KKing David

Ruminations on poker

Archive for the tag “Equity calculation”

Great Flop for Me

It was Saturday night, which means I’m playing poker in someone’s garage.  Just about everybody is a regular player, so we get to do some higher level thinking.  Level 1, of course, is just thinking about the strength of our own hand.  We like it, or we don’t like it, or we’re not sure.  Level 2 is thinking about our opponents’ hands.  The more we have played with somebody, the more we should know about their style and tendencies and use that information to our advantage.  They should be doing the same.  Level 3 is thinking about what our hand looks like to our opponents.  While we know our exact cards, they don’t, so we can consider what our hand looks like from their perspective.  Level 4 flips back to their hand.  What will they think we are putting them on?

On the button, after several players just call the big blind, I look down at JJ.  I like my hand (Level 1).  So far, no one has a hand worthy of raising.  I don’t know their exact cards, but any hand better than mine would have raised already (Level 2).  When I raise, some of the players will think I’m just attacking the limpers and won’t give me credit for a hand as strong as JJ (Level 3).  So I can raise more than normal and still get called by worse hands.

I raise to 8.5 big blinds (BBs).  The BB calls and so do two of the limpers.

Flop (37 BBs):  4d 4s 2d.  This is a great flop for me.  There are no over cards to my JJ.  While there is a diamond flush draw and a possible straight draw, a paired board makes the flush draw less attractive to anyone who has it, and the straight draw cannot be open-ended unless someone limp/called with 53.

Everybody checks to me.

I still like my hand.  It should be best here (Level 1).  While no one has shown any strength (Level 2), any of these players could have a single A, K or Q, or two diamonds, or a lower pocket pair that could turn a set, so I’m not giving them a free turn card.  I bet 20 BBs, just over one-half of the pot.  Some weaker hands will call another bet, including flush draws and low-medium pocket pairs like 55-88.  They would expect me to make a continuation bet on this flop with close to 100% of my pre-flop range, which they would think includes a lot of unpaired hands (Level 3).

The BB folds, but the next guy raises to 60 BBs.  For purposes of this blog, I’ll call him “Myles.”  Myles likes to see lots of flops and is willing and able to be bluffing here if he thinks I’m just trying to steal a pot with my favorable position.  He knows his check/raise would look very strong, and I would have to consider the possibility that he has trip 4’s or better (Level 4).  As I start to ponder the meaning of his check/raise, the next guy announces that he’s all-in for about 180 BBs.  For purposes of this blog, I’ll call him “Rob.”

Wow!  A big check/raise from Myles, followed by Rob’s check/re-raise shove.  Similar to Myles, Rob likes to see lots of flops.  Even moreso than Myles, Rob will try to steal a pot with a big bluff when the board gets scary or he thinks his opponent is weak.  Both of them initially limped in, then called my largish pre-flop raise, which makes both of them more likely than me to have a 4 or pocket 22’s.  Myles has Rob covered, while I have the smallest stack with about 75 BBs remaining after my flop bet.

Let’s try to figure out where we are (Level 2), while trying not to wet our pants.

I can rule out AA, KK, QQ based on the pre-flop betting, so the only holdings that beat me are any 4x or 22.  That’s it.  And most 4x hands are pretty junky and would have folded pre-flop.  Calling hands might include A4 (suited or unsuited) 64s, 54s, and maybe 43s.  That’s not many combinations: after eliminating the cards on the board, there are 3 possible combos of 22, 8 combos of A4, 2 combos each of 64s, 54s, 43s.

I don’t think Myles would have called my pre-flop raise with A4 off-suit, but he might with A4s, 64s or 54s.  Not with 43s.  Not with K4, Q4 or worse.  He also could have a diamond draw, with Ad2d+, Kd8d+, Qd9d+, or suited connecting diamonds from JdTd down to 6d5d.  He also could be on a pure bluff, or could have a medium pocket pair that he thinks is the best hand (55-99).  But that assumes he always check-raises with his flush draws.  In reality, sometimes he does and sometimes he doesn’t.  I’ll eliminate about half of his flush draws (including AdKd, AdQd, AdJd and KdQd all of which would have raised pre-flop), resulting in a range of 99-44, 22, A4s, AdTd-Ad8d, Ad5d, Ad3d, KdTd+, QdTd+, 6d5d, 64s, 54s.  Heads-up against that range, my JJ has 77.4% equity and I should call.

