QQ, KK, and AA.
• Some combinations of Kx would play that way, including AK, KQ, KJ, and KT.  
• An aggressive player might play 97 this way, betting until they hit their draw.  Definately 97 of diamonds, since it would have an ungodly number of outs with the flush draw.
• A flush draw being played aggressively this way might bet every street on the come, but wouldn't three bet the river without hitting something, such as an 8, a K, or maybe a T.  I would think we'd have to be looking at a pretty strong draw, such as A8 diamonds, AK diamonds, or maybe AT diamonds.

So that's the range we're up against.  Given those chances, what's my overall chance to win this?  How strong am I?

So check this out, 26 times out of 66 results, I lose.  That's 39% of the time.  36 times out of 66 results, I win, that's 55% of the time.  The board has a straight, three of a kind, and even quads on it, and yet my hand beats most of the hands that would play this same way.  Clearly, I should at least raise and then call 3 bets if it comes back.  Putting in a fourth bet is somewhat player dependent, but I chose not to.

Quite often, you find yourself in this situation and because there are so many hands that beat you, that you check/call or call the river, when in fact you should be raising with a hand that beats most of the field.

Of course, you can also do this the easy way with Pokerstove.  Just load these up options into Pokerstove and run the results:

There are shortcuts you can learn that lets you quickly figure out how many hands are out there, but that's a topic for another post.

Heads Up Poker Hand Selection

So for my Internet poker practice I’ve been almost exclusively playing heads up limit Texas Hold’em lately.   I don’t claim to be particularly good at it yet.  I’ve written before about my efforts to beat sparbot, an AI that plays a perfectly balanced game theory variant of Hold’em, but playing a real people online is a different game.  There’s some key differences in the game that are worth pointing out:

Stack size affects decision making
This is true at a full ring, and even more true heads up.  When you get down to just a few big bets, people go on tilt, calling for draws that wouldn’t otherwise make sense.

Hand standards seem appallingly broad as compared to full ring play
When you’re playing 70-80% of your hands, you don’t feel like you have any standards.  What does 60% of your hands look like?  Here’s a handy table:

Top % Of Hands	Range (Shorthand Pokerstove notation)
60%	22+,A2s+,K2s+,Q2s+,J2s+,T3s+,95s+,85s+,75s+, 64s+,54s,A2o+,K2o+,Q5o+,J7o+,T7o+,97o+,87o
70%	22+,A2s+,K2s+,Q2s+,J2s+,T2s+,93s+,84s+,74s+, 63s+,53s+,43s,A2o+,K2o+,Q3o+,J5o+,T6o+,96o+,86o+,76o
80%	22+,A2s+,K2s+,Q2s+,J2s+,T2s+,92s+,82s+,73s+, 62s+,52s+,43s,A2o+,K2o+,Q2o+,J3o+,T5o+,95o+, 85o+,75o+,65o,54o

Depending on who you ask, you should play 60-80% of your hands in heads up Limit Texas Hold'em. One wonders what you wouldn’t play in that situation, but remember 60% is the conservative hand range for heads up.  I’ve heard people talk about playing 80% of those, and that’s a lot.

I find myself raising on the button preflop with the top 30-35% of my hands or folding.  On the big blind preflop, I play a solid 70-80% of my hands, and often fold all but the top 30-40% if I get raised.

Position is huge
Tommy Angelo says that position is important in poker is like saying water is important in swimming.  It can’t be understated.  In heads up that especially true, as paying that turn bet may be the difference between a wildly unprofitable hand and a moderately profitable one.  You want to of course loosen your standards with the button, and raise a lot more of your hands.  How much depends on your opponent, of course.

You’re paying, always paying the blinds
Heads up takes a lot of getting used to because you’re always paying a blind.  That fact can start to wear on your psychologically and cause you to want to open your range, but it’s a bad temptation.  Your range is already absurd to begin with. 

I find that playing lots of heads up poker helps me with my full ring poker game, because it allows me to really focus on reading my opponents.  It’s also great practice for final tabling tournaments.   If you’re interested in practicing heads up, I suggest you try out these Top US Poker Rooms.  Many of them run heads up tables.

Poker coaching

So at the beginning of September 2008 I asked a poker player who had never coached before to be my coach.  The rate we agreed upon is in line with what I've seen others coaching, in fact a little less.  Since he's never coached before, we sort of made it up as we went along.

Every week I do homework, usually based around my play from the previous week.  I've played about 7,400 hands online since we started, and 130 hours live.

Here's my graph of live results, BB/hr.  It's taken a while but my live losses have declined.  I've eked my way up to an average profit of 0.10 big blinds per hour.  The BB/hr is a measure that poker players use to try and compare games played at different stakes.  If you play $3/$6 limit texas hold'em and $6/$12 limit texas hold'em it's hard to compare, since you'll win at different rates because of the higher stakes.  But if you divide your winnings in every session by the size of the big blind (in this case $6 for $3/$6 or $12 for $6/$12) then you can compare win rates at different stakes for the same game.

