Luckbox?!!

This week's essay deals with the question to what extent we can measure the luck factor by using PokerEV.

by Thorsten77

Solid poker players are constantly on the search for possibilities to
improve their play. A common procedure is to find leaks with the aid of
Pokertracker statistics. Basically, I'm of the opinion that we should
use Pokertracker only as an indicator – we can identify problems in our
play but we have to verify those leaks manually.

A question that appears during a down again and again: To what extent
does financial loss depend just on bad luck. We are able to quantify
this question to some extend with the assistance of the PokerEv
software. In this column, I want to introduce the „All-In Luck“-graph
of this tool which gives us an overview about whether we are overly
lucky or having more bad luck.

Poker = Skill + Luck

Many players make the mistake of putting good play on a level with
(short term) financial success. If you finish a session 2 stacks up,
you think you've played good but that's absolutely wrong. If you, for
example, go all-in preflop with 200BB and win against pocket aces with
a two pair, you may have a financial success but your play was awful.
Solely the luck factor helps us to win this hand, thus the random setup
of the five community cards.

In order to understand how to measure the luck factor, we must first
define what skill and luck is. We take the following definition for
granted: We add it towards the skill factor when our share of the pot
changes during a betting round (e.g. folds, calls, bets or raises). We
add it towards the luck factor when our equity changes due to the
appearance of new cards on flop, turn or river. The basic idea: If we
can influence our action, it counts towards skill (our actions during a
betting round) and everything else which we can't influence (the new
dealt cards on the board) counts towards luck.

That's how PokerEV calculates the luck:
PokerEV calculates every hand which had a showdown (i.e. The cards of
hero and villain are known), the so called Sklansky-Bucks. This is a
value which indicates the profit purely according to the skill factor.
This value can be put in relation to the real result in order to get an
impression whether we were lucky or unlucky. Lets take a look to the
following sample hands:

Hand 1 (the way hero has played this hand)
Known players:

hands/vp$ip/pfr/af/wts/ats/foldbb/w$sd
MP2$1.104:585/63/17/0.4/35/30/11/43
BU$0:418/47/9/0.3/33/16/6/52
Hero$985

5/10 No-Limit Hold'em (10 handed)

Preflop: Hero is UTG with K , K

Hero raises to $35.00, UTG+1 folds, UTG+2 calls $35.00, MP1 folds, MP2
raises to $60.00, 2 folds, BU calls $60.00, 2 folds, Hero raises to
$280.00, UTG+2 folds, MP2 calls $220.00, BU calls $220.00.

Flop: ($890.00) 6 , 7 , 3 (3 players)

Hero bets $410, MP2 raises to $705, BU folds, Hero calls (All-In).

Turn: ($1316.10) 6

River: ($1316.10) Q

Final Pot: $1316.10

Results follow:

MP2 shows [ 8s, Js ] a flush, Queen high
Hero shows [ Ks, Kc ] two pairs, Kings and Sixes
MP2 wins $119 USD with a flush, Queen high.
MP2 wins $2,297 USD with a flush, Queen high.

PokerEV calculates now the difference in equity per street.
Preflop
First we calculate the equity for all known hands:

equity win tie pots won pots tied
Hand 0: 81.546% 81.33% 00.22% 1392631 3689.00 { KcKs }
Hand 1: 18.454% 18.24% 00.22% 312295 3689.00 { Js8s }

Our share of the pot is now: 81,546% * $890,00 = $725,75

The Sklansky-Bucks for the preflop action are the difference between
our share of the pot and the money we have already invested in the pot:
$725,75 - $280,00 = $445,75

Thus we made a (theoretical) profit of over 40BB by pushing our good starting hand.

Flop
The calculation takes place analogically:

Board: 6s 7s 3c

equity win tie pots won pots tied
Hand 0: 65.960% 65.96% 00.00% 653 0.00 { KcKs }
Hand 1: 34.040% 34.04% 00.00% 337 0.00 { Js8s }

Our share of the money which is in the pot on the turn (here we have to
deduct the amount of money, MP2 has covered us) is: 65,960% * $1410 =
$926,74

Our Sklansky-Bucks are: $926,74 - $705,00 = $221,74

Turn and river
Since we have gone all-in on the flop, there are no more betting rounds
and therefore no change of the skill factor on the turn and on the
river.

Results
Thus in this hand we have won a sum of $445,75 + $221,74 = $667,49
Sklansky-Bucks. So we have invested our money as the favourite but
villain sucked out on this hand and therefore we lost $985 in the end.
The difference $-985-$667,49 = $-1652.49 is our luck, or rather bad
luck.

Hand 2 (an alternative play)
The interesting point of this calculation is that we get different
results with different betting lines even though it's the same hand,
i.e. the same starting hands and the same community cards. Lets assume
that hero misplays this hand by slowplaying flop and turn. As soon as
the flush comes, he pushes.

Known players:

hands/vp$ip/pfr/af/wts/ats/foldbb/w$sd
MP2$1.104:585/63/17/0.4/35/30/11/43
BU$0:418/47/9/0.3/33/16/6/52
Hero$985

5/10 No-Limit Hold'em (10 handed)

Preflop: Hero is UTG with K , K
Hero raises to $35.00, UTG+1 folds, UTG+2 calls $35.00, MP1 folds, MP2
raises to $60.00, 2 folds, BU calls $60.00, 2 folds, Hero calls $25.00,
UTG+2 folds, MP2 calls $25.00.

Flop: ($195.00) 6 , 7 , 3 (3 players)
Hero checks, MP2 checks, BU checks.

Turn: ($195.00) 6
Hero checks, MP2 checks, BU checks.

River: ($195.00) Q
Hero raises to $925.00 (All-In), MP2 calls $925.00, BU folds.

Preflop
Our share of the pot is 81,546% * $195,00 = $159,01

The Sklansky-Bucks for the preflop action are the difference between
our share of the pot and the money we have already invested in the pot:
$159,01 - $60,00 = $99.01

Flop und Turn
Everyone checks, thus our Sklansky-Bucks-value doesn't change as well.

River
We push on the river although we are beaten and hence we have no
equity. As a result, our Sklansky-Bucks are (0.00% * $1850) - $925 =
$-925

Result
So Altogether we have „earned“ $-825.99 Sklansky-Bucks. We didn't
extract value when we were favourite but we put money in the pot when
we were beaten. We had no bad luck ($-985 - $-925 = $-60), we just
played bad in this hand.

Conclusion

In this column, we've seen how we can quantify the luck factor to some extent. The all-in-luck graph shows our showdown winnings in comparison to our statistical share of the pot. According to this, we can use such programs to get an idea whether we have a good or bad run. On the other hand we have to be aware of the boundaries of such tools. There are situations where it's almost unavoidable that we invest money as a underdog: Set-over-set situations are a good example. 'If we flop several times middle set during a session and are stacked by top set every time, we would treat that intuitively as bad luck (here we have to go broke). However, this bad luck isn't indicated by PokerEV. Moreover, we should take into consideration that we can't be sure whether we played all of our hands (with or without showdown) correctly even when having a lot of bad luck. As a result, we shouldn't use software like PokerEV as a method to review our sessions, but rather as an helpful addition.

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» Thread: Luckbox