KKing David

Ruminations on poker

Archive for the tag “Variance”

Variance is a Bitch

In poker, variance is a bitch.

But she’s our bitch, so try not to be mad at her.

In a cash game yesterday, I find myself in a 3-way all-in pot after the turn card.  There was $390 in the pot after the flop betting and the turn card gave me a flush draw along with an open-ended straight draw.  The action checked around to me and I shoved my last $260, hoping everyone would fold and knowing I had a lot of backup outs.  One player called with two pair, another re-shoved with the bottom end of a straight and the first player called again.  From a strictly EV (expected value) standpoint, this was a profitable play with two callers, as my final bet was 22.2% of the total pot and I have 27.4% equity in the hand.  From a math standpoint, my EV is $321 (final pot size of $1,160 x 27.4%).  The river misses, and my actual result is zero.

Later in the same game, another all-in ensues, this time heads up on the flop.  The pot is around $1,100 again and this time I’m ahead with top two pair, and the villain big combo draw.  He hits one of them right away on the turn and wins the pot.  This time my EV is $684 (final pot size of $1,100 x 62.2%).  My actual result, again, is zero.

On these two hands combined, my EV was just over $1,000.  Instead, nyet!  I buy-in again, and before too long my pocket aces are cracked by a set of sevens (by the same guy who flopped a set of eights v. my pocket jacks much earlier).  Time to go home.

Such is the nature of variance.  The actual result is always an all-or-nothing proposition.  The expected result is the average that should occur if the same scenario were to be replayed a million times.  Being a favorite doesn’t guarantee being a winner.

Over the long haul, if you are on the right side of the 60/40’s and 70/30’s more often than not, variance will be your friend, despite tormenting you often along the way.

In the short run, this was simply a day of being on the wrong side once (insofar as very large pots is concerned) and being on the right side once, but missing both sides.  Yes, the coin toss can come up heads twice in a row even though I always guess tails.


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Too Nitty?

I may have been too nitty on this hand last night.  When this happened, I was having a bad night, having tried to turn KK into a bluff and having this backfire badly, then having QQ cracked by JJ after a villain called a large pre-flop 4-bet (and then admitted that he thought his JJ’s were in trouble).

The good news, perhaps, is that I’m aware things are going badly and trying to be careful not to let emotions overrule good decisions.

Now I have KQo in middle position.  This being a $1/2 no limit Hold’em game, I raise to $11 following one limper, which is fairly typical for me.  The button calls (I’ll call him “Mike”), one of the blinds calls, and the limper calls.

Flop ($40):  Kd 8d 7s

This looks like a good flop for me, but the flush and straight draws can hit the villains’ ranges.  It is checked to me and I bet $17.  In hindsight, this bet is too small, and should have been more than 1/2 of the pot.  But my TPGK, while good, is still just a 1-pair hand and I don’t want to bloat this pot out of control.

Mike, on the button, raise to $43, and both other players fold.  At the start of this hand, I had about $250, and Mike has me covered.

Mike is a tough player, good at hand reading and willing to bluff.  And he has position on me.  With many villains, my default in this situation is to give him credit for 2-pair plus most of the time, and top pair / over pair the rest of the time.  Let’s quickly eliminate the only over pair… AA, as he didn’t 3-bet pre-flop.  But I know Mike will play his draws aggressively, and he might have a K as well.

I decide to re-raise, $45 more.  I want to leave myself room to fold if he comes back over the top and convinces me that he’s flopped a set.  I also, however, want to find out where I am in this hand (and believe I might be good), as I realize after his raise that my C-bet was too weak.  If he calls, that suggests he is on a draw and I can re-evaluate after seeing the turn card.

Mike tanks for a bit, and seems to be considering multiple options.  Then he announces “I’m all in.”


Now I go into the tank.  The pot is indeed bloated, now approximately $220, and will cost me $150 more to call.  My hand is just one pair, and I hate going broke with just one pair (even moreso having already been felted once in this session).

I settle on this range:  88 (3 combinations), 77 (3 combos), multi-way draws (Td 9d, Jd Td, 7d Ad, 7d 6d, perhaps 7d 9d, perhaps Ad Jd and Ad Td — total of 7 combos).  I note the K is a diamond, so a top pair / flush draw cannot be in his range.  I think he would 3-bet pre-flop with Ad Qd and any AK.  Neither of my cards is a diamond.

With the sets, he has me crushed.  With the biggest draw… Td 9d, he has 15 outs and would be a favorite to win the hand.  My equity doesn’t have to be over 50% to justify calling from a math standpoint, as I would be calling $150 to win $370.  I really only need 29% equity ($150 / $520) for calling to be correct.  But I’m not really thinking about that at the table, I’m thinking about being stuck 2 full buy-ins if I lose, and that thought pisses me off.  And I’m thinking about my long-term image if I’m viewed as the guy who over plays a one pair hand (especially with less than top kicker).  The draws seem more likely than the sets, as I’m not sure he shoves a set here.  On the other hand, with a set he might think I’m overplaying AK or AA here, and shoving a set for value could be smart before the board gets scarier.