Live I'm almost a break even player, but online the results are clearly positive.  This is my running average of BB/hour for $0.25/$0.50 Limit Texas Hold'em.

 
I have always been an unprofitable online player, and I have played about 5,000 hands of $0.25/$0.50 Limit Texas Hold'em since I started my coaching.  Over time I have become consistently though mildly profitable.  It only took about 3 months of work to get there.

I've sampled the $0.50/$1.00 and $1/$2 Limit Texas Hold'em games online and I've found they change intensely by the time you get to $1/$2.   At $0.25/$0.50 you see 6 or 7 people see the flop.  At $1/$2 online 2 or 3 players see the flop.  This is analogous to the range of play here in SF as you travel from $3/$6 to $6/$12 and up to $15/$30.

The progress continues.

Poker homework: what hands beat you?

So my coach and I were talking about some different ways of doing board analysis, and he suggested I compute "the hands that beat me" on every street.  Getting significantly better at board analysis is important as I move up limits from the microstakes I've been playing.  While I'll continue to use poker bonuses on different online poker sites to pad my winnings, no bonus is big enough to keep you from being a consistently losing player.

The basic theory I'm following for hand analysis is this:

1. There are 1,326 possible Hold'em hands. 
2. On every street, it's possible to compute the number of hands that beat me and that I beat.
3. Based upon how you improve (and how many hands that used to beat you improve) it's possible to make some intelligent decisions about how to play hands that fall in that weird area that aren't the nuts, but also aren't weak enough to check-call.

Here's the hand I chose to analyze:

Full Tilt Limit Hold'em, $0.50 BB (9 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com

Preflop: Hero is MP2 with A, 3
2 folds, Hero raises, 2 folds, Button 3-bets, 2 folds, Hero calls

Flop: (7.4 SB) 4, 10, Q (2 players)
Hero bets, Button raises, Hero calls

Turn: (5.7 BB) A (2 players)
Hero bets, Button raises, Hero calls

River: (9.7 BB) 6 (2 players)
Hero bets, Button raises, Hero calls

Total pot: $6.85 (13.7 BB) | Rake: $0.30

So it isn't that hard to see why I lost.  By ignoring the hand range of a preflop 3 bettor, I should have easily saved myself at least one big bet (BB) on the river, and possibly one on the turn as well.  But another way of looking at the hand is by examining what hands I could beat that were likely to be playing.  This analysis is another way of seeing that I should have been slowing way down with this hand.  Let's go through it:

Preflop: Hero is MP2 with A, 3
2 folds, Hero raises, 2 folds, Button 3-bets, 2 folds, Hero calls

Flop: (7.4 SB) 4, 10, Q (2 players)

At this point in the hand I've got a nut draw, but actually only Ace High.  Against a random set of playable hands I can beat A2 and KJ.  All the pairs beat me (22+), all the Ace-anything with 4 kicker or better (A4+) along with all the broadways containing a T or a Q (Tx+ and Qx+).  This flop is eminently checkable.  It also shows why if I was holding AK, I could bet this flop.  Because I can beat anyone who missed the board and for many who hit the board, I could out draw them.

If I'd done the "what would a solid preflop three bettor have?" I could have narrowed his range to AK, AQ, and 88+.

Of course I don't do that, I bet, get raised, and call.

Hero bets, Button raises, Hero calls

I accurately read my opponent here for a Q but figure I can draw out with the Ace or the diamond flush.

Turn: (5.7 BB) A (2 players)

This changes things, of course.  All I see is the Ace, but though I am brought an Ace, that Ace helps a lot of other hands that can beat me.  I can beat KK,JJ,99,88,77,66,55,33,22, but I can't beat Ace-anything except A2.  I can beat Ten-anything unpaired and Queen-anything unpaired, which is what I thought my opponent had.  Had I been analyzing better, I would have seen there's little left that would raise me.

Hero bets, Button raises, Hero calls

        

River: (9.7 BB) 6 (2 players)

Finally on the river, my flush doesn't come.  This would be an opportune time to check.  Luckily I did not.  I can beat only Ace-Two, pocket pairs that didn't hit the board, and overplayed queen-something or ten-something.  Everything else hit the board better than me.

Ah, but I bet anyway, and predictably got raised.  My opponent shows down Ace-Queen, no surprise.

It's a good technique for analyzing where you are in a hand, and I hope to do more of it (and a more mathematical version update to this soon.)

Incidently if you're hunting for a new online poker site, make sure you read one or two poker reviews before picking one.  Or you can just find a poker site toplist from someone you trust.