But Rob went all-in, AFTER seeing Myles’ check/raise.  That scares the shit out of me.  He could have the same 22 or 4x hands as Myles could, plus I have to include K4s, Q4s and 43s in his range as I’ve seen Rob surprise the hell out of people before when he makes a junky call and hits the flop hard.  I’ll also include A4o.  He too could have a flush draw, but if he does in this spot, it should only be an A-high flush draw (as with Myles, excluding AdKd, AdQd or AdJd as he would have raised pre-flop with these stronger suited aces).  Rob shouldn’t be shoving here with weaker flush draws because he should know Myles might be on a flush draw too, and shoving a non-nut flush draw and getting called by a nut flush draw would be disastrous.  Rob’s resulting range is stronger than Myles’ range: 99-44, 22, A4s, A4o, AdTd-Ad3d, K4s, Q4s, 64s, 54s, 43s.

Against both of these ranges, my equity is 39.7%, compared to 35.8% for Rob and 24.5% for Myles.  Something about a check-raise following by a check-re-raise makes me feel quite certain that I’m crushed here on this flop that initially looked so good for me, and I expected the math to be even worse that this.  It will cost me 75 BBs to call, for a chance to win (assuming Myles also calls) approx. 320 BBs.  If my equity is greater than 75/320 = 23.4%, calling would be the mathematically correct play.

I take my time, and finally fold.  I couldn’t work out all of the math in my head at the table, so I went with the old “Hashtag: they always have it” and concluded that at least one of them had me crushed.

Myles takes his time, asks Rob if he has a 4 and if so how good is his kicker.  Then he declares that he might as well gamble and calls the all-in bet.

The turn is Qc.  I don’t recall the exact river card, only that it wasn’t a high card or a diamond and didn’t change anything.

Rob turns over Ad6d.  He did indeed have the A-high flush draw.  We can debate the merits of shoving over the top of Myles’ check/raise there, but that’s what he did.  Myles turns over Qd9d, a weaker flush draw.

This burns me up when I first see it, as I was ahead of both of them when I folded.  Later I entered their exact hands and my equity was 53.7%.  Putting in 33.3% of the money and having 53.7% equity is a profitable play all night long, and I definitely should have called.

Then Myles sees that the queen on the turn paired one of his hole cards, giving him 2-pair queens and fours, and he scoops in a pot that totals over 415 BBs.  My JJ would have lost anyway.  That doesn’t change the conclusion that I should have called, however.  Against the ranges I constructed and against the actual hands, calling would be the correct play.  If both Myles’ and Rob’s cards were face up, I would call, especially knowing their flush outs partially cancel each other (and I was holding another out with Jd).  But I folded instead, then got the reverse of “lucky” since part of the draw hit anyway.  What looked like such a great flop for me cost me about 1/4 of my stack and I was lucky not to lose all of it.


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Stuck in No Man’s Land

Last night I was at a low-stakes, private poker game marked by some very loose play.  There was frequent straddling as much as 13 BB’s, along with very light pre-flop raising (like 95s), light 3-betting, and light calling of 3-bets (with hands like T4s and 53s – the latter making quad 5’s).

It was a poker table ripe for Justin Bieber to sing, Roller Coaster, Roller Coaster.

For the most part, I was taking good advantage of this.  I bought in for 140 Big Blinds (“BBs”), felted one of the players with AQ v KQ on a Q-high flop, then felted the same player again with TT v JT after he limp/re-raised all-in with a short stack pre-flop, and built my stack to over 300 BBs.

A little later, I look down at AKo in early position, and raise to 7 BBs.  While this may seem like a large initial raise to online or casino players, it wasn’t unusual here.  My starting hand is very strong, but plays best post-flop against just one or two villains.  If I only raise to 4 BBs, everybody at the table might call and it becomes hard to know where you stand after the flop and turn.  There is one caller, then another player re-raises to 21 BBs.  For purposes of this blog post, I’ll call him “Mitch.”

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This is the first time I’ve played poker with Mitch.  He is a young white guy, early-to-mid 20’s, dressed like he just came from a  strange 70’s themed party – wearing what appears to be bicycling shorts, a casual shirt, old school nearly knee high basketball socks (white, with wide colorful stripes at the top of his calves), and low-cut white Chuck Taylors or similar footwear.  With a cap sporting the logo of Nag’s Head’s Lucky 12 Tavern and dark sunglasses to look like a real poker player, the whole look makes quite an impression.  I don’t really care how people look or dress, other than sometimes there are clues that help in profiling them as poker players – loose/tight or passive/aggressive or gambly or playing with a very small bankroll or whatever.  I suppose the impression here was not to be surprised by unconventionality.

