Betting for Protection

Replay Poker Poker Strategy
1

I find this one of the harder decisions to make live at a poker table, where I have a middle strength holding, and I’m trying to weigh the benefits of betting to get weaker hands to fold, against the problem that the bet seems mostly unlikely to get better hands to fold, or weaker hands to call.

So I thought I’d look at a few imaginary situations to try and see how the EV penciled out. Let’s imagine we raised pre-flop with 7h7c, and get a rainbow flop of Ad6s2h. Next, we’ll assume that we are ahead 2/3 of the time, and that the hands behind us are KQo-KTo,QJo-QTo,JTo,JTs,T9s,98s,65s, against which we have just under 26% equity, which we’ll round down to 25% for simplicity. We’ll assume that we’re losing to a few Ax hands and a small number of higher pocket pairs, against which we are almost drawing dead (we’ll round the equity up to 10%, though it is 8%). Does it make sense to make a 1/2 pot bet with one opponent?

We’ll assume the hands behind us will always fold, and that the hands ahead of us will always call, and we’ll say the pot is $100, and the bet puts us all in. This won’t quite match reality most of the time, but should still provide some useful insight. So 2/3 of the time, we’ll be getting worse hands to fold, improving our equity share from $75 to $100, for a $25 gain, and 1/3 of the time we’ll have $20 equity in a $200 pot to help offset the 90% of the time we lose a $50 bet.

To simplify visualizing this, lets run this 30 times:

  • 20 times a worse hand folds, and we pick up $100, for $2,000
  • 10 times a better hand calls
    • 9 times we lose our $50 bet for a loss of $450
    • 1 time we win $150

If it had gone to showdown 30 times, we would have had 75% of the pot 20 times, for $1,500, and 10% of the pot 10 times, for $100, for a net of $1,600 ($3,000 total pot). Above, betting half pot, we win $1,700. So in this simple test case, our protection bet does perform better than checking.

You can probably tweak this quite easily to generate a scenario where you are better off checking.

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2

Simple modification of the above, with everything the same, but now we consider making a pot sized, $100 all in bet.

  • 20 folds from worse hands, with the same $2,000
  • 1 call from a better hand, now winning us $200
  • 9 calls from better hands, now costing us $900

Now we net to $1,300, loosing relative to the $1,500 performance achieved if we check down.

Now is probably also the time to consider, what if it doesn’t check down? Well, if we assume we make perfect calling decisions that converge to zero EV, then from one lens, you’d think that shouldn’t actually change the situation. Unfortunately, if your opponent starts betting, if they use an intelligent mix of bluffs and value, the reality is that they will tend to over realize equity, while you under realize. Against a perfect opponent, your under realization can be quite large, especially given that none of us make perfect, mathematically optimal calling decisions. But on the flip side, against many opponents, it is possible to find +EV defensive lines, as their play will be very unbalanced.

So on the whole, in practice, I think you’ll find that against certain opponents the defensive line, just checking and making call decisions, will be best, and that against others, you’re better off taking a higher frequency of aggressive lines with marginal holdings.

3

So in the first two examples, our hand was fairly vulnerable to many of the hands behind, with unpaired over cards typically having 6 outs against us, increasing the value derived from getting those hands to fold. You’ll have many other spots where you are ahead of most of your opponents range, and your cards will be even more vulnerable, which further increases the increase in our equity share of the pot from folds from worse hands.

What are some of the factors impacting the value of protection bets?

  • how much of our opponent’s range we are ahead of
  • our equity against the hands in our opponent’s we are currently losing to
  • our equity against the hands in our opponent’s range we are ahead of
  • how much we are risking relative to the pot with our bet

There are obviously other important factors that can impact the EV of a protection bet, but I think these are at least a good starting point.

