## Secrets to Folding Ranges and Bet Sizing

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:
JJ,88,33,AJs-A9s,A7s,KTs+,QTs+,J9s+,T9s,AJo,KJo,QTo+,JTo

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).

Figure 3-4

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

Figure 3-5

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[1])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[1])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

Figure 3-6

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