Reluctantly, I fold.  This wasn’t a math fold, it was a variance fold.  I’d already suffered more variance (see above re QQ losing a large pot to JJ) in this session than I like, wasn’t prepared to buy-in again if I went all-in and lost here, and was sitting on the left of a couple of players who have a history of spewing off lots of chips.  I like my chances if I keep playing.

After saying I thought he had something like Td 9d, he says I’m close and some prodding gets Mike to tell me he had a 7d and another diamond, for bottom pair and a flush draw (14 outs).

Against the range above, my equity is 27.2%.  Against only Td 9d, the drawing hand with the most outs, my equity is 43%.  Against 7Xdd, my equity is 47%.  Gambling for sure, but high enough to call.

Methinks I should have called.  We’ll never know.  But given how poorly the rest of the session went,  I might as well have gambled here.

RIP Bill Hubbard

For a few weeks last winter, I took some poker coaching from Bill “Ain’t No Limit” Hubbard.  Although I suspended the coaching at a time when there were too many concepts swirling around in my head and I needed to slow down and digest them better, he taught me a lot – an awful lot – about how to navigate through live cash games of Texas Hold’em.

Sadly, Bill passed away in May.  Even more sadly, I only learned about his passing yesterday, while searching on the TwoPlusTwo forums for something completely unrelated.  RIP Bill… may the memory of the righteous be a blessing.

Our last email exchange came in mid-April, after a bad beat in a nearly $1,400 cash game pot.  I wrote:

Bill, Link below to a cash game hand at 2/5 during WSOP Circuit stop in NC.  Villain was a very good player but also very aggressive and caught 2x in large bluffs recently.  Your thoughts???  ShareMyPair link here.

Bill replied the next morning:

This is a cooler which you cannot get away from.  She lost money overall in the hand and you won overall in the hand.  Variance had you lose this time.  No biggie.  She gambled and won this time, but loses most always.

Bill’s short reply integrates two concepts he worked hard to teach, and helped me move past this hand a little faster than I would have otherwise.

The first is variance.  Over the short run, variance can be a real bitch.  You will lose big pots that you thought you should win.  Bad beats, coolers, suck outs, etc. will occur seemingly too often.  Losing big pots is painful.  It hurts the ego, hurts the bankroll, hurts the confidence, hurts the table image, and hurts some more.  If you are going to play a lot of no limit poker, you better accept the fact that variance will be there to bitch-slap you from time to time just when you least expect it.  But over the long run, variance is your friend.  It is the reason winning players are able to win, as it is variance that keeps losing players coming back to the games.  Without variance – in this case referring to the big hands that are won by overall losing players – the good games would dry up.  More and more losing players would go gamble elsewhere, to find another source of variance (blackjack?  craps?  roulette?  horse racing?) even though they are still likely to lose in the long run.  Meanwhile, a winning player, who can get money in the pot over and over with a positive expected value, as a 51% or 65% or 90% favorite, is going to keep winning over the long run.

The second concept is reciprocality.  Bill taught reciprocality as originally described by Tommy Angelo:

Reciprocality says that when you and your opponents would do the same thing in a given situation, no money moves, and when you do something different, it does.

In the subject hand, the she-Villain called a pre-flop raise from one of the blinds with 4-3 off suit.  I would fold.  So in this given situation, I would not do the same thing as the Villain.  In the short run, she won a large pot.  That’s variance.  In the long run, she will lose much more by playing this way than she will win.  In this particular hand there was a perfect storm.  She has 4-3.  I have 5-5.  The flop is A-T-2.  She has, in reality, only two outs to make a wheel straight.  I have the same two outs to make a set. without which I would not be putting any more money into this multi-way pot.  Even after all the money goes in the middle on the turn, I still have 10 outs to win.

Reciprocality is both a very simple and a very deep concept.  You can think of this existing on every single move in a poker game.  Often the right play does not involve any reciprocality.  For a very simple example, imagine a heads-up game, where the Villain makes a large pre-flop raise and you have 3-2 off suit.  You fold, of course.  The Villain would do the same thing if the roles were reversed.  While the Villain wins this individual hand, over the long run you will break even with respect to each other as it relates to this exact situation.  Your reciprocal edge comes when you play differently from the Villains.  The biggest source of reciprocal profit, in my opinion, happens to be the simplest.  This is folding marginal hands pre-flop, especially out-of-position.  Folding troublesome hands that others would play is a huge source of profit, by enabling you to retain more of the money you win with your good hands.  Other sources of reciprocal profit come from bet sizing that is different from Villains bet sizing, well executed bluffs that Villains would not attempt, and so on.

Thanks again Bill for some excellent lessons.

Now I’m going to re-read the reciprocality section in Tommy Angelo’s classic Elements of Poker.

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