Dealing with a blinds thief / stealing the blinds / defending your blind

It happens all the time in Hold'em: you're in the big blind and some jackass goes to steal your big blind.  Stealing blinds is good money in a casino that doesn't rake until the flop, but to be successful at it you have to be able to play after the flop or pick on a weak player who always folds to your raise.  Take the situation I've shown below:

Assuming you've got a small or medium pair, nines through twos, your odds against anything from a tight raiser through a loose raiser are pretty good.  Assuming your opponent is willing to raise with 12% of his hands, you and him are 44%/56%.  Assuming he'd steal with half of all the hands he is dealt, you're actually a slight favorite (54.5% / 45.5%).

Though you're not going to have the advantage of position, if you can play after the flop you might be able to take control of the hand if you hit one of your hole cards on the board.  The pot is offering you a little better than 3 to 1 odds to call, and at no time are you a 3 to 1 underdog with these cards.

But what if you don't have a pair?  I've computed some other useful odds against an opponent who would be willing to raise half of their hands:

Assuming your opponent steals with half his hands
Your hole cards	Your showdown equity
Any two Broadway cards (AKQJT)	59%
Any two suited cards	43.4%
Any pair	62.2%
Any Ace or King	52.8%

The upshot of this is that you're unlikely to be much of an underdog when you sense someone is stealing your blind, and while you may want to call for meta-game reasons, such as you don't want to establish the fact that your blind is easy to steal, you have a little math behind you as well. I computed all the math here with PokerStove, an awesome tool you should be using to scenario out these situations.

Things that make me happy

My poker tutor doesn't think I'm a complete idiot.  He sat behind me today while I played a 3 hour session at my local cardroom and gave me a lot of really good advice, none of which was, "You need to go find a lower stakes game while you figure out how to play poker." :)  A number of hands he said he would have played just the same as I actually did.

I complete the drip irrigation system for Sarah's vegetable garden.  It's very conservative in the amount of water it uses.

Modeling $3/$6 players

I'm doing some math modeling of hand equity of various hands with pokerstove.  What happens to JJ at a table when someone raises,and you've got 2, 3, 4 players?  What if they're solid players?  What if one is a complete donk?  Does the hand have a positive or negative expected value?

If you were doing a player model, would you use these profiles?  Remember, this is casino $3/$6, the lowest level of limit hold'em offered.

Typical raiser:

• TT+ (tens or better);
• ATs+ (Ace-Ten-suited up through Ace-Jack-suited); and
• KJs, KQs, AQo, AKo, and KQo

Typical caller of said raiser:

• 22+; (any pair, in the hopes of flopping a set)
• A2s+ (any suited ace for a flush or two pair);
• 54s (all suited connectors bigger than 54 for a straight or baby flush); and
• ATo+ (all Aces with a ten kicker or better, hoping I'm raising with a small ace or KK-TT)

And just for good measure, when I'm doing the math for callers, I'm assuming that the fifth caller of the raise is a complete donk, and will call with the following hands:

• 22+ (any pair);
• A2s+ or A2o+ (any ace, suited or unsuited, with any crappy kicker);
• 32s+ or 32o+ (any connector, suited or not); and
• K2s+, Q2s+, and J2s+ (any suited piece of junk hoping for a flush).

Do I need to tell you that the "complete" donk profile is a negative expected value play? 

Are there some bad habits of low limit players you know of that I should include in this math?  (I mean, besides obsessively playing 72 for show value.)

How do you play Aces when there's an Aces cracked bonus available?

For reasons more complicated than I can explain here, my weekday schedule has me awake when everyone else is asleep from 4:30am or 5am onwards.  Tuesday through Friday I've been spending 2-3 hours every morning at my local poker room.  (Yes it's surprisingly full at that time of the morning)

From 6-9am they have a bonus: $100 if you get your Aces cracked.  Since I've been playing almost exclusively $3/$6 limit hold'em, this sets up a fascinating dynamic for those interested in how to maximize value.  I've been dealt Aces at this time of day at this game almost three times, so it's worth examining it as a poker question.

This morning I was in the big blind and dealt bi-racial Aces (red and black) of hearts and clubs (AhAc).  Six random players called, which includes the small blind, and I'm put to a decision.  Given the stakes of the table, I think I want to see my Aces cracked.  The $100 bonus is greater than the size of the pot I'm likely to win.  I want some other player to catch up and beat me.  I really really want everyone to play this hand.  So I check.  The flop comes AdQd3c.  Crap, I've hit a set.  Suddenly it's more likely that I'm going to win this pot, and I don't want to win $21 (-$4 rake), I want to win $100.  The small blind bets out, I call, and two other players call.  Pot is $29.  Turn is a 9c.  Small blind checks, I check and hope someone with a club flush draw decides to stay in now.  Everyone checks.