Earlier in the game, Mitch had called a river all-in bluff on a very scary board (K-9-7-6-5) with KTo and won a large pot.  At the time, I was thinking that I would have folded there.  Before that, he had called a pre-flop raise from me with 92s and made a backdoor flush to beat my trip kings.

I’ve also noticed that Mitch is very friendly with another player, the one that I’ve already felted twice.  Apparently they drove to this game together and have been chatty between hands.  Mitch’s friend has a wild streak, making several large bluffs, showing his bluffs multiple times when were successful, and generally playing in a way that indicates a complete disregard for the value of his money.  Do birds of a feather flock together?

After Mitch’s 3-bet, there are two callers.  Both are very loose players who like to see lots of flops.  Perhaps both have played more than I have with Mitch and their calls indicate a certain lack of respect for his 3-bet.  I have experience with these callers, and think either of them would 4-bet here if holding a monster hand.

With all this in mind, I decide to make a sizable 4-bet myself.  With one ace and one king, I have blockers against Mitch having either of the hands I fear most – pocket aces or pocket kings.  Having started the betting from early position, I can credibly represent a monster pocket pair.  If I raise large enough, the two players who called Mitch’s bet would be forced to fold.  I make it 105 BBs.

Take that!

One player who called my original raise quickly folds.

But Mitch starts counting his entire stack.  He has 130 BBs more on top of my raise, and ships it all in.  I have him covered.

Right then it dawns on me that I’m in No Man’s Land, that terrible spot where you realize charging forward is a mistake and retreating is no good either.  In my youth I played a lot of competitive tennis.  On a tennis court, No Man’s Land refers to the area in front of the baseline, where it is difficult to make normal groundstrokes, but behind the service line, where you cannot make volleys either, at least not hitting the ball at a height that creates enough leverage to hit the ball hard or use sharp angles.  In No Man’s Land, all of your options are bad, unless you enjoy being yelled at by your tennis coach.

Another player folds.  The last player hems and haws a bit, asks for a count of Mitch’s chips, and also goes all-in, for less than Mitch’s stack.  For purposes of this blog, I’ll call him “Chuck.”  [This is really important, as I know Chuck (or whatever his real name might be) desperately covets a mention in this blog.  I hope he leaves a snarky comment after reading this.]  Chuck had about 180 BBs at the start of the hand.  His call surprised me, as noted earlier I thought my 4-bet would squeeze him out.  Even when he called, I interpreted that more as a desire to gamble over a huge pot than an indication of great strength.  Still, he could have at least one ace or king, or both, that would cancel some of my outs in the event Mitch has something like QQ or JJ.

Even so, I really don’t think Mitch has QQ or JJ.  Despite my blockers, he virtually always will have AA or KK here.  My 4-bet was so strong that his 5-bet must be stronger.  Hopefully it is KK and my ace is a live card.  Otherwise I’ll be crushed.  This is where my mistake becomes more clear.  I failed to make my 4-bet small enough to keep an exit strategy available.

Let’s review.  I’ve put 105 BBs into the pot.  Mitch has put in 235.  Chuck has put in 180.  Two other players put in 7 and 21, respectively, and later folded.  So the pot has 538 BBs in it, and it will cost me 130 more to call.  I’m getting pot odds of 4.14-to-1 to call, meaning I have to expect to win at least 19.5% of the time for calling to be mathematically, theoretically the proper thing to do.  How can I really justify folding here, even though it’s obvious that I’m in big trouble?

Some more math… heads up against Mitch, the villain I’m most worried about, if his range is AA/KK – which I consider most likely despite my blockers – and nothing else, my equity is 18.6%.  If I think he would also shove here with AKs or QQ, my equity is 33.3%.  Despite all the loose play at this game, I can only assume Mitch has a monster.  After all, loose players still get dealt monster hands just as frequently as tight players.  And not so long ago, I wrote a post entitled “Hashtag: They Always Have It.”  Mitch didn’t hesitate much before going all-in, so now I have to go with this read.

That’s heads up.  What about Chuck?  His range should be wider that Mitch’s, as his body language when calling all-in didn’t ooze great strength.  But he could have blockers to some of my outs.  Let’s give him a range of TT+, AQs+ or AK.  Against that range and Mitch’s AA/KK, my equity drops to 13.1%.  If we again widen Mitch’s range to include AKs and QQ, my equity improves to 20.4%.

