The Statistics of Poker Data Mining Statistics Applied to Small Stakes No-limit Hold'em - Steve Selbrede

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Here is a summary of the book “The Statistics of Poker” by Steve Selbrede:

• The book uses statistical analysis of large poker databases to identify patterns and “truths” about how poker games are played at low stakes. This is modeled after the way astronomers analyze large datasets to understand phenomena they cannot directly experiment on.

• It assumes the reader has basic poker knowledge and aims to refine their game by exploiting typical mistakes and weaknesses of opponents. It does not teach beginning poker strategy.

• Statistical concepts covered include VPIP (voluntarily putting money in the pot), PFR (pre-flop raise), position awareness, tendencies from different betting positions, and post-flop, turn and river statistics.

• The book provides charts and examples to analyze a player’s own stats and identify leaks compared to optimal ranges. It explains how to construct a starting hand chart.

• Additional chapters discuss comparing stats across stakes, set mining, whether poker is a game of skill, table selection, and other miscellaneous topics.

• The goal is for readers to study specific concepts, find flaws in their own game, and implement adjustments - not just casually read it. Statistical understanding can improve one’s poker knowledge beyond fixing individual leaks.

So in summary, the book uses a data-driven statistical approach to analyze low-stakes poker games, identify typical mistakes, and provide tools and strategies for players to evaluate and improve their own game.

Here is a summary of the key points from the provided text:

• The primary goal of the book is to help players identify and fix leaks in their poker game by analyzing large volumes of poker hand data.

• It compares poker skills and abilities to a bucket with leaks of different sizes - the goal is to plug the leaks to reduce money lost.

• The book will focus on analyzing data from No Limit Hold’em games played at stakes between $0.50/$1 and $2/$4 online, as these stakes see developing players.

• Over 6 million poker hands from these limits will be analyzed to identify statistical patterns and optimal strategies. More data provides more confident conclusions.

• Statistical analysis of hand histories allows identifying individual player tendencies and strategies, which can then be exploited by opponents.

• A major hurdle for players is overcoming cognitive biases like confirmation bias when analyzing their own game. The data and analysis aims to provide an objective viewpoint.

• The goal is not to provide formulaic strategies but to help players identify potential leaks in their game, understand how to measure these leaks, and then find ways to gradually plug each leak through study and adjustment.

• The chapter examines win rates and player statistics from a large database of online poker hands to gain insights.

• More experienced players tend to have higher win rates. Players see the most improvement in their first 10,000-30,000 hands, after which skill levels stabilize.

• Even the most experienced players (over 80,000 hands) only averaged around $1,100 in profits each. Low-stakes online poker provides a small income at best.

• Binning and grouping player data by total hands dealt provides a more accurate view of win rates than plotting individual datapoints. It accounts for the fact that some datapoints represent many more hands than others.

• Around 1/3 of top players were winners, and the percentage of winners increases with experience level. Claims that only a few percent of players win are exaggerated.

• Heads Up Displays (HUDs) that provide statistics on opponents are extremely useful for multi-tabling. They allow players to quickly access stats like VPIP during a game. Customizing the HUD to prioritize important stats is important.

• Experience generally leads to improved skills and results, but significant gains tend to level off after 40,000-50,000 hands for most players. Ongoing learning is required to maintain an edge.

• Experience leads to profitability in poker, but studying stats can help accelerate the learning process. Two important pre-flop stats are VPIP and PFR.

• VPIP measures a player’s looseness by calculating the percentage of hands they voluntarily put money in the pot. Tighter players with lower VPIPs tend to be more profitable. The optimal VPIP appears to be around 15%.

• PFR measures aggression by calculating the percentage of hands a player raises pre-flop. More aggressive players with higher PFRs tend to be more profitable, with the optimal PFR around 11.5%.

• The aggression ratio (PFR/VPIP) combines these stats and peaks at around 0.81, indicating we should raise most but not all of the hands we play.

