Wiser Sizing: Turn transitions on a tricolor texture

¹, but only by coincidence. This post digs a little deeper into a common scenario, playing a 3-bet pot out of position on a tricolor texture.

We 3-bet a BT open from the SB with AcAsQc3d and are called. The flop comes down:

Kd6s4c

This flop type (K high, unpaired, 0-straight, tricolor) occurs over 5% of the time, and so is a worthy candidate for deeper analysis. We are primarily concerned with the turn play today, yet it would be remiss of me not to quickly remind the reader of a few pointers on flop strategy.

Tricolor flop fundamentals

One strategy employed by many regulars is to pot/call this part of their range on the flop. Since we are effectively shoving here, it is worth investigating how frequently our opponent is forced to stack off against a shove (if his only options are push/fold). We’ll choose reasonably favorable pre-flop sizing for this discussion: raise to 3BB, 3-bet to 10BB and a call (plus the BB) leads to a pot of 21BB on the flop, 90BB behind for an SPR of 4.3. If we ‘shove’ here… Our opponent has two pair plus 20% of the time and a 13+out wrap 5% of the time, together with {pair with 3 live cards + OESD} 5% of the time². Additionally, he will hold {live pair+gutter} 8% of the time. If he only gets these hands in, and folds everything else he will be stacking off with 34% of his range³ and have a 63.5% equity edge. We need our opponent to fold over 46% of the time on the flop here to break-even, and so at first analysis this strategy with this hand looks OK. However, betting this size with our air is less than ideal, since our opponent can happily shove the remainder of his OESDs when we fold after potting more than 22% of the time and thereby increase his continuation frequency to around 40%. Our line is still plus EV with our whole range, and yet it appears we are making relatively little money on a good flop texture for us⁴ . Should our opponent adjust to simply shoving any pair we are going to be losing a lot of money range versus range until we check/fold some of our air or pot/call very wide.

What, then, of a smaller sizing? Against a flop shoving range of {(KK,66,44,K6,K4,64,75:(K,6,4,3,8),53:(K,6,4,2),(K,6,4):(87,85,52,32,73)))} our Aces have 36.5% equity, meaning if we C-bet fewer than 15BB we could consider bet/folding. If our opponent took to shoving any pair or any K we would of course be correct to bet/call. Since naked AA without a gutter lies outside of the top 35% of our range, our opponent is going to need to be shoving with most {pair + 3 live cards} before bet/folding this hand becomes a mistake. Once this happens, we will be bet/calling 60% of the time even if we C-bet 100% of our 3-bet range, and our opponent’s hyper-aggressive shoving strategy becomes far worse than it would against pot-size C-betting strategy. It is worth noting that continuing to C-bet a high frequency here with a smaller sizing is far more effective than reducing our C-bet frequency with a pot-size C-bet, since the latter notifies the defender that we have adjusted before he has committed himself.

Having decided on a small C-bet sizing (We shall assume 10BB for the remainder of the article) we now proceed to the turn⁵ .

What constitutes a ‘good’ turn?

There are two broad categories of opponent to consider before addressing this question: ‘fast-players’ and ‘slow-players’. For the purposes of this article we will assume fast-players shove all of the strong hands we were concerned with above, and so continue with a flop range comprised of:

Fast-players‘ turn range
{(K,6,4,75)!((KK,66,44,K6,K4,64,75:(K,6,4,3,8),53:(K,6,4,2),(K,6,4):(87,85,52,32,73)))}

We will assume slow-players retain the sets in their range until the turn but shove bottom two pair and the combo draws.

Slow-players’ turn range
{(K,6,4,75)!((64,75:(K,6,4,3,8),53:(K,6,4,2),(K,6,4):(87,85,52,32,73)))}

These ranges are necessarily caricatures, but reflect the different thought processes behind the most common flop strategies we encounter among regulars.

Against fast-players, we have a 2:1 equity edge going to the turn and can find no transition where we have less than 50% equity hand versus range (the worst card is apparently the 8s). The low board-pairing cards and rainbow gut-shots all see us with a 73-27 equity advantage and most other cards keep us at the classic narrow 60-40 mark. This is a rather significant advantage, given that our hand is only in the top 40-45% of our 3-betting range.

The story against slow-players is more complex, our raw equity edge fading to 54-46 as soon as the sets and strong two-pairs are retained. We are in fact a dog hand versus range on 21/45 possible turns! Unsurprisingly the eights are the worst cards in the deck for us, and our equity drops to below 40% hand versus range.  We retain a 60-40 edge on the board pairing and gut-shot cards, and hover between 40-50% on most other turns.

To bet or not to bet?