Chuck could have some random suited connectors too – perhaps suspecting that Mitch and I have all the high cards and hoping for a hand like 98s to sneak to victory.  So I’ll add 98s and 87s to his range.  This, with Mitch at AA/KK would leave me with equity of 13.8%.  With the wider range for Mitch, I’m at 21.6%.  Chuck’s range has far less impact on how I stand than Mitch’s range, but if Chuck’s actual cards include any aces it kills a very important out for me.

I’m not doing all this math in my head at the table.  With Chuck’s chips in the middle now, it seems like a mandatory call.  I make the crying call, not at all happy, but would still have nearly 100 BBs left if I call here and lose.  If I had made a smaller 4-bet, say in the neighborhood of 60-75 BBs, I would have less hesitation about folding and saving my chips.

As the dealer sorts out the main pot and side pot, Chuck asks who has pocket aces.  Mitch says he has cowboys, i.e., pocket kings.  I actually feel a slight sense of relief at hearing this.  I say that I have one ace, but not two of them, and turn over my Ace of spades.  Mitch turns over his King of spades, then a red king to go along with it. Chuck doesn’t turn over either of his cards, but looks like he’s in a lot of pain.

One more bit of math:  against Mitch’s exact hand, which we now know for sure (and ignoring Chuck, since we still don’t know what he had), my equity is 30.3%.  If Chuck had folded to Mitch’s all-in bet, the pot would have been 389 BBs with 130 more for me to call.  I would need to have greater than 25.0% equity to justify calling.  While calling would be correct, it is only correct because of my betting mistake when I made such a large 4-bet that I stepped into No Man’s Land and pot-committed myself without consciously intending to do so.

If you’ve read this far, I’m pleased to report that a beautiful ace fell on the flop, and I won the whole freakin’ thing.  That’s poker I guess, and I’ve certainly been on the other side many, many times.

My stack grew a little bit more by the end of the night and I booked a very nice profit of 700+ BBs.

Thinking about Mitch’s 70’s theme appearance… That’s the way, uh-huh, uh-huh, I like it!

Gotta Win the Races

In a few days, I’m heading to Las Vegas for my first trip ever (can you say… Bucket List?) to the World Series of Poker.  I will be playing in exactly one bracelet event, with a $1,500 buy-in, starting June 20.

So a couple days ago I switched from my normal cash game mode to a tournament mode.  I played an online tournament on Thursday, and played in live, private tournaments on Friday and Saturday nights.

Let’s get real here, very quickly, and acknowledge that these tournaments aren’t going to be representative of what I should expect at the WSOP.  But at least they involved more players who I do not play with regularly, and the basic issue that the blinds increase in scheduled increments, creating various inflection points along the way.  And when you bust out, you’re out.  Finished.  Over.  Done.

On Friday, there were 47 players in the tournament, with a $50 buy-in plus $10 bounty.  Blinds increased every 20 minutes.  The prize money goes to the last 5 players.  I did pretty well, played a mini-“Survivor” and made it to the final 4.  Then we negotiated a “chop” of the remaining money, giving a larger share to the guy with the biggest stack and splitting the balance equally among the other three.  I had the 2nd largest stack, although my lead over 3rd and 4th place was slim… no more than 3-4 big blinds.

On Saturday, there were 16 players, with a $60 buy-in, plus re-entry for the first hour, plus a $10 add-on at the end of an hour.  Blinds increased every 15 minutes.  The prize money goes to the last 3 players.  Again, I hung on for a good while, busting out in 6th place.

Here’s the thing:  in both tournaments, there are points where significant risks are required.  Let’s call a “big risk” any situation where you are going to commit all or a sizable portion of your chip stack before the flop.  This is when you have the least amount of information — only your two hole cards.  When you go all-in and another player calls, or another players goes all-in and you call, you cannot ever be assured of winning.  With pockets AA’s, you might be somewhere between 77-94% favorite, but never 100%.  And some additional times you’ll be doing the same on the flop, with two cards still to come.

Often times the odds will be fairly close to 50/50.  When this happens, we call it a “race” or a “coin flip.”  I suppose it’s fair to call it a race whenever neither player is a greater than 60% favorite (although I have not seen any semi-official definition).  Even at 70/30, the underdog is going to win often enough to make it pretty nerve-wracking.

Here are some of the hands from Friday and Saturday nights that stand out:

Friday – Coachman’s Trail tournament (format:  my cards, my percentage equity at the time we went all-in, “>” or “<” to indicate that I won / lost, villain’s cards, villain’s percentage.  (Percentages may be slightly off as I don’t remember the suits from every hand.  This is in the order they occurred to the best of my recollection.)