Restating those same bullets in light of our initial two examples:

  • we assumed we were ahead of 2/3 of our opponent’s rannge
  • we had 75% equity against the hands that would fold to a bet that were behind
  • we had 10% equity against the hands that would call our bet
  • we tried 1/2 pot and pot

What happens with KdKs on a flop of Ah8c3d rainbow? Let’s say we faced a CO raise and 3 bet pre-flop, and got called by the CO. Lets give the CO a flatting range of AQo, QQ-77, AKs through A4s, KQs-KTs, QJs-QTs, JTs-J9s, T9s-54s.

  • We’re ahead of all of the non-ace holdings except 88 for 82 combos, and have about 87% equity against the cards behind us
    • 30 combos of pairs
    • 52 combinations of suited cards
  • We’re behind to 55 combos, with about 8.5% equity against the hands we are behind
    • 16 AQ
    • 36 other suited aces
    • 3 combos of 88

So we’re ahead of about 60% of our opponents range, and there is a fairly low likelihood of hands behind passing the hands ahead both when we are ahead and when we are behind. How does a half pot bet fair now, again assuming that all hands ahead will call, and all hands behind will fold? Let’s run 60 hands where we bet, and 60 where we don’t:

  • Betting 1/2 pot gets a $2,650 share of the 60 pots

    • 36 times we’ll bet and get folds, winning our $100 pot for $3,600 in winnings
    • 24 times we’ll bet and get called, but will suck out and win about 2 times, losing our $50 bet 22 times ($1,100 in losses), and winning the pot and the calling bet twice for $150 more winnings

  • Checking down: 62% equity of $100 pot, 60 times, for $3,720 in winnings

So here, if it checks down to the river (which it probably won’t unless we’re ahead), we win much more than if we try to make a protection bet.

There’s obviously a lot of complexity I’m glossing over in the checking lines, but I’m hoping this still illustrates how a marginal hand on a static board derives less benefit from a protection bet than does a marginal hand that is at greater risk of being out-drawn.

4

So we’ve had a few simplified examples, where betting for protection did slightly better than checking (when our hand was moderately vulnerable to being out drawn), and where we lost money versus checking (when most of our opponent’s range was either well ahead of us or well behind, and there weren’t a lot of outs in either direction). Should we use that to make protection bets whenever we think we might be ahead and there will be a lot of outs against us?

I tend to think it is not that simple. First, you really need to look at each situation, what range you think you’re up against, and from there both how often you are ahead and how much equity the hands behind you have. Further, you need to consider how you plan on protecting your checking range. If 90% of the time a check from you means you have absolutely nothing, then your checks will be quite exploitable, and so many of these hands are also natural candidates to include to strengthen your checking range. So while it is true that your individual hand might generate a slightly higher EV with a protection bet, your entire range may generate more EV if at least some of those hands are grouped into your checking range.

5

I’d like to respectfully disagree with the crazy post above. I think Yorunoame is clearly taking too many passive lines if he’s living by that advise.

  • play the lines each hand is incentivized to take… you’ll have more than enough diversity to protect your checking range if you do that well
  • these protection bets, in the real world, will often get worse hands to call, and better hands to fold, even when you don’t think that is likely, and that will further increase the EV of betting
  • these protection bets usually do better with smaller bet sizes, and so it’s natural anyway to be taking quite broad ranges with your smaller bets

So just figure out which of your marginal hands benefit a lot from getting weaker hands to fold, considering how much of your opponent’s range you think you are likely ahead of. Do the math a few times off-table, and you’ll start to get a sense of when it makes sense and when it doesn’t.

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6

Wow, hold on there, you reckless, mostly out of control donkey. Just stop and think a moment.

What do you do when you get called? Are you going to fire another protection bet on the turn, when you are now probably overwhelmingly behind? Will you then turn your hand into a complete bluff on the river? Assuming you aren’t planning on compounding your foolishness (are you going to fire 3 bullets with every hand?), it seems you really need to think a little bit more about how you are going to keep your ranges balanced across all three streets, in light of various actions. It sounds to me like a small bet on the flop from you, followed by a check is a sure sign anyone can just take the pot away from you with anything.

