Poker Software and Analysis

Abstract

In No Limit Poker, players often like to raise from the button, with the aimof stealing the blinds. These steals can be of any size between the minimumraise (equivalent to one big blind) and the stealer's full stack. It is foundthat there is not a single optimal level, but that as the steal size getsexcessively large the expected value tends to drop.

Introduction

This is a page of charts for NL Holdem games from Pokerstars. Thedatasource is PokerFTP.

Method

A Java application was written to analyse the data from PokerFTP.

Hands with where players other than the small and big blind wereexcluded.

A steal attempt is defined as when the action is folded to the button, andthe button raises. They are therefore risking their steal amount in order towin 1.5 big blinds (posted by the small and big blind).

For example, if the button raises the action to 2 big blinds, they arerisking 2 big blinds to win 1.5 big blinds. For the purposes of this analysis,I have assumed that the steal attempt results in a loss if the small and bigblinds do not both fold. Therefore, for stealing to be +EV, it needs to besuccessful more than 57% (2.0 / (1.5 + 2.0)) of the time.

Generalising the equation from the example, breakeven success rate is:

100 * (Steal Size) / (Steal Size + 1.5) %.

Steal Success Rate By Steal Size

The "Steal Success Rate By Steal Size" charts show how the observed successrates vary with Steal Size, along with 95% confidence bounds (LB and UB). Thebreakeven line is also plotted. The observed success rates need to be above thebreakeven line for steals to be +EV.

EV

The "Steal Expected Value by Steal Size" charts show how the expected valueof a steal varies with steal size.

The expected value for a particular steal size is calculated by using theobserved success rate as the expected success rate. The calculation is:

Steal ExpectedValue =

(Steal SuccessRate * 1.5 ) - (Steal Fail Rate * Steal Size)

Results

Below are the charts representing my results.

Filters: 0.1$/0.25$, Num Seats : 9, Site : PS, Game Types : Hold'em NoLimit, Min Num Hands Played : 1000, Inc/Exc Plyrs : 21,477 (04.27%) /481,244

Steal Expected Values by VPIP

Steal Success Rates by VPIP

Filters: 0.25$/0.5$, Num Seats : 9, Site : PS, Game Types : Hold'em NoLimit, Min Num Hands Played : 1000, Inc/Exc Plyrs : 17,296 (05.09%) /322,703

Steal Expected Values by VPIP

Steal Success Rates by VPIP

Filters: 0.5$/1.0$, Num Seats : 9, Site : PS, Game Types : Hold'em NoLimit, Min Num Hands Played : 1000, Inc/Exc Plyrs : 13,452 (04.56%) /281,747

Steal Expected Values by VPIP

Steal Success Rates by VPIP

Filters: 1.0$/2.0$, Num Seats : 9, Site : PS, Game Types : Hold'em NoLimit, Min Num Hands Played : 1000, Inc/Exc Plyrs : 6,630 (04.99%) /126,183

Steal Expected Values by VPIP

Steal Success Rates by VPIP

Filters: 2.0$/4.0$, Num Seats : 9, Site : PS, Game Types : Hold'em NoLimit, Min Num Hands Played : 1000, Inc/Exc Plyrs : 1,878 (03.86%) / 46,825

Steal Expected Values by VPIP

Steal Success Rates by VPIP

Filters: 3.0$/6.0$, Num Seats : 9, Site : PS, Game Types : Hold'em NoLimit, Min Num Hands Played : 1000, Inc/Exc Plyrs : 858 (03.14%) / 26,456

Steal Expected Values by VPIP

Steal Success Rates by VPIP

Filters: 5.0$/10.0$, Num Seats : 9, Site : PS, Game Types : Hold'em NoLimit, Min Num Hands Played : 1000, Inc/Exc Plyrs : 482 (04.50%) / 10,239

Steal Expected Values by VPIP

Steal Success Rates by VPIP

Filters: 10.0$/20.0$, Num Seats : 9, Site : PS, Game Types : Hold'em No Limit, Min Num Hands Played : 1000, Inc/Exc Plyrs : 146 (04.89%) / 2,838

Steal Expected Values by VPIP

Steal Success Rates by VPIP

Filters: 25.0$/50.0$, Num Seats : 9, Site : PS, Game Types : Hold'em NoLimit, Min Num Hands Played : 1000, Inc/Exc Plyrs : 105 (06.01%) / 1,641

Steal Expected Values by VPIP

Steal Success Rates by VPIP

Filters: 100.0$/200.0$, Num Seats : 9, Site : PS, Game Types : Hold'em NoLimit, Min Num Hands Played : 1000, Inc/Exc Plyrs : 0 (00.00%) / 10

Steal Expected Values by VPIP

Steal Success Rates by VPIP

From observing the "Steal Success Rate By Steal Size" charts, we can seethat for all limits, the observed success rates fail to consistently breakabove the breakeven lines. This shows that stealing, with the sole aim ofwinning the blinds, was generally unsuccessful in the sample data.

From the "Expected Value" charts, we can see that the expected values tendto fall off as the steal sizes become very large.

At the higher limits, the range of steal sizes is smaller. This is partiallydue to a smaller player base, and possibly because the players are morecautious.

For limits from $0.25/$0.50 to $2/$4, it also appears that very low stealsare non optimal. As the EV appears to rise as the steal size increase from 2.0to 4.0.

Conclusion

It is hard to choose a correct optimal steal size from these charts as theEVs vary in a non continuous manner as the steal size varies. Min raises can beseen to be non optimal. And so too are excessively large raises.

Most Poker literature recommends a 4BB raise. There is not much evidence tocontradict this, though on the $0.5/$1.0 tables, the EV seems a little higherfor steal sizes between 5.0 BB and 7.0 BB.

However, seeing as the EV's in the charts are all negative, stealing for thesake of stealing is -EV. So before stealing, it is important to have a goodread on the victims. This can be done through manual observation, though aneasier, and perhaps more reliable solution, could be to use a Poker trackingtool such as PokerOffice or Poker Tracker.