Secrets to Folding Ranges and Proper Bet Sizing
Let’s say you are going to make a river bluff versus an opponent. You have deduced that he either has a top pair type hand, a missed flush draw, a missed straight draw, or a slow-played set that has made a full house. Your opponent hasn’t played a lot with you and it’s unlikely he will read into your sizing too much, so you have a plethora of bet sizes from which to choose, and need to figure out what the best one is for your holdings (a bluff). If you are betting for value, you would want to bet the maximum he would call without increasing his folding range. But since you are bluffing, you will want to bet the minimum amount that gets him to fold without increasing his calling range.
Let’s look at an example of our opponent’s ranges.
For simplicity’s sake, we will assume he has no raising range. Let’s just say the board is Jd 8d 3c 4s 4h and you believe your opponent has:
After paying attention to our opponent’s tendencies we believe he will call up to a 1.25 PSB with top pair hands, he will not call any bets over ¼ pot with missed flush draws and straight draws, and will call all bets with full houses.
(For the example he isn’t raising, it’s just an example.) It’s very important to
calculate the frequency at which your opponent has each of these possible hands to help determine the best amount to bet, in order to to get the most folds. There are 12 combinations of off suit hands, 4combinations of suited hands, and 6 combinations of pocket pairs. When there are board cards that hit
an opponent’s range, it also makes it slightly less likely that an opponent has paired, since one of the cards in their range is now on the board. When you originally had someone on 16 combinations of AJ, they can now only have 12 (here they lose the 4 Ax Jd combos).
There are 82 total hand combinations, 25/82 will fold to any ¼ PSB or higher, 73/82 will fold to any 1.25 PSB or higher, and 9 will not fold to any bet. Take a look at this graph and pay close attention to the inflection points
In NLHE we have many different choices of what size to bet, but if we are faced with this situation, there is really no point in betting any other amounts other than right around each red dot. If we only want draws to fold we should bet just over .25P. If we want top pair to call, we should bet just under 1.25P. And if we want top pair to fold, we should bet just over 1.25P. This graph is saying, “To best exploit our opponent, bet the minimum or maximum needed to get our desired result.” In real life situations, the graph may be more of a straight line than this tiered representation, but there is still abet amount that, if we exceed, will be an overly costly bluff, or a value-bet that gets more folds than we wanted. Try to visualize your opponent’s hand range in sections like this to first understand how many hands make up each section, then what size of bet will give you your desired result. After dissecting their range and assigning it a graph like this one, the question then becomes, “Should I be trying to bluff my opponent off of missed draws only, or also top pair -type hands?
“ Let’scalculate the value of each bet to find out. Some of the variables that should be pretty straight forward are P (pot size), meaning regardless of whether the pot is $1 or $1000, we are betting in terms of potsize, and believe he will call in terms of pot size and that is all that matters, and our equity (H) when called is 0 (making your opponent’s V=1). Let’s say you have 25o for simplicity’s sake.
Betting .25P wins us the pot 25/82 = 30.5% of the time. Using the fold equity equation we get: EV = .305P +(1-.305)(0*P-.25P)EV = .305P + (.695*)(-.25P)EV = .305P – .174P
EV = .131PBetting 1.25P wins us the pot (25+48)/82 = 89% of the time. EV = .89P + (1-.89)(0*P –1.25P)EV = .89P +(.11)*(-1.25P)EV = .89P – .137PEV = .753P
Let’s talk about some of the key factors in the profitability behind this bluff. First of all, we noticed our opponent has a very specific range. It’s not super loose, but it is loose in the sense that there are some offsuit broadways and suited aces. This might be a spot you see when you are button to BB, maybe cutoff to button. This will never truly exist in real life, there will always be some unknowns; we are just simplifying for the sake of the example. Secondly, our opponent is not slowplaying a ton, no overpairs, no two pair-type hands. Thirdly, we are assuming our opponent is passive with all their flush draws, including the combo draws. And finally, the most important thing is that we know our opponent will fold certain hands in very specific ways. Sometimes people will look you up with top pair even when you overbet, or maybe even bluff you with their missed draw. There’s no way to know for sure what they will do, so this example is only slightly applicable to real life, but the underlining principle as far as finding the best bet size based on how their folding range changes, is what is really important. This graph represents the value of getting folds with different bet sizes using the above calling ranges
Here is a math breakdown of how I got my results if you care to double check, or run it yourself to practice. Betting ¼ PSB wins us the pot 25/82 times, so our EV is: EV = .305 + (.695)*(-.25P)EV = .131PBetting ½ PSB wins us the pot 25/82 times still, so our EV is: EV = .305P + (.695)*(-.5P)EV = -.043PBetting ¾ PSB wins us the pot 25/82 times yet again, so our EV is: EV = .305P + (.695)*(-.75P)EV = -.216
Betting 1 PSB wins us the pot… 25/82 times, so our EV is:
EV = .305P + (.695)*(-.1P)EV = -.39PBetting 1.25P wins us the pot (25+48)/82 = 89% of the time.EV = .89P +(.11)*(-1.25P)EV = .753PBetting 1.5P wins us the pot (25+48)/82 = 89% of the time. EV = .89P +(.11)*(-1.5P)EV = .725PBetting 1.75P wins us the pot (25+48)/82 = 89% of the time. EV = .89P +(.11)*(-1.75P)EV = .6975PBetting 2P wins us the pot (25+48)/82 = 89% of the time. EV = .89P +(.11)*(-2P)
EV = .67P
Since an opponent’s calling range doesn’t change when you bet between .25P and 1.25P, as your bet size increases, your bluff profitability decreases. And the same goes for any bet over 1.25P. It’s very important to find what the right sizing is in NL and PL games to maximize profitability. You can’t just auto-bet ¾ pot on every street and assume that is the best play. It can be a very good play and certainly won’t give any tells away about your sizing, but the truth is, you need to base your sizing on your opponent, not yourself. The argument for keeping a sense of “unexploitable” sizing which no one can read into is usually an excuse for auto-piloting and doesn’t take advantage of your different sizing options. Besides, they can still read into your ranges, and from there, make the best decision. Most of the time I am varying my bet size, it is not based on my hand strength, but instead on my opponents hand strength, and the board texture. Why are you betting ¾ pot on a K77 flop when your opponent will only call with Kx 7x or AA and maybe some medium pairs? This is a perfect spot for a smaller bet with your entire range. The time to change your bet size with your actual hand is when you know your opponent to have very static ranges (like the above example) and you are looking to exploit that with whatever hand you have. For instance, you make a full house on the river and you know your opponent has a flush and will never fold. This is an easy overbet shove. Look for spots like this where you just know you are getting looked up and you are at the tip top of your range and that will be a good spot for adjusting bet-sizing. Let board texture help you determine your optimal bet-sizing and you willshave off small leaks in your game by improving the value of your bluffs, while at the same time allowing yourself to extract more value with your good hands.