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The Art of Bet-Sizing

Many of my students seem to have problems with sizing their bets and I think this is something that many micro-stakes players can work on to boost their win-rate. I wrote this article to share some thoughts on how we should size our bets. There might be a part 2 for this, if I do think of more stuff to write about.

Exploitative Approach

Here are some goals of Exploitative Bet-Sizing.

  • To bluff as cheaply as possible (to risk the least amount of money to generate the maximum amount of fold equity)
  • To gain as much value as possible (picking a bet size that gets you called by as many hands as possible)
  • Simplify the decision process and avoid putting yourself into difficult spots

1. Bluff as cheaply as possible

Example 1
The Pot has 40BB on the River. Hero has a bluff and is deciding whether to bluff with a half pot bet or a full pot bet. If he bets half pot, Villain will fold 33.3% of the time. If he bets full pot, Villain will fold 55% of the time. Which size maximizes his EV in this spot?

This is a pretty simple spot which can easily be calculated. Let’s have a look at which is the superior bet-size.
EV(Bluff) = Fold Equity X Pot Size – Call Frequency X Bet Size
EV(Half Pot Bet) = 33.3% X 40 – 66.7% X 20 = 0BB
EV(Full Pot Bet) = 55% X 40 – 45% X 40 = 4BB

Even though Hero’s half pot bet is “cheaper”, the effect of his Fold Equity dropping outweighs the lower price that he is giving himself on a bluff.

2. Maximizing your Value with value bets

Example 2
The Pot has 40BB on the River. Hero has the nuts and is deciding whether he should value bet with a half pot or a full pot bet. If he bets half pot, Villain will fold 33.3% of the time. If he bets full pot, Villain will fold 50% of the time. Which size maximizes his EV in this spot?

We are a similar same spot now, but the only difference is that we now have a value hand. Let’s compare the EV of both sizes again.
EV(Value Bet) = Villain’s Calling Frequency X Bet Size
EV(Half Pot Bet) = 66.7% X 20 = 13.33BB
EV(Full Pot Bet) = 50% X 40 = 20BB

Once again, you can see that in this case, the size that maximizes our value is the full pot bet.

Pros and Cons of the Exploitative Approach

+Allows you to maximize the EV of your bluffs
+Allows you to maximize the EV of your value bets
+Works well against weak opposition who only play according to their hand and are not thinking about their opposition

-Exploitative Play leaves one open for exploitation from the opposition

To put this simply, if you are always betting small when you are bluffing and always betting large when you have something, any observant opponent will be able to hand-read you better and make good decisions against your various lines, allowing him to gain the upper hand. For this reason, we need to think about constructing balanced ranges for all streets in order to cover our asses.

Bluffing Pinochio

 

Don’t make obvious bluffs

 

The Game-Theory Optimal Approach

The GTO strategy will probably include a ton of different bet/raise sizes with mixed frequencies, even for earlier streets (Preflop and Flop) and will probably be way too complicated for humans to compute at this point in time. Having multiple raise sizes or even limps as part of our preflop strategy will make our decision trees too broad and complex and is probably impossible to compute without software. With that in mind, let’s think of how we can make GTO principles more applicable as part of our solid, well-balanced strategy.

The Balanced Approach

At this stage, we have acknowledged the limitations of our human minds. We still want our strategies to have some balance, even if they may not be achieving the highest EV possible. If every poker hand can be broken down into a decision tree, the Preflop stages of the game will be at the top, and the River stages of the game will be at the bottom. Our goal is to keep the upper end of our decision tree simpler, and perhaps allow ourselves room for more varied bet-sizes during the later streets (Turn and River). Using 1 bet/raise size for Preflop and Flop scenarios also makes more sense because it’s more important to keep our ranges disguised while they are still wide. With all the concepts in mind, here are some tips on how to approach bet sizing.

Balancing

Preflop
Level 1: Raise 3 or 4BB in every single position – This is usually taught to beginners to avoid confusing them and making the game overly complex when they are still starting out.
Level 2: Vary our PF strategy based on position – (e.g. Raise 4BB in UTG, 3BB in CO, 2BB in BU) – You want to be raising larger in earlier positions for isolation purposes, since having multiple players come into the hand is not going to be ideal most of the time. Opening ranges will also tend to be stronger in earlier positions, so raising larger to maximize value makes sense. On the other hand, opening smaller allows you to steal with wide ranges from late positions. Generally, you want to be altering your raise sizes based on your position as well as your raising frequency. For example, I might want to be opening 40% in the BU to 3BB, or 60% in the BU to 2BB. Both strategies could work, but raising 60% to 3BB is probably too loose and puts too much dead money into the pot with a weak range.
Level 3: Having more than 1 different strategy based on opponents and table dynamics – This tends to be more true in later positions, where the opponents remaining are fewer in number, allowing for greater adjustment to our strategies. For example, if it is folded to you in the SB, you have the option of raising to 2BB, 3BB or even completing the SB. Either of the 3 options could yield the highest EV but this highly depends on how villain reacts to each of the different bet sizes.
GTO Level: Multiple bet sizes in every position with well-balanced ranges

Flop
I would recommend only having a single bet size on the Flop against tougher opposition. You can look to make some small adjustments vs unobservant opponents – Bluff with a smaller bet size, value bet with a larger bet size, in spots where their calling ranges are inelastic.

Price Elasticity of Demand
This is a key concept covered in micro-economics. To explain PED in layman terms in a single sentence, when demand is inelastic, a business can continue to raise its prices to maximize its profits, since its customers are “forced” to purchase its goods anyway.

