Equity, Variance and Tilt

In my last three cash games I have had the worst downswing that I can remember. I have dropped close to 10 buyins in >1000 hands at the $1/$3 level (playing with 100BB stacks), which constitutes almost 15% of my bankroll. This is absolutely absurd for my playing style within such a minute sample of hands; I have never experienced anything remotely close to this in my four years playing poker.

While most bad poker players or people who no little to nothing about poker would immediately say, “see, I told you poker is all about luck” and “there is little skill involved,” I know 100% this NOT to be the case. Poker is a game based on mathematics and it has only been in the past year and half when I have started to take an interest in the numbers aspect of the game. Using more math in my game has been the best decision I have ever made, pokerwise. For example, until recently I didn’t know that one’s river play is always a math based decision. Now, I have adjusted my play accordingly and have been rewarded. As a poker player, one should not be concerned with the outcome of any single hand as long as the correct decision was made when all the money went into the pot. If my decision is mathematically correct, I am making money in the long run, which is the ultimate goal. However, it becomes increasingly frustrating when I get my money in good, only to have the pot stripped away from me due to variance.

During my downswing I am running far below equity. What I mean by equity is that if I am playing a $1/$2 NL cash game and both myself and op have 100 BB (Big Blind) stacks ($200 each at the beginning of the hand), with me holding AA vs. his JJ, I should expect to win this pot 80% of the time. Here, if we are all in preflop for a $400 pot, my equity is 80%, so on average I should win $320 from the pot. Over my sample size I am running 1.5k below equity. I really hope it ends soon.

Let’s take a look at a few examples:

(All hands are full ring NL with $1/$3 blinds)

Hand 1:

7 limpers. I complete in SB with 2h5c. BB checks.
Flop: Ah 3h 4s
I check. MP bets $20. MP+1 calls $20. I raise to $65 total.
MP raises all in for $300 total. I call all-in for $235.

Here I call $2 dollars in the SB hoping to hit two pair or a straight and I flop the nut straight on a coordinated board. MP leads, I raise, and MP 3-bets me all in. Of course I am never folding my hand at this point as I have the best possible hand, but I must assign villain a range of hands. Likely holdings include A4, A3, 33, 44 as op is a weak player, never going to 3-bet without a made hand (i.e. he just calls with a flush draw. A better op might do this with a pair and f/draw). Against his perceived range I am around 66% to win this hand.

In reality, I call and op turns over 33 for bottom set and makes a FH by the river when the board pairs an Ace. With the total pot being (7*$3) + $20 + (2*$300) = $641. My equity for the hand is 66% therefore, I should expect on average to win $641*0.66 = $423 from the pot. However, he hits his outs and I am down one buy in.

Hand 2:

5 limpers. I raise on the button with AhAd to $25. I get three callers.
Flop: Kh Qc 2s
Everyone checks to me and I bet $70. MP calls $70. 2 folds.
Turn: 3h
Op checks. I bet $150. Op min-raises to $300 total. I go all in for $28 more.

Total pot = $4(blinds)+ $6(limpers) + (4*25) = $110 preflop
$110 + ($70*2) + (328*2) = $906 total pot

Here, op is semi-competent but the loosest player at the table, who constantly calls preflop raises with marginal starting hands out of position. At this point, a range must be assigned to villain. He limp-called $25 preflop so his range can include any two cards. On the flop, I bet 2/3rds of the pot and he calls. Here I can safely assume villain does not have KK or QQ. His most likely holdings are Kx, Qx and sometimes KQ, J 10, or 22. The turn is a blank, the 3h. Villain checks again. At this point we can eliminate KQ, and 22 from his range because op always leads the turn in the hands when he perceives himself to be ahead. In other words, op would bet the turn with these holdings for what he believes to be a “value bet” to chase me off any draws that I have. Since he checked to me, I can assume his most likely holdings are Kx and rarely Kxhh. I bet, $150, or a little less than 2/3rds of the pot in order to a) show I have committed myself to the pot and b) give op the opportunity to raise me. Op takes the bait, minimum raises me and I happily call all in with the rest of my stack. At this point I am 95% sure I am up against some sort of one pair hand. I am delighted when he turns over QdJs for middle pair, weak kicker with no flush draw. Unfortunately, the river brings a J making my opponent two pair. He drags the 300 BB pot. Although, I lost the pot, I am happy with my play because I am way ahead of his perceived range. In the long run, this is a profitable play.

Let’s take a look at my equity when we get it all in on the turn. When all the money goes in I am an 88% favorite to win the pot. However, using Poker Stove to adjust to his perceived hand range, with AA I have 84% equity, meaning on average, I should win $906*0.84 = $761 from the pot. However, this was not the case, and I lost a huge pot.

I attribute this downswing not to bad luck or bad beats, but Variance. Variance is a statistical measure of how ones results will be dispersed. It is not merely a bankroll swing. Any mathematician knows poker can be profitable; it is a skill game but with an element of chance due to how the cards are randomly distributed. Variance is the element of chance in the short run. And I can’t stand it. However, as I said earlier, as long as the decision you make is mathematically correct, you WILL make money in the long run.