• Other important pre-flop stats include the aggression factor (AF) and aggression frequency (AFq), which measure how often a player’s actions are aggressive rather than passive.

• A well-designed HUD can provide stats that give insights into opponents’ tendencies, helping players make more informed decisions. Studying stats can help improve results more quickly than experience alone.

• AF and AFq are useful as postflop stats to see how a player plays different flop, turn and river actions, but they are not that useful to display on a HUD for making preflop decisions.

• There is no consensus on the precise ranking of starting poker hands. Different experts use different methods like PokerStove equity, SAGE game theory models, or the Sklansky-Chubukov system. Hand values can vary based on factors like limit vs no limit, heads up vs tournaments, etc.

• The passage discusses several approaches to ranking hands - PokerStove equity, SAGE power index, Sklansky-Chubukov, and introduces a new SEQ ranking system that aims to improve on PokerStove by accounting for a hand’s ability to flop big hands or draws.

• There is a concept of “hand groups” where small differences in rankings are ignored and hands are placed into broader tiers. This simplifies decision making.

• There is a difference between CPFR (calling a raise after putting money in) vs CCPF (cold calling a raise without first acting). CCPF is a better indicator of how wide a player plays against opens.

• The “gap concept” suggests players need a better hand to call a raise than they would need to raise first in themselves. CCPF should generally be lower than RFI according to this concept.

• The passage discusses the optimal ranges and ratios for various pre-flop stats like VPIP, PFR, and aggression ratio based on analyzing large poker databases.

• It notes that the average experienced player is too loose and passive compared to the optimal values, which costs them losses. However, being too tight can also be problematic.

• Two example students, Frodo and Sam, are analyzed based on their pre-flop stats. Frodo is too tight and passive, while Sam is too loose and passive. Recommendations are given for how each could improve by adjusting their ranges.

• Position awareness is important. Players should play more hands in late position than early position. Both students have decent position awareness but still need to refine their ranges.

• The gap concept compares the optimal opening raise percentage to the optimal defend percentage as a way to analyzeprofitability. However, it is less meaningful comparing an individual villain’s raise to one’s defend range since post-flop play and position come into factor.

• Additional analysis graphs are included in the appendix looking at relationships between various pre-flop stats and win rates based on larger samples of players with more experience.

• Figures 2.8f, 2.8g, and 2.8i-k show relationships between various poker statistics like win rate, return on win rate percentage (RWPC), pre-flop aggression factor (AF), and opportunities (number of hands played). The curves suggest potential optimal values around 14% for RWPC and 7% for AF.

• Figure 2.8i plots win rate against AF and shows two best-fit curves. Point A may be anomalous.

• Figure 2.8j extrapolates the curve to suggest an optimal AF of 2.4, matching Figure 2.8g. The actual downturn is likely due to variance from low-AF players who got lucky.

• Figure 2.8k compares the average statistics for all players versus the top 2,000 players. The “peak” shows the theoretically optimal values based on the curves.

• Figure 2.8L compares opportunities (hands played) for all players versus the top 2,000 players.

In summary, these figures examine relationships between various poker metrics and identify potentially optimal values based on curve fitting and extrapolation of the data points. They suggest metrics where average players could improve to increase their win rates.

Here is a summary of the key points about hen moving from Early Position to the button:

• As position gets later, it is more profitable to open up your ranges and play more hands. You should play closer to the optimal VPIP in later positions compared to early position.

• Mr. Average plays too passively in late position and on the button. He only slightly too passive in early positions according to the graphs.

• Having a higher PFR/VPIP aggression ratio is associated with higher win rates. Mr. Average’s ratio of 0.44 is too low and is leaking money compared to the optimal ratio of around 0.75-0.8.

• When given steal opportunities on the button and cutoff, it is optimal to attempt to steal around 40% of the time from the button and 25% from the cutoff according to the graphs. The best players may attempt to steal even more.