We’re probably both in agreement that protection bets can work in theory, some of the time, and are just disagreeing about how large a fraction of our marginal hands we should be betting with. As you carve up your range, you want to keep things as difficult as you can for your opponents across all line types.

7

The mock argument here… I really am a bit conflicted about when I should bet with marginal hands that seem unlikely to get better hands to fold or worse hands to call. As you become more aggressive, what constitutes a hand in this class moves down, and you can start betting for pure thin value with weaker hands, but you’ll still have a class of hands that can sometimes benefit from a bet even when the bet itself seems to have no way of making money.

I also find myself amazed at what a strange gradient these hands can have:

  • I have a weak hand that is mostly ahead on a dry board, that is not particularly vulnerable to overcards: a protection bet is mostly a loser
  • I have a weak hand on a dry board that is mostly ahead, but many turn and river cards could push my opponent’s range past me: a protection bet might be a good move
  • I have a weak hand on a wet board that is mostly ahead: oh oh, we haven’t covered this yet

Obviously this last bullet opens up a whole new can of worms. Your initial reaction might be that your hand is even more vulnerable now, with much of your opponent’s range having more outs than in the dry board scenarios. If you knew your opponent was passive and would play predictably, folding their trash, calling with their draws, and raising with their made, premium hands, a protection bet could probably pencil out again, as the calls with draws seem like they might be pushing it into a value category, but in this scenario, many of your opponent’s will not play so predictably, and will raise with many of their draws, and this hand class will usually have a hard time holding up to sustained aggression across multiple streets (and will in general under realize its equity).

What to do? Maybe some of the players stronger than me can comment. I’m still working on it.

8

Hi,

I think you may be conflating two issues into one, and perhaps that is causing you difficulty.

The two issues, as I see it, are:

1.Betting for Protection
2.Betting with a Merged Range / Medium Strength Hands

Betting for Protection is something we want to do when our hand is ahead but vulnerable to being out drawn. This isn’t necessarily a weak hand. e.g. Top set, no heart, on a board with two hearts.

Betting with a Merged Range is where we bet small with a very wide range with hands of all strengths. Strong, middling, draws, maybe throw some trash in there just for good measure. This is as opposed to betting with a Polarised Range, where we be big with only very strong hands and good draws, with nothing in the middle. Whether we bet merged or polarised is a function of the board and the situation. It is not related to betting for protection.

I’m not an expert in bet sizing (it’s a very complex topic), but as far as I understand it, in general terms, we should bet polarised on high and/or connected boards (eg Ah Kh Ts), and bet with a merged range on lower and/or dry boards (eg Jh 7s 4c). (Assuming we were pre-flop aggressor. I think it’s actually to do with Range Advantage, but that’s a whole other topic that I don’t fully understand)

Whichever way we decide to bet, merged or polarised, this is a separate decision. Once we have made this decision, we then have to decide which hands in our range go into our betting range, and which ones go into our checking range. This is where betting for protection comes in.

If we take your example of an Ad 6s 2h board. We pick our bet sizing (merged seems fine here). We then have to allocate the hands into our betting and checking ranges. In this instance, with the A on the board, obviously all pocket pairs K to 7 are behind if our opponent has an A. So they are all fairly similar in that regard. However, if our opponent doesn’t have an A, they are very different. KK cannot be out drawn by an over card coming on the turn, but 77 can be out drawn if anything 8 to K comes out. Therefore, we can see in this instance that betting has advantages for 77 that are not present for KK. So we should bet for protection with our 77, and put KK in our checking range.

This also has the advantage of protecting our checking range. If our opponent decides to bet, we can call with our KK and hope he is bluffing, or betting something lower than an A for value.

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9

Great post.

I’m not conflicted about betting strong, vulnerable hands, like any set on a wet board. It’s not always easy to launch into the attack, but I think it is typically the right move. I think the hardest part for me is probably deciding which middle strength hands should go into a betting range on the turn. I tend to check most of them, unless they have additional equity that allows them to be happy with more polarized bets, but have wondered if I shouldn’t be making middle sized bets here with more.