Let me give you an example. Say I’m playing in a NL shorthanded (6 players) cash game. I’ve been playing LAG (loose aggressive) and my style has been frustrating my opponents. We start the hand with the same size stack (100BBs) and I raise UTG (under the gun) with AKhh and my opponent three bets me. I reraise all in and he calls me, showing AQo. This is good for me as I am going to win the pot 75% of the time. Simultaneously, it means he will win my stack one out of every four times we go all in with the same holdings. In other words, I should expect to lose my stack in a similar scenario. It is frustrating when it happens, but it should not upset me. Of course, I am human and it does sometimes affect my game.

Over the course of hundreds of thousands of hands the natural variance will equal out. As long as my bankroll can maintain these swings, I should show a profit, which I have.

Mike Caro, the Mad Genius of Poker wrote the following about Variance in one periodical:

1 Poker Hand – Chance predominates
100 Poker Hands – Skill begins to have an influence
1000 Poker Hands – Skill now the single biggest factor
10000 Poker Hands – The effect of chance now minimal
100,000 Poker Hands – The effect of chance now all but gone.

When I do lose a big pot when I am large favorite to win the hand, it will sometimes have a negative impact on my game. This is called Tilt. I become frustrated, open too many pots with marginal holdings, will two and three barrel bluff on the turn and river as well as play way too many bad holdings out of position, which is about the worst thing you can do in poker. Hopefully, after I finish reading Zen and the Art of Poker, tilt will not influence my decision making process. If I can cleanse myself of tilt, there is no way I am going to lose money.

Now that I have covered Equity, Variance and touched upon the subject of tilt (which I most likely will have to address later :) let’s talk about a few more hands I played last night and just about how my last three sessions have gone, in general. In my last three sessions, I have had pocket aces four times, and lost 3 out of 4. Usually, this hand is my biggest money maker, but over this hand sample it has probably cost me the most. Last night, when holding AA I lost to QJ and 78, although I lost the minimum to the latter. With suited connectors, I flopped 6 open ended straight draws and 5 four card flushes. I missed every draw, which is quite a feat in itself. I have hit three sets during this entire sample. Once I took an opponents stack, another time an opponent made a flush against me on the river and I check called his bet and then in another hand I flopped a set on a monotone board (all one suit) and had to check fold to pressure on the turn with four of the same suit on the board. Ultimately, I haven’t been hitting. Now, it’s one thing to outplay your opponent. I can do this. However, I cannot outplay four opponents. I cannot bluff four people out of a pot! I can do this against one other player, using my hand reading skills because it is + EV (expected value). I just haven’t made any big hands in multi way pots and had them hold up. Hands 1 and 2 show this trend as does the following hand:

Hand 3:

MP (middle position) raises to $20. MP+1 calls. I call from the cutoff with A2dd. ($64 in the pot)
Flop: Ac 2s 8s
MP bets $20. MP+1 folds. I raise to $60. MP calls.
Turn: Jd
MP checks. I bet $80. MP calls $80.
River: 10c
MP bets $100. I call $100.

MP is the same maniac from Hand 2. His range here is Ax or any pocket pair. He continues with a weak bet on the flop (probably thinking he is trappig me) and I raise him 3x with two pair. At this point I know I have the best hand. In retrospect I should have made the raise to $100 because my hand is easily beaten. However, op never folds top pair and I don’t want the pot to get too out of control. When the turn comes a J and op check/calls my bet I know I am ahead and put him on AK, AQ, A10 and sometime A9. My turn bet is far too small. I bet $80 into $180 which is just a terrible under bet. I seriously misplayed my hand here as I should really bet $150 and fold to a turn shove to get some value out of my hand. Op calls and the river is a 10. Op leads for $100 into a $340 pot and getting 4.4:1, I am forced to call as I only need to be good here one in four and a half times to be profitable in the long run. Op turns over A 10 for rivered two pair. Sick. Ultimately, my fault, for playing the hand so weak, but he was calling no matter the price because he is such a terrible loose player. Online, at $1/$2 or $2/$4 they would always fold on the turn in this situation. However, my opponent is terrible and doesn't know any better.

Another hand of note was when a nit (which is a really tight player) raised to $20 UTG. UTG+1, a similar type nit calls and I raise to $70 with QsQd. Both call my reraise. Here, UTGs range is AK, JJ, 1010, with UTG+1 more polarized to AK and 1010.
Flop: Ac 10c 6c.
Worst. Flop. Ever. That hit both their ranges very hard and I don’t even have a club! UTG goes all in for $200ish and UTG+1 calls quickly. Instantly, I know they both have AK. I muck in disgust and they both show AK (I can’t believe the ace came down) with UTG freerolling with the K of clubs. The club draw misses and they chop the pot and my $70. Standard for how I’ve been running. But, I lost the minimum and was way ahead until the flop.

Omaha HL has been an absolute joke for me. The way we play is basically bingo. There is little skill involved minus value betting. It’s mindless poker and I can’t stand it. You just have to make a hand. And I haven’t made more than 2 nut hands and gotten paid. Every time I have A2 it’s high cards. When I have four high cards it’s all low cards. Then the same player keeps winning the monies and I consider him to be terrible, mainly because he just spews chips everywhere. But he has been on fire as of late and no one seems to be able to take a pot off of him. I laugh though, knowing his luck will run out and that he has already gifted me thousands of dollars over the past two years.

I know it will all turn around. I play too well in No Limit not to make money. I really do need to improve my Hi/Lo game, but what am I supposed to do in that bingo game? I am confident that Variance will become my bitch once again. Till next time.