River is a 10d.  If there was a diamond flush draw out there, they've just made their hand and beat me.  Also, a straight, though I can't imagine anyone betting a straight on a flush board like that.  The small blind checks, I check also, and a middle position player bets.  The next two players fold and it's up to me.  I've played this hand so passively he might be betting with just a queen, but he could also have two pair.  I decide I want to shove a little more money in the pot in case I win it so I raise.  My opponent just calls.  The pot is now $53 and my opponent shows KsJd for a straight.  I show my set of Aces and the floorman comes over to give me $100 for cracked Aces.

So how should one play this?  According to pokerstove my equity against 6 random hands is 43%.  I believe that means I need to have at least $43 in the pot to have earned the equity my Aces deserve. 

The only really complicated decision is before the flop.  Assuming nobody folds, I could have pumped the pot to $42 immediately.  (At $3/$6, nobody folds when the big blind raises)  However I believe that unless someone had hit something and gleefully tried to take the pot from me, it would have stayed there and my gut shot straight drawing opponent might have folded had anyone bet on the turn.  Adding another two big bets to the pot ($12) would have put it at $54 (-$4 rake), pretty much the same thing I ended up with.

I think the right play here is to let as many players in as possible, and then play the hand without too much emphasis on value because you're dancing the knife edge between winning a respectable pot on the river and chasing away anyone drawing thin who might catch up and win you the $100 bonus.  What do you think?

As another aside, should I count the $100 bonus in my totals?  I religiously record every session's numbers and weird spikes like this certainly warp my numbers.  So far this year I've won $227 total over 52.5 hours of play, averaging out to about $4.33 / hr.  A session with $100 jammed into it certainly warps that a bit, but one assumes the rake has a downward effect on it as well.

This is totally situational as well.  The Bad Beat Jackpot, which I'm incredibly tired of hearing the $3/$6 players obsess about, stands at $170,000 right now.  Were I to hit it and win $85,000, it couldn't possibly be right to put it into my numbers.  Even my portion of the table share at $6,000 or so would make me look like an unfairly brilliant low limit hold'em player. 

I've had aces cracked in this situation twice, winning the pot once.  Since my early cardroom shift appears to be my poker time for the forseeable future, I'd be curious what you think about the right mathematical strategy here.

A raid in Maryland; my poker game; my big yard project

It hasn't hit the news yet, but there was another SWAT team raid of a poker game in Maryland in the last week.  This time it appears they just confiscated the money and chips, cards, and tables.  Perhaps they will press charges later, but on the whole, I suspect this is just easy money and easy ways to up their misdemeanor/felony count.  Raiding a poker game run by ordinary people is very unlikely to turn violent, or even turn up a weapon.  You go in, collect the cash, take down names, and notify them later of their charges.   60 days surveillance by a detective and one night's work by a SWAT team.

My poker game continues to be in free fall.  I'm focusing entirely on my limit hold'em game using the math I've worked out at the direction of my coach.  While my game is better, my results are not.  I know I'm playing better hands, and playing them in a more positive expected value manner, but I don't have any bottom line result yet.  It will come, and thankfully I'm playing at stakes suited to my bankroll...

Finally, I started a big yard project Sunday.  We're clearing an 18'x22' spot in the backyard to be Sarah's formal vegetable and herb garden.  I pulled up almost half a dozen bamboo plants that had been planted a while ago.  If you ever feel the need to plant decorative bamboo, let me urge you not to.  It's like burying nuclear waste in your backyard: it creates problems for the next owners of your house down the line.

I pulled up one plant and found six different runners growing outwards from the plant, trying to spread.  As I tore up flagstones chasing each on with my shovel, I began to get aggro.  Every time I finished one I looked at the remaining bamboo with my giant bolt cutters in one hand and my newly purchased Home Depot axe in the other, asking, "Who's NEXT?  Who wants a piece of the Shabster!?  Bring it on, frakkers!"

We literally now have over a hundred pounds of compostable material in our yard that has to go.  I've moved it into a temporary spot so I can grade and till the remaining soil.  For the grading task I'm using a line level with some string and leftover rebar.  It's going to be a lot of work, but I've got the strength, and time, and it doesn't require any complex skills.  Once I've got the yard leveled we'll build the retaining walls around it, and then bring in 6 inches worth of dirt.  Sarah says we need compost, and I think that's an awesomely huge amount of dirt.  This calculator says I need 6.3 cubic yards of dirt, and this other calculator says that dirt is going to weigh a total of 21,262 lbs, which will also equal over 500 bags.

I'm going to have to do this in stages, as there's no way in hell I can lug that much dirt in at once.   Even if I hired every day laborer in the city.