The range breakdown above should have convinced you that “potting for value” on the turn with naked AA is an obsolete concept against a player capable of slow-playing this flop. We shall proceed assuming that we are facing the ‘slow-play’ range described above. If we consider the innocuous 9s, the hand v hand equity is distributed as shown:

The pot size is 41BB on the turn, and we have 80BB behind, so a pot-size turn bet would be committing. We see that fully 50% of our opponent’s range is a 68-32 or better favorite against us. Since, before we bet, we need 40% equity to be correct to get the money in with a given hand, the bet flop small/pot turn line only serves to allow our opponent to play near-perfectly and stack us at will. The reason it is such a common line amongst mid-high stakes regulars is that they have got as far as ‘potting flop here is bad’ but still ‘don’t want to play a river because they are all scary’. Yet potting one street simply to avoid a decision on a later street is not a sound justification for a betting line. A reasonable rejoinder might be, “If I am doing this with the top 35% of my range also, what’s the problem?” The short answer to this is that our opponent has almost as many very strong hands in his range as we have, and so is unlikely to face a lot of tough decisions once faced with a push/fold turn spot with an SPR of 2. Furthermore, this sizing is terrible for the air part of our range and since the 9s is not an atypical turn card (Equity distributions are similar hand v hand on most other turns), we will be either check/folding or pot/folding with far too high a frequency when called on the flop.

What, then, about betting small? It is important to understand what we are trying to achieve by choosing a smaller bet size, and that is to provide us with the ability to represent many different board run-outs on the river. Should we bet 20 into 41, we would need 30% equity to call a turn shove. Referring once again to the above graphic, we find that we only start to have this much equity against any hands in our opponent’s range once he shoves over 50% of the time! In fact, we can bet/fold correctly until our opponent starts shoving over us with 70% of his range. This does lead to quite an amusing dynamic where our opponent may counter-exploit us by flatting this flop wide and shoving many turns. Fortunately, with a solid block of 40% of hands which are comfortable calls on most turn cards, we should be safe from exploitation as long as we check/fold some of our air.

Putting your opponent in check

If we check and our opponent bets 30BB into 41BB, then a check-shove with only 20% equity when called would require our opponent to fold at least 36% of the time to break even. Unfortunately, we don’t average 20% equity against our opponent’s betting range until he starts betting at least 60% of the time when checked to, thus making check-raising this hand a dubious play even if he stabs 100% of the time. Check-shoving the top of our range is certainly reasonable (although it completely unbalances our turn betting range) against players willing to stab the weaker parts of their range.

Check-calling with this part of our range merely invites our opponent to take the pot away from us on the river since we won’t check-call a strong made hand here.

With the amount of equity we have in the pot, check-folding only becomes superior to betting once our opponent is extremely passive. It is worth noting that if he will only bet 50% of the time on the turn when checked to this line allows us to get to showdown often with minimal difficulty.

Stuck on the river with you

If you follow my advice in this blog in your regular games you are going to start playing a lot more rivers, and this particular spots sees you OOP on the river with an SPR of 1. Since this post is about turn transitions I won’t be helping you with that…

…Still here? Great. Having half-pot the flop and turn with your whole continuing range, you arrive on most rivers in better shape than your opponent. The reason for this is that few opponents can stand to just flat a set or decent two pair on the turn and yet we still have all of those in our range. With our actual hand, in contrast to the turn transitions, the rivers bring a lot of variation in hand v range strength:

It’s pretty illuminating that on most ‘bricks’ if we check we should check/fold (even if our opponent shoves his entire range on those cards we don’t have 33% equity). Only on 14 cards would our equity be high enough to check-call, predictably enough the board pairing cards and the remaining Aces. The story of whether to shove on other cards becomes a decision of whether or not to bluff. It’s worth noting that our opponent will only have a backdoor flush around 18% of the time on flush run-outs if he calls the flop and turn wide so it’s worth bluffing those cards (especially non-straight rivers) until he demonstrates he can ‘hero-call’ two pair. Similarly, he will only have the backdoor straights around 7% of the time, compared with a huge number of weak two pairs that complete on the river. If he is unwilling to call those two pairs then almost every river becomes an easy shove. In general I would be more prepared to represent the ‘higher straights’ and to give up on the lower cards. Take care to check/call such rivers with the top of your range against those opponents who are folding to shoves but willing to shove river when checked to.

This post ended up being immensely long, so thanks to all those who read to the end! As always, I had a lot of fun writing it and will be modifying my game as a result. Thank you to all the new subscribers, I am planning a site re-design this month so stay tuned for news on that front. As ever, good luck at the tables,

Quad