• Having too high of a steal success rate does not necessarily correlate with maximum profit since your success rate will go down as your attempt rate increases. The optimal is to balance attempt rate and success rate for maximum profit.

• Online, using a HUD to track opponents’ fold to steal percentages can help determine which players are more exploitable to steal from by calculating the expected value of each steal attempt. Selectivity is important when opponents do not fold to steals often.

So in summary, players should tighten up in early position but open up more hands and play more aggressively as they get to more advantageous later positions like the button according to the optimal ranges and strategy adjustments presented.

• An overall RFI stat has limited usefulness, as what constitutes good aggressive play depends on the specific positional situation.

• Figures 3.5a and 3.5b show that winning players tend to Raise First-In (RFI) more often than losing players, especially in late positions like the button where position is important. But RFI percentages should vary by position.

• RFI opportunities are more common in early positions but calls are risky since others can enter the pot. Late positions have fewer RFI opportunities but calling a raise keeps position and opponents behind are few.

• Figures also show limping first-in (LFI) correlates with weaker profits across all positions, implying it’s best to minimize LFI percentage, possibly to zero.

• When there are previous callers (limpers), raising them can be profitable to isolate weak players or induce incorrect pot odds. Figures 3.6a and 3.6b show raising limpers (RWPC) correlates with higher profits, especially on the button where Mr. Average is too passive.

• Limping behind limpers (LWPC) also correlates with weaker profits, though optimal LWPC percentages are 4-8% depending on position, such as with small/medium pairs for set value in passive tables.

• We can limp behind multiple limpers in late positions with speculative hands that have potential for a big hand but aren’t very likely. These hands should not be dominated and it’s best when opponents behind are not aggressive or we have positional advantage.

• We might limp behind a single limper with a big hand if opponents behind tend to punish limpers.

• When defending against a preflop raise, we should normally fold all but our best hands due to the gap concept. We may consider 3-betting (reraising) or cold calling depending on the situation.

• Reraising works best with our top hands to steal the blinds or trap opponents. We can also reraise with some hands below our top range situationally.

• Cold calling can be done more often in better positions. The optimal cold call percentage is around 7% from the button and lower in earlier positions.

• Squeezing is 3-betting after a loose opponent raises and another opponent calls. It works best against loose aggressive raisers when the caller may not have a strong hand. Positional advantage and knowledge of opponents’ tendencies is important.

• Optimal squeeze percentages are similar to 3-bet percentages, around 4% from the button. Some squeezing can be done with speculative non-premium hands situationally as a “bluff.”

• Mr. Average does not squeeze or 3-bet enough compared to optimal strategies, but the costs of deviation are small according to the data. Squeeze opportunities are infrequent so analysis is less precise.

• There were only around 320,000 - 340,000 squeeze opportunities for the top 2,000 players, and optimal squeezing rate is around 3-4%, so not many hands are actually squeezed.

• Cold calling a squeeze (overcalling a raise) has better implied odds than cold calling a single raise, since there is already money in the pot from other players. The data suggests overcallers can double their range from around 6% to 12%.

• Button steals have positive expected value against most blinds, even with weak hands like J8o or 72o, because of the folding equity from the blinds. Having HUD stats on fold to steal percentages is very useful for determining when to steal.

• Position awareness, as measured by VPIP position adjustment (PAW), is a key predictor of player profit. The optimal VPIP PAW is around 1.6, with slightly higher values also acceptable. Players should adjust their ranges based on their position.

• A leaky player like “Frodo” was identified as not position aware based on a PAW of 1.2. He was playing too tight in late position and on the button. The recommendation was to construct starting hand charts to help identify which additional hands to play in those positions to improve.

• Optimal VPIP and PFR percentages are tighter in early position and looser on the button, due to better positional advantage later.

• Most players are too loose and passive in all positions.

• Profit increases with more stealing attempts from the button and cutoff.

• The PFR/VPIP ratio detects loose-passive “fish”; the optimal ratio increases from early position to the button.

