Statistical greed

I've explored the theme of greed in poker in this blog before. Poker greed can take many different forms; one of them is statistical. In general, any form of poker greed is bad, since it can cause you to convince yourself to make poker decisions you wouldn't normally make. What do I mean by statistical greed? When you want to have a winning session so badly, you start to throw caution to the winds. What's so great about a winning session where you only win a small amount? To be honest, nothing much. The difference between a winning session where you win $1,000 and a losing session where you lose $1,000 is essentially nothing, assuming you're playing at a table where the blinds are $100/$200, and the maximum starting stack is $40,000. My problem is, I've been seduced by my own concept of the golden ratio to overvalue winning sessions of any kind, including sessions where I only win a small amount. Last night, I hit the felt on hand 46, and reupped for the max. Seventy hands later, I won my biggest pot of the night, $36,100, with a jack high straight. This took my stack up to $79,043, which meant that if I'd quit right then, I would have ended the night with just a small loss of $957. However, my statistical greed kicked in, and I kept playing. When I was dealt pocket rockets on hand 125, I thought for sure I'd been given the keys to a winning session. Unfortunately for me, an opponent hit a set of fours on a flop of Ks 4s Qd, and went all in. I called, and lost $32,783 on the hand. I quit three hands later, 12 hands too late.

During current Hold'em session you were dealt 128 hands and saw flop:
 - 13 out of 17 times while in big blind (76%)
 - 7 out of 16 times while in small blind (43%)
 - 43 out of 95 times in other positions (45%)
 - a total of 63 out of 128 (49%)
 Pots won at showdown - 5 of 14 (35%)
 Pots won without showdown - 5

delta: $-34,640
cash game no limit hold'em balance: $5,009,230
balance: $7,458,638

If I had a hammer

Having the dealer button is a huge advantage. It's so huge, you should virtually always pay the minimum bet (a big blind) to see the flop, which you'll have the opportunity to do if everyone else either folds or limps in. Sometimes, you can hit some really big hands on the flop with really crappy hole cards. I love it when I get dealt a hammer (deuce seven offsuit) and have the dealer button; I will always pay the minimum in that situation. If I pair both hole cards on the flop, the strength of my hand is even more hidden than it would be with a normal stealth two pair. Practically the only bright spot of last night's session was when this exact stealth scenario came up for me. On hand 141, I was dealt a hammer. The flop came Qh 7s 2h, and a player who acted before me went all in with his last $4,800. I called, and ended up winning a pot worth $10,505 with a full house, sevens full of deuces.

During current Hold'em session you were dealt 189 hands and saw flop:
 - 15 out of 24 times while in big blind (62%)
 - 13 out of 26 times while in small blind (50%)
 - 62 out of 139 times in other positions (44%)
 - a total of 90 out of 189 (47%)
 Pots won at showdown - 6 of 22 (27%)
 Pots won without showdown - 13

delta: $-80,000
cash game no limit hold'em balance: $5,043,870
balance: $7,493,278

Fading a flush

Last night, I had a winning session largely on the strength of a big hand where I faded a flush. I was dealt Ac Ad, the flop came 2d Ts Qd, and the turn card was 5s. I went all in on the turn, and got one caller. He'd been dealt 6d Jd, and was banking on making his flush draw. He drew a blank on the river, though, which was 3h. It definitely hurt his chances that I'd been dealt one of his outs. I raked in a pot worth $81,596. Since I was an 82% favorite to win after the turn, my use of the term "fade" here may not be strictly correct, but I like the alliteration it lends to the title of this post.

During current Hold'em session you were dealt 35 hands and saw flop:
 - 5 out of 5 times while in big blind (100%)
 - 1 out of 5 times while in small blind (20%)
 - 13 out of 25 times in other positions (52%)
 - a total of 19 out of 35 (54%)
 Pots won at showdown - 3 of 5 (60%)
 Pots won without showdown - 4

delta: $52,776
cash game no limit hold'em balance: $5,123,870
balance: $7,573,278

I'm not such a git after all

It turned out I was being too harsh on myself for losing nearly a million play dollars on fully matured, high card hands. There are many different ways of losing nearly a million play dollars, and it turned out my way wasn't as bad as I'd thought. A refinement to my fully matured hands tool helped me prove this; I added the capability to ignore hands where no money was spent on the river. I realized that a lot of the money I'd lost on high card hands was likely due to draws which didn't pan out. When you're on a draw, you often won't know until the river whether you've made it, and you often have to pay a considerable amount to see the river. When you don't make your draw, there's no sense spending any money after the river card comes off unless you're stone bluffing. Here are my numbers for fully matured hands where I spent money on the river:

    -61970     251741    -313711   247     -250.89   high card
     34262    1537124   -1502862   892       38.41   one pair
   1249117    2930509   -1681392   996     1254.13   two pair
   1312402    2067816    -755414   372     3527.96   three of a kind
   1869556    2389464    -519908   352     5311.24   straight
   1358099    1712298    -354199   256     5305.07   flush
   1551215    1728457    -177242   225     6894.29   full house
    100786     100786          0    16     6299.12   four of a kind
     73800      73800          0     4    18450.00   straight flush
     53200      53200          0     1    53200.00   royal flush

   7540467   12845195   -5304728  3361     2243.52

The money I've lost on high card hands in this scenario is a much saner figure.

