## Luck Factors

Luck Factor 1 (LF1) = Number of Wins (NW) / Expected Number of Wins (EXNW). EXNW comes from your preflop expected equity. If your preflop expected equity is 45%, 0.45 is added to your EXNW. If you win the hand +1 is added to your NW, if you lose nothing is added to NW. Split pots add to NW based on percentage of the pot won. As with all LF's, a value greater than 1 indicates you won more than expected based on preflop equity.

Luck Factor 2 (LF2) = Suckout Percentage (SOP) / Bad Beat Percentage (BBP). If LF2 > 1, your SOP is greater than your BBP and you have been lucky. To see how PokerShowdown defines a bad beat event see the Bad Beat Definition section below.

Luck Factor 3 (LF3) = Average Suckout Factor (ASOF) / Average Bad Beat Factor (ABBF). Each bad beat/suckout event has a quantity associated with it that refects the severity of the bad beat. If LF3 > 1, your ASOF is greater than your ABBF and you have been lucky with respect to this statistic.

Luck Factor 4 (LF4) = Good Cooler (GC) / Bad Cooler (BC). A cooler is defined as a strong hand vs even stronger hand. Classic examples are AA vs KK or flopping set over set. It is unluckly to be on the losing end of this situation. This luck factor will quantify how often that has happened. As with all LF's, a value greater than 1 indicates you have been on the winning end of this situation more often than the losing end. The criteria for coolers is as as follows:
Preflop: KK or QQ and behind (less than 50% equity)
Flop: Top pair or better and behind (less than 50% equity)
Turn: Two pair or better and behind (less than 50% equity)
River: A set or better and behind (less than 50% equity)

Luck Factor 5 (LF5) = Starting Hand Strength (SHS). It should be possible to determine if a player is receiving stronger-than-average (or weaker-than-average) hole cards. The SHS statistic is calculated by assigning the below numeric values to the starting hand tiers found here
Tier1: value 8
Tier2: value 7
Tier3: value 6
Tier4: value 5
Tier5: value 4
Tier6: value 3
Tier7: value 2
Tier8: value 1
All remaining starting hands: value 0.12575
The Tier9 values has been calibrated such that over a large number of random hands the Average Starting Hand String (ASHS) will converge to 1. This has been verified by running tests that generate millions of random starting hands and verifying ASHS is very close to 1.

Luck Factor (LF) is a combination of LF1 and LF2. LF is a good measure for if that player has been lucky/unlucky over the period being evaluated. In the future, additional luck factors may be included in the overall luck factor LF.

A Bad Beat Opportunity (BBO) is an event that has the potential to turn into a bad beat. This happens when a player puts +EV money into the pot and another player puts -EV money into the pot. If the -EV player wins, this event turns into a bad beat. The type of action does not matter (call, bet, raise). The earliest round when the +EV/-EV situation happened determines which player is elibible for the bad beat. Later action does not change this since the -EV player should not have continued in the hand (should've folded instead of the -EV action). A solid player will typically try to bet enough to make it -EV for their opponent to continue. If the -EV player continues, they have an opportunity to suckout and give the +EV player a bad beat.

Bad Beat Percentage (BBP) is the ratio of Bad Beat Opportunities that turned into Bad Beats = Number of Bad Beats (NBB) / Number of Bad Beat Opportunities (NBBO). Likewise for Suckout Percentage (SOP). LF2 is SOP / BBP. LF2 could not simply be Number of Suckouts (NSO) / Number of Bad Beats (NBB) because a solid or tight player will always have more bad beats than suckouts. This is simply because they have more Bad Beat Opportunities as they are making more +EV bets and many online players are content putting -EV money in the pot hoping to suckout. Thus LF2 is SOP / BBP which should trend to a value of 1 over the long run if everything is truly random.

## How It Works

PokerShowdown processes the hand histories of supported sites for showdowns where the hole cards are known. Among these showdowns, PokerShowdown identifies events that, if everything is truly random, players will have a 50% chance of being on the positive side of that event, and 50% chance of being on the negative side of that event, over a large number of showdowns. That event is commonly known as a bad beat (positive side = suckout, negative side = bad beat). With how PokerShowdown defines a bad beat event, if the hand histories being processed find 1 million bad beat events, then there will be 1 million bad beats, and 1 million suckouts, not one more or one less. That being said, why should any one player experience one more often than the other? The answer is they shouldn't over the long run.

PokerShowdown defines some ratios (LuckFactors = LFs) that make it easy to determine if a player has been lucky/unlucky with regard to that statistic. In general, a value greater than 1 indicates good luck (shaded green), and a value less than 1 indicates bad luck (shaded red). For example, LF2 = SOP/BBP, so if a players SOP > BBP, they experienced suckouts more often that bad beats, and have been lucky.

Another way PokerShowdowns measures luck, is by the severity of a bad beat. There are really two ways to measure bad beat severity: odds that were overcome, and the amount of chips won (or not won). These measurements are combined to make "bad beat factor (BBF)" and "suckout factor (SOF)". As an example, if someone hits a one-outer on the river after calling bets from behind each round, the odds overcome were pretty high. However, if blinds were small, and the bets were minimal, and the pot size was relatively small, then the "chips not won" was small. Contrast that with that same exact one-outer occurring at a final table with huge blinds and a huge pot. The BBF and SOF values would be much higher in the latter situation. Each bad beat event has a BBF and SOF associated with it. A player's average BBF and SOF is combined to from LF3. Again, if LF3 is greater than one, their average SOF has been greater than their average BBF, so their average SO has been more 'severe' than their average BB. So they have been lucky with regard to that statistic.