• Optimal RFI percentage is higher on the button compared to early position.

• Limping first in is generally a mistake. Limping behind other limpers can be okay with postflop position.

• Players under-raise limpers, especially from late positions where raising 20% from the button and 13% in the hijack is optimal.

• Cold calling a raise should be low (4%) in early position but can be higher on the button (8%) due to position.

• Squeezing is more profitable than just raising, since a caller improves odds of showing down the best hand.

• Blinds are unprofitable, with an average “blind tax” loss of around 1 BB per orbit.

• Stealing from the small blind should be done over 30% of the time when last to act.

• Limping or raising behind limpers depends on positions and number of limpers. Overall position is still important despite having acted last preflop.

• Figure 4.3a shows that the optimal percentage to call a raise (limp with connection, LWPC) from the small blind is around 34%. The average player does this 50% of the time, which is too often.

• Figure 4.3b indicates the optimal percentage to raise limpers (raise with position, RWPC) is around 9% from the small blind and 12% from the big blind. However, this latter stat includes blind vs. blind games where raising more is standard. The optimum is likely similar for both blinds, around 9%.

• When facing a previous raise from the blinds, the optimum percentage to call (call pre-flop raise, CPFR) is much lower than the curves suggest, due to including blind steal attempts. The author estimates the CPFR should be similar to early position, around 4%.

• Figure 4.4b shows the optimal percentage to re-raise a previous raise from the blinds is around 4% for either blind position.

• In total, the optimal defending range from the blinds is estimated to be around 16% for the big blind and 11% for the small blind, whereas average players defend 24.3% and 17.3% respectively, calling too often.

• Premium hands from the blinds should usually be re-raised rather than called due to post-flop position, except in blind vs. blind situations.

• Examples are provided to illustrate calculating expected value of calling vs. raising from the small blind based on opponent stats and ranges. Overall, playing the blinds optimally requires a balanced and disciplined strategy.

• Raising from the small blind when there are limpers ahead of you should be done about 1/3 of the time, depending on the number of limpers. But completing with any two cards is a big leak, and you will be out of position postflop.

• Raising limpers from the blinds should mainly be done with a tight early position range, except for blind vs. blind play.

• Calling a preflop raise from the blinds is generally a losing strategy and should only be done about 7% of the time given the positional disadvantage postflop.

• Keeping your strategy hidden from data miners is tricky. You can’t simply 3-bet the top 4% of hands and call with the next 7% from the small blind - you need to call with some strong hands and add a few weaker hands to achieve around a 4% 3-bet frequency.

• Use your HUD to identify players who are likely exploitable with a small blind 3-bet, especially those who are multi-tabling or data mining. Adjust your strategy against specific opponents.

Here is a summary of the key points in a chart:

Starting Hand Chart Analysis

Raising Range (VPIP/PFR %)

• Tight passive (15/10)
• Tight aggressive (20/15)
• Loose aggressive (30/25)

Position

• Early position (fold more, see more flops)
• Late position (raise more, see fewer flops)

Pot odds

• Out of position (need better hands)
• In position (wider value range, drawing hands)

stack sizes

• Deep stacked (bluff more)
• Short stacked (value bets only)

Villain type

• Nit (wider ranges)
• LAG (tighter value ranges, bluff less)

Flop textures

• Wet boards (bluff/continuation bet less)
• Dry boards (wider bluffing range)

The chart should provide guidelines but also allow flexibility based on reading opponents. Adjust over time based on tracking stats and results.

• CBet frequency should be higher when in position (IP) versus out of position (OP). IP CBet optimum is 83% vs 73% for OP.

• CBet frequency depends on number of opponents. Heads-up pots require a higher CBet rate (73%) than multi-way pots (51%).

• When acted upon by a raise to your OP CBet, the optimal response is to fold about 2/3 of the time, call and raise each around 18% of the time.

• When checked to on your IP CBet and then check-raised, the optimal response is similar to an OP CBet raise - fold slightly less often.

