Earlier this week, young hotshot du jour Fedor Holz kicked off the year with a bang by winning the Triton Super High Roller Cali Cup at the WPT National Philippines. With its $200,000 buy-in, the Cali Cup is the World Poker Tour’s highest-stakes event to date, so naturally Holz was up against some pretty stiff competition in Dan Colman, Steve O’Dwyer, Phil Ivey and David Peters, plus Macau high-rollers Devan Tang and Paul Phua. More impressive still, the win made it back-to-back for Holz in six-figure buy-in events, as he also won the $100,000 Alpha8 event at the WPT Five Diamond World Poker Classic in Las Vegas last month.

The stream was exciting to watch, but unfortunately lacked hole cards. That of course made it a bit harder to follow the action, but also presented plenty of opportunity to exercise one’s strategic muscles by trying to do some hand analysis without having one’s perception skewed by knowing what both players were holding.

I wasn’t able to watch the whole thing, but of the part I saw, the most interesting situation I saw was the river in Hand #58, in which a large third-barrel bet by Holz sent O’Dwyer into the tank for a good five minutes before eliciting a fold. Since O’Dwyer did finally lay his hand down, we’ll never know what either had for sure, but let’s walk through the hand and try to speculate.

Fedor Holz (57 BB) – Under the Gun
Steve O’Dwyer (53 BB) – Button

Preflop (Pot: 95,000)

Play is down to four players, with the other two remaining being Tang and Peters. One of the commentators on the live stream (Tony Dunst and Mike McDonald) remarked that Holz had seemed fairly quiet to him, but examining the hand histories, it seems that Holz had been the preflop aggressor in six out of 22 hands since the elimination of Ivey in 5th, so just about average. O’Dwyer, on the other hand, had been involved in a disproportionate number of hands in the preceding two orbits.

Holz raises to 125,000 from first position, and O’Dwyer calls on the Button. Both blinds fold.

Flop (Pot: 345,000) – Jd 8d 6c

It’s a wet flop, and one which you would ordinarily assume would connect harder with a Button caller’s range than a preflop raiser’s. Down to four players, however, it’s harder to assume that, as Holz would certainly be opening with many suited connectors and gappers, plus all sorts of broadway type hands which could contain a Jack.

Still, when you take out from O’Dwyer’s range the hands that he would be likely to 3-bet – his best Aces, big pairs, and also the sort of Ace or King blocker with a rag hands that he could bluff with – then it’s probably fair to say O’Dwyer is more likely than Holz to have paired one or more of the board cards.

Still, although Holz may have some kind of check-calling or even check-raising range here, I think he’s still continuation betting a lot, which he does, for 210,000.

O’Dwyer calls, and I think that almost certainly means he has some piece of the board; not necessarily a big hand, but it’s extremely easy for him to have at least, say, a gutshot or one pair with some additional backdoor equity on this texture. It’s also not the sort of board you’d expect a player to float on a lot when they haven’t connected, nor to try to get to realize some thin showdown equity like Ace high or a small pair.

Turn (Pot: 765,000) – 9d

The turn is the Nine of Diamonds, probably the most significant card in the deck, as it completes straight and flush draws and is also likely to make two-pair for someone who flopped top or middle pair, or give other kinds of hands additional outs. In other words, it’s very likely to have helped O’Dwyer at least a bit if he had a piece of the initial flop. It’s much harder to guess at its effect for Holz, whose range is considerably wider.

Holz bets 385,000. Although it’s a half-pot bet, the opinion in the commentary booth was that it was a bit small for the texture and that the sizing meant that Holz would likely be intending to bet again on the river. Nonetheless, O’Dwyer calls.

River (Pot: 1,535,000) – Ah

Here we get to the really tough part of the hand, both for O’Dwyer and for us as observers. The river brings an offsuit Ace and Holz fires out another almost half-pot bet, for 720,000. This is now a fairly large sizing, both given the board and players’ stacks; at this point, Holz has about half of his stack in the middle, so betting and folding to a shove would be quite painful if he has a strong but non-nut hand, so conventional wisdom would be that his river bet seems polarizing – either he’s bluffing or he has something strong enough that he’s willing to stack off with it, i.e. probably a flush.