1.  AKo (45%) > 55 (55%).  Knocked out opponent.

2. JJ (50%) = JJ (50%).   Chopped pot.  Villain shoved over my opening raise, then picked up a flush draw on turn but missed.  Whew.

3.  A9s (30.5%) < AKo (69.5%).  Doubled up opponent.  I had raised first, he shoved, not too much more to call and I had the bigger stack.  Same villain as #2.

4. AA (80%) > TT (20%).  Doubled up my stack.

5. QQ (80%) > TT (20%).  Knocked out opponent.  This was the very next hand after #4.  Mini-heater.

6. KJo (73.2%) < K3o (26.8%).  Doubled up opponent, who had gotten short stacked and made a “fuck it” call that was less than my pre-flop raise.

7. K9o (57.8%) > QJo (42.2%).  Doubled up my stack.  Villain open-limped in cutoff and appeared weak.  I shoved on button hoping to have just enough fold equity to get rid of him.  He called anyway.

8. KQs (44.1%) > ATo (55.8%).  Doubled up my stack.  Flopped flush draw giving me lots of outs, hit flush on river.

9.  TT (80%) > 88 (20%).  Doubled up my stack.  Villain was loose, aggressive, big stack.  Now at 5 players remaining.

In this group, I won 6, lost 2 and chopped 1.  Both losses came when I had a big enough stack to survive the beating.  4 of the wins came when I was the shorter stack (and 2 of these were 80/20 situations so not exactly races.  But still…).

My simple average equity in these hands was 60.1%.  My “win rate” of 6.5 out of 9 is 72.2%.  So without weighting for stack sizes or Independent Chip Model theories and such other fancy analysis, I performed slightly better than expected on this small sample of hands.  Most importantly, there were 5 times that a loss would have knocked me out of the tournament and I survived them all.  This is a must to go deep in a no limit holdem tournament, especially with the blinds increasing so quickly.  When we finally negotiated the chop, even the biggest stack had only about 15-17 big blinds remaining.

Saturday – John D.’s house tournament.

1.  KK (78.6%) > QQ (11.1%) < Q6s (10.3%).  WTF?  Villain #2 UTG min-raises,  Villain #1 UTG+1 re-raises, and I shove on the button with KK.  V2 has slightly less than one-half of her starting stack and we have not yet reached the end of the re-entry period, so she makes a tilted, “fuck-it, I’ll just re-buy” call with Qs6s and V1 also calls with QQ.  I love this spot.  Then a 6 comes on the flop and another 6 on the river.  I make a very tiny profit on the side pot and knock out V1, while V2 pulls in chips equal to about 135% of a starting stack.  OMG.

2.  8c 3c (44.2%) < Ks Qc (55.8%) after flop of Kc 8d 7c.  After 2 limps, I completed from the small blind (AND THEREIN LIES THE REAL MISTAKE!!!) with total garbage.  But I hit the flop pretty good, with middle pair and a flush draw.  We are 6-handed and the blinds are big, such that I begin the hand with 10.5 BBs.  I open shove into a pot of 4 BBs, a massive over bet designed to put maximum pressure on the villains knowing I have a lot of equity.  Guy on button calls (why did he limp and not raise with KQo on the button???).  Turn is another 7, pairing the board and eliminating some of my outs as now I cannot win by pairing my kicker.  River is a 3, pairing my kicker.

Trying to remember other races from this tournament and cannot think of any.  I know I didn’t knock out anyone else as I only had one bounty to cash in afterwards.  I cannot recall any other hands where I doubled up my stack.

Both of these hands were weird, and the first one doesn’t really qualify as a “race” other than how it illustrates what can happen in tournaments.

My simple average equity for these two hands is 61.4%.  I won the side pot on the first hand but lost the main pot.  So let’s just say I won 1 out of 3 pots for a win rate of 33.3%.  Performed worse than expected and finished out of the money.

Friday –> variance is my friend.  Saturday –> variance is my enemy.  Inevitably, gotta win some key races to survive.

On to the cash game.  A key hand there (see #1 again from the Saturday tournament) is where again I have KK and raise to 7 BBs pre-flop.  2 callers and then a short stack makes a “Fuck it!” shove for 25 BBs.  I go all-in to isolate him and he turns over 33.  KK (80%) < 33 (20%) after he spikes another 3 on the turn.  Sigh.

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