• When facing a Donk Bet (when checked to as preflop raiser and then bet into), the optimal response may be to fold 60%, call 22% and raise 18%. Alternatively, calling nearly everything may also be profitable.

• Experienced players tend to mostly just call Donk Bets to trap with strong hands and float with weak hands.

• A preflop float with a flop bet is called a “Flop Float Bet”. The goal is to call a preflop raiser IP with a weak hand and take the pot if they fail to CBet flop.

So in summary, CBet frequency and responses to raises/bets depend on position, opponents, and villains’ tendencies which can be tracked with a HUD. Both folding and calling/trapping responses can be profitable depending on the situation.

• Villains that CBet too infrequently miss opportunities to steal pots when players miss the flop and check-fold. However, some players will call preflop raises with strong but not overpowering hands and float (bet on the flop after checking) rather than re-raising. Their flop bet does not necessarily signify a weak hand trying to steal the pot.

• When a player raises preflop and checks the flop, leaving an opponent in position to float bet, this creates a “float defense opportunity” where the player can call, fold, or raise the float bet. Optimal play is to fold most of the time (over 80%), call less than 20% of the time, and raise around the same rate as average players (8.5%).

• Figures show that having called a preflop raise, the optimal response to an in-position opponent’s continuation bet is to fold about 63% of the time, call around 25% and raise around 12%. Even optimal play results in losses, so calling preflop raises should be avoided.

• Out of position, the optimal response to a continuation bet is only slightly different - folding 69% of the time instead of 63%. So position is only a small factor in float defense. Average players fold too infrequently.

• Donk betting (betting into the preflop raiser on the flop) is never optimal - the optimal donk bet percentage is zero or close to it.

• Floating the flop (calling preflop and betting after the preflop raiser checks) is optimal around 70% of the time when in position postflop. Villains typically fold to floats over 80% of the time.

• In limped pots in position, the optimal play is to open (bet) the flop over 88% of the time when opponents check, as they typically show weakness by doing so. Average players fail to exploit this, opening far too infrequently.

• The article discusses various flop aggression stats that can be used to analyze player tendencies and optimize profitability post-flop.

• Flop aggression factor (AF) compares the rate of betting and raising to calling on the flop. Higher AF is generally more profitable, though it does not account for folding.

• Flop aggression frequency (AFq) compares the rate of betting, raising and folding to the total number of possible actions on the flop. Around 57% AFq seems optimal for profitability.

• On average, players have significantly lower AF and AFq than optimal levels, suggesting room for improvement by being more aggressive post-flop through betting/raising more and calling/folding less often.

• Tracking these stats in a HUD can help identify opponents who are too timid post-flop and exploitably weak, as well as areas for self-improvement by raising one’s own AFq through adjustments to preflop strategy and flop play.

In summary, the article analyzes various flop aggression metrics and argues that overall profitability can be increased by players adopting a more aggressive approach post-flop through higher rates of betting, raising and folding. Tracking these stats in a HUD is recommended.

Here is a summary of the key points about turn statistics:

• About 40% of hands reach the turn, with 55% of flop hands reaching the turn. On average 41% of dealt hands see the turn.

• The top 2,000 most experienced players are much more profitable at the turn than average players, winning 67 BB/100 compared to 2 BB/100 for all players. Position is important, with IP profit being double that of OP.

• Over 70% of turns are heads-up, with an average of 2.37 players seeing the turn.

• Turn statistics may be less reliable than earlier streets since they are based on fewer hands. Stats with more observations like CBet opportunities IP are more reliable than less frequent stats like CBet-FaceRaise opportunities IP.

• Contrary to intuition, the most profitable IP players reached the turn with only 17% of their flop hands, indicating better players fold more incorrectly on the flop. Less skilled players call too often with marginal hands.

• The quality of opponents likely decreases from earlier streets to later streets as better players fold earlier, making turn and river optima possibly less reliable than flop optima.