Assuming that the commentators were right, and that Holz’s turn bet did look like he was planning on betting the river, then by calling the turn O’Dwyer must have likewise been planning on calling the river a fair bit. Instead he goes into the tank for a good long time. It could be that Fedor’s sizing gave him pause, but I think the Ace has much more to do with it, even though it doesn’t complete any additional draws.

What’s in an Ace?

Let’s assume for a moment that O’Dwyer has a hand like Queen-Jack, as I think that’s a hand that’s close to the middle of his call-call-tank-fold range on this runout. Furthermore, assuming Holz really is polarized here, many other hands O’Dwyer could have would be strategically almost no different, as they’d still beat Holz’s bluffs and lose to his value hands.

The pot odds tell us that O’Dwyer needs to be good 25% of the time to make a profitable call on the river when facing a half-pot bet with a bluff catcher sort of hand. It’s easy enough to imagine what sorts of value hands Holz could have: for starters, he’s certainly raising any suited Ace four-handed, so unless O’Dwyer holds the Ace of Diamonds himself, every possible nut flush is in Holz’s range, plus a few other flushes like King-Queen of Diamonds.

But this also tells us what sort of hands Holz would be most likely to be bluffing with on the turn if planning to run three barrels: Any unsuited Ace of Diamonds. By holding that card, he’d know that his bluff would be plausible to O’Dwyer, plus he’d have a decent shot of actually making the nuts on the river.

This is why the Ace on the river is so relevant; if Holz was semibluffing with such a hand, then he would have rivered top pair, and the normal thing to do when backing into top pair while semibluffing a nut flush draw on a wet board would be to switch to a check-call line on the river and hope to induce one’s opponent to bluff.

If the Ace falling on the river means that Holz is unlikely to have a naked Ace of Diamonds, then we have to search pretty hard to find likely three-barrel bluffing hands. The only thing I can think of are a few combinations that would have seemed to have showdown equity on the turn, but which Holz decides to turn into bluffs on the river – pocket Sevens, say, or something like Queen-Nine.

Could Holz be merging with an Ace?

Okay, but what if Holz was trying to level O’Dwyer by betting with an Ace of Diamonds after all? This would be what I call a Schrodinger’s Bet, in that it could end up working either as a bluff or a value bet, even if Holz himself doesn’t know which it is when he makes it. That is, if O’Dwyer believes that Holz’s river bet is either the nuts or nothing, then he could equally easily end up laying down the best hand with two pair, or paying off with a worse one pair. This happens more in cash games, I’m told, but I’ve seen similar things done in tournaments before.

In any case, if O’Dwyer does have a one-pair hand, then the possibility that Holz could have an Ace after all doesn’t change much for him. If Holz doesn’t have enough bluffs to be worth calling him ordinarily, then adding in an Ace as a possibility just makes O’Dwyer’s odds worse, unless he’s willing to go all-in on a bluff, which doesn’t seem like a good idea. It’s much more of an interesting question if we hypothesize that O’Dwyer might have made a big laydown with two pair. That’s not impossible, but I feel like four-handed with a tricky player like Holz, it’s tough to fold two pair getting 3-1 pot odds on the river.

Overall, then, I think the most likely scenario is that O’Dwyer did have something like a Jack, probably with some additional equity on the turn (a gutshot, maybe one Diamond, etc.) and that he did make the correct fold. Obviously, I’m nowhere close to being in these players’ league, however, so I decided it would be interesting to get a second opinion. So, I called in Andrew Brokos, who is a pro player and the brains behind the Thinking Poker blog and podcast.

Ask Andrew

Alex: When you see Holz’s turn bet, are you expecting him to fire the river almost always? If so, is it the sizing or the board texture or both?