Elasticity of Demand

 

From this graph, you can see that the profit is graphically represented by the area of the rectangle (Price X Quantity). When demand is more elastic, one should decrease price to maximize profit. The opposite is true when demand is more inelastic – One should increase the price the resulting fall in demand is less than proportionate, leading in an overall increase in profits.

Bet-Size Elasticity

Now, you might be wondering how this is even related to poker. The fact is that in many flop cbet situations, players are often going to be inelastic against changes in bet sizes, especially if they are not so competent. In situations where our opponents’ continuation ranges are inelastic against changes in bet-sizes, we want to be bluffing small and value betting large whenever possible.

Elasticity of Bet size (bluff)

 

 

So here, we have a graph which looks kind of similar to the PED graph. The concept is almost the same here. The EV of our value bets is represented by the area of the rectangle and as we can see here, when our opponents are bet-size inelastic, we maximize our EV by betting larger (Area A > Area B) and when our opponents are bet-size elastic, we maximize our EV by betting smaller (Area D > Area C).

The converse is true for the EV of our bluffs, since as you can tell from the equation that EV(Bluff) is inversely proportionate to the area of the rectangles, due to this part of the equation “-Call Frequency X Bet-size”. When our opponents are bet-size inelastic, we maximize our EV by bluffing smaller (Area B < Area A) and when our opponents are bet-size elastic, we maximize our EV by betting larger (Area C < Area D).

Application to Flop Situations

Since we are thinking of how to derive balanced ranges, we want to be using a single flop cbet size based on the situation. Here are some things to think about.

  1. Determine our value:bluff ratio. In most single-raised pot situations where both players are in late positions, both players will have a ton of weak hands (in terms of absolute hand strength).
  2. Weigh the pros and cons of value betting vs bluffing. If we have more bluffs in our betting range, then being able to bluff cheaply should be our main priority. If we have more value hands, then valuebetting as large as possible should be our main priority.
  3. Study the board texture. Continuation ranges tend to be more inelastic on higher boards and more elastic on lower boards.
  4. Determine an optimal bet-size for your entire range (both bluffs and value hands)

This approach to formulating your Flop cbet size is most applicable to single-raised pots. It is somewhat different from the traditional approach of betting smaller on dry boards and larger on wet boards.

Example 3

  • Ac Qd 5s Single Raised Pot: Most players will not continue with anything worse than a gutshot or a Queen. Thus, it probably makes more sense to use a smaller bet-size of 40-50% of the pot to bet here, since we should have significantly more bluffs in single-raised pots as compared to value hands.
  • 5h 5d 7s SRP: On this texture, people will float with all kinds of overcards and those hands typically have ~25% equity. It would probably be advantageous for you to increase your bet-size in order to increase your fold equity and deny your opponent the opportunity to float hands as weak as JT. I would typically bet 65-80% of the pot here. Against a half pot bet, most players will call with any broadway, all King highs and Ace highs (in late positions) but against a larger pot bet, many players will fold KX and only call with AX+.
  • Js Td 9d SRP: Our betting range will be pretty strong on this flop texture. We want to be maximizing our value with our strong range, and also not give villain the opportunity to float with all sorts of weak hands with some sort of equty. Betting 80%+ of the pot would be reasonable here.
  • Qd 5d 2d SPR: Here is another spot where this approach differs greatly from conventional wisdom. Conventional wisdom states that we should be betting huge here for protection from draws. On the other hand, you should note that our opponents’ calling ranges are highly inelastic
  • Ah 2h 7d 4BP: Our 4betting range contains many AX hands and it would be difficult for our opponents to continue with anything less than a mid-pair. Betting extremely small (30%-35% pot) would be nice with our entire range.
  • Js 7c 5c 5BP: We make a min 5bet and our opponent calls. Our range is extremely strong here with at least a third of our range being JJ+. Our opponent calls the min 5bet merely to try and hit something, and is mostly in a fit or fold mode. The most suitable bet size in such a situation would be an extremely small one (25% pot), since villain would often be shoving or folding and not calling so often.

Turn: Now there is probably more room to use multiple bet-sizes here. I don’t have too much to say here, but anywhere between 60-80% of the pot will typically be a good size. If the board is extremely draw heavy (at least 1 flush draw and 2 straight cards), you might want to be betting on the larger side with strong draws and nutted hands (2-pairs or better). Of course, it’s also important to bet slightly smaller with nutted hands and draws some of the time in order to protect our thin value hands, which would prefer betting smaller, from heavy aggression.

On boards with straight draws and 2 flush draws (Jd Th 5d 7h), it would often make sense to have an overbetting range of 1.5X the size of the pot with strong draws (nut flush draws, straight-flush draws) and monsters. I don’t like overbetting with weaker draws so much since you may end up isolating yourself vs better draws and building a huge pot with a non-nut draw will often be a bad idea.

River: River scenarios are easiest to analyze because ranges are narrowest here. It’s also important to ensure that you play rivers well, since river pots tend to be the largest, assuming that both players did add more money into the pot both on the flop and on the turn.

River scenarios will often have one player being very polarized (the aggressor) relative to the other guy (the caller). In such situations, it’s often better to use larger bet sizes with your strong hands as well as your bluffs, though it would probably be better to bet smaller with thin value hands such as TPTK.

In future articles, we will look into maximizing the EV of our entire range, as opposed to maximizing the EV of a single hand.

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1 comment for “The Art of Bet-Sizing

  1. Bogdan Luciano
    October 10, 2014 at 3:42 pm

    Nice job

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