• Position remains very important at the turn, with IP profit being much higher than OP profit for experienced players. Aggressive and profitable play requires strong postflop play as well as position.

• The r value of 2.37 for players seeing the turn means that for every 1 IP (in position) player, there are 1.37 OP (out of position) players on average.

• This implies the optimal percentage of hands seen OP should be around 23%, which is close to what the curve in Figure 7.0c shows.

• Figure 7.0c shows a curve plotting turn positional profit against the percentage of turns seen for top players. It indicates the optimal percentage to see the turn IP is around 33% and OP is around 23%.

• Mr. Average sees too many turns both IP and OP, around 37% IP and 28% OP according to the figure, which is a losing strategy.

• To improve their turn seeing percentages, players should call fewer flop bets and bet more flops themselves to shift the percentages closer to the optimal values.

• If a player’s turn seeing percentages are far from optimal, they need to analyze potential leaks in their flop play that may be causing it, such as checking too often on the flop IP or betting too infrequently OP.

• Turn check/raising can be a profitable play under certain circumstances, such as when the villain is aggressive or you have a strong hand and want to raise their turn float bet. However, the optimal rate to turn check/raise is low, around 5%, so it should be used selectively.

• When facing an opponent’s turn check/raise, the optimal response is to fold 54% of the time and call 33% of the time according to the statistics. Straying far from these rates can be very expensive.

• It’s difficult to get meaningful read on an opponent’s turn check/raise frequency from their HUD stats, since these situations occur infrequently, less than 0.5% of hands. But one can evaluate their own play compared to theoretical optimal rates with a large enough database of own hands.

• In both turning and facing turn check/raises, the situation requires caution and selecting spots carefully according to opponent tendencies and hand strength, rather than using it routinely or far from the optimal statistical response.

• The passage discusses turn aggression factors and statistics to evaluate a player’s turn play.

• The Turn Aggression Factor (AF) is defined as (Bets + Raises) / Calls. It measures how often a player’s turn actions are aggressive (betting or raising) versus passive (calling).

• Figures 7.5a and 7.5b show that an optimal Turn AF is around 3.0, both in and out of position. Mr. Average has a substantially lower AF than optimal when in position.

• Mr. Average plays too passively when in position by checking too often and calling bets too often rather than raising or betting. This leads to leakage of around 15 big blinds per 100 hands.

• The Turn Aggression Frequency (AFq) includes folds in the calculation and is defined as (Bets + Raises) / (Bets + Raises + Calls + Folds) x 100.

• AFq shows Mr. Average is optimal in position but too aggressive out of position due to overcalling and not folding enough.

• Two examples are provided of analyzing villains’ turn stats and identifying leaks - one player is too aggressive on the turn and the other sees too many turns due to weak preflop play and postflop passivity.

• The optimum turn CBet percentage is position dependent, being 35% in-position and 21% out of position. Most players CBet the turn too frequently.

• In-position turn profit is about double the out-of-position profit.

• Hero should rarely Donkbet the turn, probably less than 1% of the time, as Donkbetting is a big leak.

• Floating the turn can be very profitable near the optimum of 58%.

• Hero should rarely check-raise the turn, as perhaps 5% is optimal. If you have a good hand, bet it.

• Your Turn Aggression Factor should be much lower than your Flop Aggression Factor. Position does not have a big influence on optimum Turn AF.

• Your overall Turn Aggression Frequency should be lower than your Flop AFq. Position has a moderate influence on this, with 46% optimal when in position and 35% when not.

In summary, the key points are around position dependent turn betting strategies, avoiding Donkbetting, the profitability of floating, and adjusting turn aggression compared to flop aggression.

• If stacks are small relative to big blind sizes, around 100 BBs or less, river c-bets may need to be all-in bets to avoid multiple callers.

• In-position river c-bet percentages should be higher than out-of-position, around 50% vs 30% on average. Mr. Average c-bets too much when out of position and not enough when in position.

