Petty Theft: Policing a Small Blind Steal

¹. Most of those circumstances can be mapped to some mathematically representable parameter. We shall use the term ‘hard parameter’ to distinguish a parameter whose impact can be mapped directly to an optimal strategy from a ‘soft parameter’. ‘Soft Parameters’ must be assigned a weighting and considered in concert before any useful strategic information can be drawn from them.

When the BB faces a raise from the SB his opponent is risking 2.5BB to win a 1.5BB pot with a pot-sized raise (or 1.5BB to win 1.5BB with a min-raise). We immediately identify ‘BB fold to SB Steal’ as a hard parameter²; if we fold more than 50% to a min-raise or 62.5% to a pot-sized raise our opponent may raise any 4 cards profitably. Thus this number alone informs us as to the minimum width we must defend to an SB steal as part of an optimal strategy. Of course in practice, unless our response is to 3-bet our entire range, our opponent will see a flop sometimes with any hand he opens with. Accordingly, even if he plays nit-or-fold (say only continuing with top two+, a wrap, or a flush draw) he will still win a fraction of every pot. Tabulated below is the frequency with which our opponent will flop {Top two+, Wrap, FD} when called after raising with a given range fraction.

 

Range Fraction (HU rankings)	Top two+, Wrap, FD
	27%
35%-40%	26%
45%-50%	25%
55%-60%	23.5%
65%-70%	23%
75%-80%	23%
85%-90%	22%
95%-100%	20%

You will notice that even the very worst hands flop something playable at least 1/5th of the time. If we take the extremely conservative estimate that our opponents lose the entire pot 4/5 of the time when we call and retain half the pot 1/5 of the time when we call, we see that their EV when we call is 0.2*0.5 – 0.8*2.5= -1.9bb when they pot-size raise pre-flop. If we never 3-bet then we must defend at least 45% of the time to prevent our opponent potting any four cards pre-flop. A similar calculation yields a minimum of 58% defensive width versus a min-raise. Note that few players are as incompetent as assumed in the above calculation post-flop, and so these numbers represent an absolute floor to our defensive range. Any decision to defend tighter than this against a given player is an exploitative adjustment to that player’s tighter opening range. This is because our opponent could deviate unilaterally to opening any four cards to exploit us when we fold with a higher frequency than calculated.

Soft Parameters

Now we have ascertained the minimum width we must defend from the BB we turn our eyes to the more difficult task of deciding just how wide to defend. One of the ‘soft parameters’ we can use is the equity for a given fraction of our range against our opponent’s total range. The reason this is so valuable is that as ranges widen we are no longer as concerned with polarization potential as we are when tight. Mediocre two pair will commonly get to show down in position BB versus SB. Furthermore, most 6max players are very poor at playing wide ranges out of position post-flop. This soft parameter is tabulated in the heat map below:

The reader will naturally use other ‘soft parameters’ to determine his pre-flop decision, not least his post-flop edge in both single-raised and 3-bet pots, his opponent’s fold to 3-bet and his opponent’s 4-bet range³. However, the value of the heat map displayed above should not be underestimated. You may use it to improve your consistency in hand evaluation. If you are happy defending a 59th percentile hand against a 40% open from a given player, then you should be happy to defend a 79th percentile hand against a 60% open from a similar player. If there is ‘no way’ you would defend a 79th percentile hand against a 50% open, you should be cautious defending a 49th percentile hand against a 25% open.

To conclude, I will provide the reader with a few equity reference points against a 25% opening range:

AJ92:Axx is in the 35th percentile and has 43.5% equity
JJ95ss is in the 11th percentile and has 46.5% equity
KQ96ss is in the 27th percentile and has 43.5% equity
T874ds is in the 47th percentile and has 43% equity

I would consider all of these hands playable from the BB versus a 25% SB steal despite the fact that I would fold most of them were I on the button facing the same opening range. Closing the action for a discounted price is a fine option, and I would encourage you to take that option whenever you can.

 

Blind play is the absolute best starting point for practicing innovative post-flop play. You are typically in position against a wide range and have no fear of being squeezed pre-flop. If the reader is looking to be more aggressive but is unsure where to start then this is the place to spew a little with creative lines. I would also like to extend my thanks to those readers who have recently translated articles on my blog into Russian and Japanese. Expect to see some exciting developments on this site in April.

Good luck at the tables,
Quad