During current Hold'em session you were dealt 63 hands and saw flop:
 - 10 out of 12 times while in big blind (83%)
 - 6 out of 10 times while in small blind (60%)
 - 22 out of 41 times in other positions (53%)
 - a total of 38 out of 63 (60%)
 Pots won at showdown - 7 of 14 (50%)
 Pots won without showdown - 9

delta: $-75,192
cash game no limit hold'em balance: $5,071,094
balance: $7,520,502

A leak in my game

Statistics can reveal some strange things. You many think you know what kind of poker player you are, and that you know exactly how you play; however, statistics can show you weaknesses you never knew you had. Today I wrote a tool to aggregate the information collected by the fully matured hands tool I wrote yesterday. Here's what it spat out:

   -985371     298806   -1284177   947    -1040.52   high card
  -1637083    3534546   -5171629  2897     -565.10   one pair
   2380855    6176729   -3795874  1990     1196.41   two pair
   2293885    3471194   -1177309   534     4295.66   three of a kind
   2335811    3073895    -738084   460     5077.85   straight
   2040368    2639192    -598824   328     6220.63   flush
   2676134    3050901    -374767   309     8660.63   full house
    183246     183246          0    22     8329.36   four of a kind
     73800      73800          0     4    18450.00   straight flush
     55688      55688          0     2    27844.00   royal flush

   9417333   22557997  -13140664  7493     1256.82

From left to right, the columns contain net delta, positive delta, negative delta, number of hands, average delta per hand, and hand type. I'm flabbergasted to discover that I've lost nearly a million play dollars playing high card hands. What a git I am :-)

During current Hold'em session you were dealt 153 hands and saw flop:
 - 24 out of 26 times while in big blind (92%)
 - 16 out of 26 times while in small blind (61%)
 - 63 out of 101 times in other positions (62%)
 - a total of 103 out of 153 (67%)
 Pots won at showdown - 10 of 31 (32%)
 Pots won without showdown - 22

delta: $-70,762
cash game no limit hold'em balance: $5,146,286
balance: $7,595,694

3.5 million folded on the river

After thinking about it some more, I realized that my definition of a fully matured hand was flawed. There's only one criterion which needs to be satisfied - namely, that the hand was live when the river card was revealed. That means that there's another possible outcome in addition to the four I mentioned in yesterday's post - namely, that the hand was folded on the river. Since my original definition excluded hands which were folded on the river, I was understating the number of losing hands and the amount lost with losing hands, and therefore overstating the net amount won. Here are the correct numbers, including the hands from last night's session:

      7,439  number of fully matured cash game no limit hold'em hands I've played since turning on auto-save
      3,216  number of winning hands
      4,223  number of losing hands
$22,510,218  amount won with winning hands
$13,039,907  amount lost with losing hands
$ 9,470,311  net amount won

It's vitally important to be able to fold hands on the river. Clearly, you don't want to fold the majority of your fully matured hands, since that would call into question why you let them fully mature in the first place; however, you're going to have to fold a healthy percentage of them.

Just for fun, I wrote some tools to figure out how much play money I've folded on the river since turning on the auto-save feature of the PokerStars software. It comes out to a whopping $3,466,693. The thing is, that was almost certainly play money well lost :-)

During current Hold'em session you were dealt 61 hands and saw flop:
 - 6 out of 8 times while in big blind (75%)
 - 5 out of 8 times while in small blind (62%)
 - 24 out of 45 times in other positions (53%)
 - a total of 35 out of 61 (57%)
 Pots won at showdown - 6 of 11 (54%)
 Pots won without showdown - 6

delta: $27,090
cash game no limit hold'em balance: $5,217,048
balance: $7,666,456

Fully matured hand stats

Poker playing is like gardening. It's necessary to tend carefully to your hands in order for them to mature. You must nip some hands in the bud in order for others to thrive. Every time you're dealt a new hand, by definition it's incomplete and immature. You have only two cards, and you need five. Not only that, you need the best five you can find in the total of seven you might end up seeing.

The longer I play poker, the more data I collect, and the more tools I create to help me make sense of that data. Today I wrote some tools to collect statistics on fully matured hands. What do I mean by a fully matured hand? It must satisfy the following two criteria:

1. I saw the full complement of 5 community cards (aka the board)
2. I didn't fold

There are 4 possible outcomes for a fully matured hand:

1. I lost at showdown
2. I split the pot at showdown
3. I won the pot at showdown
4. I won the pot without a showdown

Here are the stats I calculated today:

      5,158  number of fully matured cash game no limit hold'em hands I've played since turning on auto-save
      3,209  number of winning hands
      1,949  number of losing hands
$22,445,892  amount won with winning hands
$ 9,559,514  amount lost with losing hands
$12,886,378  net amount won

During current Hold'em session you were dealt 74 hands and saw flop:
 - 7 out of 9 times while in big blind (77%)
 - 4 out of 11 times while in small blind (36%)
 - 26 out of 54 times in other positions (48%)
 - a total of 37 out of 74 (50%)
 Pots won at showdown - 4 of 5 (80%)
 Pots won without showdown - 5

delta: $5,452
cash game no limit hold'em balance: $5,189,958
balance: $7,639,366