• It is rare for an opponent to raise a hero’s river c-bet, occurring around 1,000 times IP and 5,000 times OP out of millions of hands. There appears to be two optimal response percentages - usually fold one type of situation, usually call in another.

• When defending against an opponent’s river c-bet with a strong hand or draw, implied odds are usually better than pot odds if stacks are deep and opponent has shown strength on earlier streets.

• When in position with a strong hand on the river, the optimal response is mostly to fold (48%), call less (34%), rarely raise (18%). Out of position, there are two optimal call percentages around 21% and 57%, and fold percentages around 71% and 41%.

• Donk betting the river around 12% of the time when calling the turn is better than checking to induce bluffs or get value, as checking weakens the hand and opponents may check back.

• When facing a river donk bet as the aggressor on the turn, we should call and fold at similar rates according to the data. Calling about 33% of the time and folding 67% seems close to optimal.

• We may consider donking the river ourselves as a bluff when we miss our draw but a scare card appears that could represent a missed draw for our opponent.

• Floating the river by betting ourselves after checking involves taking risky value bets and bluffs sometimes without a strong hand. We need to make judgment calls based on the situation and opponent.

• Checking the river then calling a float bet about 1/3 of the time and raising only 3% of the time appears close to optimal based on the data. Mr. Average plays this close to optimally as well.

• Check-raising the river should be done very rarely, around 2% of the time according to the data. Value betting strong hands is better than checking them hoping to check-raise.

• The optimal river aggression factor is around 3.1 regardless of position. Mr. Average is too passive in position and too aggressive out of position compared to this.

• The optimal river aggression frequency (including folds) is about 38% overall, close to the average turn aggression frequency of 40%. Mr. Average is close to optimal in position but not out of position according to these stats.

Here are the key points about comparing different poker stakes based on the information provided:

• Win rates tend to improve as the stakes increase, from NL10 to NL200. NL50 probably has the most recreational players, while NL200 has fewer but better players on average.

• The most experienced players in each game have better win rates than average, showing the value of experience.

• The optimal VPIP is around 14% across all stakes examined, showing fundamental strategy does not change much.

• Non-optimal VPIP is more costly at higher limits, as better players will punish mistakes more.

• Optimal PFR is also around 10-11% across stakes, indicating fundamental postflop strategy is similar.

• VPIP and PFR curves flatten at lower limits, suggesting those games play more similarly to each other than to higher limits.

• Recreational players have similar loose VPIPs around 20% at all stakes, leaving room for profits by playing optimally.

• While strategy may be similar, the level of competition tends to increase with stakes, making higher limit games relatively more difficult. Overall, optimal strategies do not appear to change dramatically across these stake levels. Experience and skill, rather than strategy adjustments, seem most important for moving up successfully.

Here is a summary of the key points from the passage:

• The NL50/100 value from this edition is higher than other editions likely due to more selective criteria. The top 2,000 players represent a higher quality average.

• The average database player and average top player have similar preflop fold percentages at a given stakes level.

• The average player is less aggressive than optimal, especially at lower stakes levels. Higher stakes players leak less value and are closer to optimal.

• Higher stakes players like NL200 are more aggressive preflop on average than lower stakes. This is likely due to more experience.

• Position awareness is similar across stakes levels except NL10 which benefits more from greater position awareness.

• Various pre-flop stats like raise first in, raise with callers, limp with callers indicate NL200 players play tougher by being more aggressive and less likely to limp behind.

• Overall, the smaller stakes games play similarly preflop but NL200 begins to be noticeably tougher with more aggression. Experience increases win rates up to around 2.3 BB/100 at 60,000 hands played for NL200 players.

In summary, while optimal play is similar across stakes levels, higher limit games have tougher more experienced opponents playing closer to optimal levels, making them harder to profit from long term compared to lower stakes games.