LuckFactor1 (LF1) is the ratio of number of actual wins (NW) over the expected number of wins (EXNW). So if the player has more wins than expected, they have been lucky, and vice versa. The expected number of wins comes directly from preflop expected win percentages of each showdown.

Any of these stats can be calculated over different periods (Cumulative stats period). These include per day, per month, or all time.

Click on any cumulative stats row, and the lower frame will show the showdowns that went into calculating those statistics. You can drill down to the lowest level by double clicking on a showdown row. This will bring up an annotated hand history for that showdown (annotated lines start with ###). An example of an annotated line is below:

Player player_name allin (955)
### player_name (Ad,8d): BET: 955, EXEQ: 29.30574, APOT: 1525, PO: 1.596859, EV: -0.5320287, BB: 1, GB: 0, FAV: 0
BET: amount called or bet
EXEQ: expected equity at this point in the hand
APOT: available pot (chips available to be won by this player)
PO: pot odds
EV: expected value
BB: bad bet (player put chips in pot while EXEQ < 50% AND expected value less than zero)
GB: good bet (player put chips in pot while EXEQ > 50% OR expected value greater than zero)
FAV: player is favorite to win (highest EXEQ amonng players still in hand)

Some showdowns are not included in the cumulative stats (rows that are shaded grey). One reason is split pots where more than one player won chips. This can be complicated to figure out and doesn't occur often enough to be worth including. Also, if any player mucks their cards, that showdown is not included in their stats. Some hand histories actually show mucked cards, so it is possible to calculate all the necessary probabilities. However, because a player only mucks if they lose, including mucked hands could bias the results.

I use PokerShowdown every time I have a session of online poker.   I feel I've come up with a great set of statistics that capture and quantify how much luck (good or bad) a player has experienced.   This tool does not focus on poker skill as other popular poker tools do.  Below I plotted my LF (Luck Factor) for January 2017 vs tournament profit.   There is an obvious correlation between getting lucky and profiting in touraments (or having bad luck and not cashing).

### Statistic Details

• Stats Columns
• NS (Number Showdowns): Number of showdowns processed (can vary based on exclude options).
• NW (Number Wins): Number of actual showdown wins.
• EXNW (Expected Number of Wins): Expected number of wins based on accumulated preflop expected win percentages of all processed showdowns.
• SD (Standard Deviation): Standard deviation of distribution of random variable Win (value = 1 for a win, 0 for a loss, with probability of preflop expected win percentage for each event).
• NSD (Number Standard Deviations): Number of standard deviations NW is from EXNW.
• PC (Percentage Confidence): Probability of EXNW falling outside the expected result (NW > NSD from EXNW).
• LF1 (Luck Factor1): NW/EXNW with scaling factor.
• AEXWP (Average Expected Win Percentage): Average preflop expected win percentage among processed showdowns.
• NBB (Number Bad Beats): Number of bad beats among processed showdowns.
• NBB_O (Number Bad Beat Opportunities): Number of bad beat opportunities among processed showdowns.
• BBP (Bad Beat Percentage): NBB/NBB_0
• NSO (Number Suckouts): Number of suckouts among processed showdowns.
• NSO_O (Number Suckout Opportunities): Number of suckout opportunities among processed showdowns.
• SOP (Suckout Percentage): NSO/NSO_0
• LF2 (Luck Factor2): SOP/BBP
• ABB_F (Avearge Bad Beat Factor): Average bad beat factor among processed showdowns.
• ASO_F (Avearge Suckout Factor): Average suckout factor among processed showdowns.
• LF3 (Luck Factor3): ASO_F/ABB_F
• LF (Luck Factor): Combination of LF1,LF2,LF3 with scaling factors.
• Showdown Columns
• ExWp (Expected Win Percentage): Preflop expected win percentage.
• Won (Won): A flag indicating if this player won the showdown.
• Bb (Bad Beat): A flag indication if this player experienced a bad beat.
• So (Suckout): A flag indication if this player experienced a suckout.
• BbO (Bad Beat Opportunity): A flag indicating if this was a bad beat opportunitiy for this player.
• SoO (Suckout Opportunity): A flag indicating if this was a suckout opportunitiy for this player.
• BbF (Bad Beat Factor): A measure indicating the severity of a bad beat.
• SoF (Suckout Factor): A measure indicating the severity of a bad beat.
• Ribha (Run Into Big Hand Ahead): A lucky situation where this player held a big hand against a player with a slightly less big hand.
• Ribhb (Run Into Big Hand Behind): An unlucky situation where this player held a big hand against a player with a slightly bigger hand.
• exclude (Exclude): Showdown is excluded from calculated statistics.
• ExcludeReason (Exclude Reason): Reason showdown is excluded from calculated statistics
• Important Concepts
• Bad bet: A player puts money into the pot (bet, call, raise etc) while expected value < 0
• Good bet: A player puts money into the pot (bet, call, raise etc) while expected value >= 0
• Bad beat: A player makes a good bet and another player makes a bad bet. The player who made the bad bet wins. The player who made the good bet receives a bad beat and the winning player receives a suckout. There are other conditions but that is the main idea.
• Suckout: Same event as above. For every player that receives a bad beat there is also one and only one other player that receives a suckout. Therefore the total number of bad beats = total number of suckouts over all processed showdowns.
• Bad beat opportunity: A player makes a good bet and another player makes a bad bet. May or may not lead to a bad beat.
• Suckout opportunity: Same event as above.