• The “50,000 hand rule” refers to the idea that a player needs to play around 50,000 hands of poker to become truly successful at a particular game. This requires more than just mindlessly playing many tables - the player needs time to analyze specific situations, opponents, and stats.

• Part of analyzing those 50,000 hands is replaying key hands and noticing subtle leaks in one’s stats. The player should try different approaches and re-evaluate.

• If a player has achieved winning results over 50,000 hands at a lower stake like NL50, it is unlikely they would need another 50,000 hands to reach their potential after moving up to NL100, as they’ve already gained substantial experience.

• Data mining, or importing one’s own hand histories into a tracking program, is generally considered acceptable and a smart way for players to improve. However, purchasing hand histories that one did not play is against the terms of service of most poker sites and more questionable ethically.

• When playing pocket pairs, a player needs to consider the proper implied odds for set mining situations like seeing a flop after a limp or calling a raise. Just looking at overall profits can miss opportunities to improve play with certain pair strengths or board textures. Analyzing pair stats in more depth can reveal leaks.

• The passage discusses the importance of table and seat selection for improving one’s win rate in poker. Good table selection involves choosing tables with losing, loose players and avoiding tables full of very strong, aggressive winners.

• When selecting a seat, optimal positions are to have loose, losing players on one’s right and tight, passive players who don’t defend their blinds well on one’s left. This maximizes having the better players in position relative to oneself.

• The example table analyzed shows several positive features for the hero’s position, including two loose losing players to the right, two tight solid winners who don’t defend well on the left, and new/weak players in some positions as well. However, there are also some potential negatives like one aggressive blind stealer that would require study.

• Overall, careful selection of favorable tables and seats can provide exploitative opportunities and improve one’s results by choosing to play against inferior opposition when possible. Table selection is an important skill in poker.

Here is a summary of the key points about 6-max no limit hold’em from the article:

• 6-max games are more popular online than full ring games, especially at higher stakes. This means players need to transition to 6-max to advance.

• 6-max is not entirely a subset of full ring, as players tend to be more aggressive than they would be in the same position in a full ring game.

• The most experienced 6-max players are about as profitable as the top full ring players, but less experienced 6-max players are worse off.

• Optimal VPIP and PFR percentages are slightly higher in 6-max compared to full ring in the same position, to account for being first in more often with fewer players.

• Peak profits are higher in 6-max at all positions compared to full ring.

• Blinds come around more often in 6-max but optimal blind play can reduce losses compared to full ring.

• Mr. Average players analyzed tended to be too loose from early positions and too passive, especially from late positions like the button, costing them potential profits.

So in summary, 6-max rewards more aggressive play compared to full ring due to positional advantages, but optimal strategies are still shaped similarly regarding factors like VPIP and PFR as position changes.

• The figures compare profitability and various poker metrics between 6-max and full ring games. Overall, optimal full ring strategy seems to translate well to 6-max, but with some differences.

• PFR% is higher in late positions for 6-max compared to full ring. This makes sense as there are more opportunities to raise in late position with fewer players.

• Peak profit is higher for blinds in 6-max than full ring. This suggests playing the blinds more aggressively by completing less and raising more often in 6-max.

• The optimal PFR/VPIP ratio decreases closer to the button position in both formats, allowing some limps or calls. It is lower in the blinds, perhaps allowing more speculative cold calls.

• Peak profit and optimal ratios are generally higher for 6-max, indicating it may reward more aggressive strategies compared to full ring.

• While full ring strategies carry over, optimal stats may differ between the two formats. Reaction to situations should be similar, but exact stats like PFR% may vary based on player count.

• More detailed analysis of additional poker metrics on every street could reveal further subtle strategic differences between 6-max and full ring.

The number of hands a player faced a 3-bet preflop is recorded as cnt_p_3bet_def_opp. This refers to the number of times the player had to act (call, raise, or fold) after their opponent 3-bet them preflop. It provides information about how often the player was put to difficult decisions postflop by an opponent’s aggressive preflop raising.