I’m reluctant to disagree with Dunst and McDonald, but I’m also reluctant to make assumption like this about a top-notch player. Suppose that O’Dwyer assumed this about Holz, that he would very often bet again on the river. He would then not want to call on the turn with hands that would fold to a bet on a majority of rivers. Thus, he’d end up folding the turn quite often, essentially treating the turn bet as a much larger bet than it is. Holz would then have quite a lot of incentive to make this small turn bet with quite a few bluffs, planning to give up if called. It’s not impossible that these two great players are trying to “level” each other, but I think it’s more likely that neither of them is playing so exploitably against the other.

Holz’s small (given the texture) bet is consistent with a depolarized range. That is, he may well be betting quite a few different types of hands, from very weak (draws with possibly live overcards) to very strong (straights and flushes) plus everything, such as pair plus draw, two-pair, overpairs, and sets, in between. Those hands in the middle benefit a lot from betting, because although they won’t be way ahead of a calling range, they gain tangibly from O’Dwyer’s folds, have reasonable equity when called, and are generally too good to check and fold to a bet. At the same time, the more money O’Dwyer is willing to put into the pot, the less strong these “middling” hands become, which means that Holz would prefer not to make a large bet with them.

If Holz were to bet only these mid-strength hands with this sizing, then O’Dwyer could easily exploit him by raising. This gives Holz incentive to use this sizing with his very strong hands as well, hoping to induce that raise. And now, because Holz is betting so many fair-to-strong hands with this sizing, O’Dwyer has a lot of incentive to fold some of his weaker holdings, especially those that are not likely to improve on the river, which gives Holz incentive to throw some bluffs into his half-potting range.

It’s possible that a poker supercomputer might employ a variety of bet sizes on the turn, none of which could easily be exploited. However, I think human players are far more likely to employ a range building process similar to what I outlined above, where they try to find a single, good size for their betting range. I can’t pretend to know Holz’s process, though.

Alex: What do you think is O’Dwyer’s median holding once he tank-folds the river? What’s your minimum you’d consider calling with, and what’s the minimum for it to be a pretty easy call?

For me, a hand is an easy call if it’s either ahead of hands my opponent could bet for value, or has a significant blocker to his value betting range (and enough showdown value to beat his bluffs, of course). I’m not terribly confident in this, but my best guess is that Holz is not betting worse than two-pair for value, and may not even be betting all of his two-pairs. This is because of what you say about the significance of an Ace on the river – it makes it tough for Holz to find bluffs, and consequently he can’t get away with a lot of thin value betting, either.

So, I’d say any Aces Up would be an “easy call” for O’Dwyer. His other two-pairs will probably also be calls, though they may be pure bluff-catchers. Even so, holding two-pair makes it less likely that you’ll be shown a set or higher two-pair. I guess two-pair with a diamond might fall into the “easy call” category because of the blocker value.

Alex: Do you think Holz is actually balanced here, i.e. bluffing about 25% of the time? Does he ever have air, and if not, what kinds of hands is he turning into three-barrel bluffs?

I think if I were playing against Holz, I’d try to play a balanced strategy against him. Whether he’s trying to outplay O’Dwyer here I don’t feel qualified to say, but I think for any of us mere mortals, trying to outguess Fedor Holz will be a losing proposition.

The most obvious bluffing candidates for Holz would be KQ or KT with a diamond. These hands seem like good turn semi-bluffs and easy river bluffs precisely because that Ace improves so much of Holz’s range. It’s not impossible that O’Dwyer is slowplaying something, but because he’s been calling while Holz has been betting, we should expect Holz to have a lot more nut-type hands in his range than O’Dwyer does. That means that on the river, Holz’s strategy with those nut hands (by “nut” here I don’t mean the literal nuts, but rather any hands strong enough to be ahead of O’Dwyer’s calling range) should probably be to make the largest bet that he can balance with bluffs. The constraint on his bet size isn’t the effective stacks but rather the number of hands that benefit from bluffing, ie hands with no showdown value such as KQ or KT. Basically, his range is plenty strong enough that he has an easy bluff with any no-pair hand that sees the river, and probably he will also benefit from turning his weakest pairs, such as T9 or T8, into bluffs.

Alex: Would you ever bet-fold the Ace of Diamonds after you back into top pair on the river here, or would that always be a check for you?

A bare Ad strikes me as a very good check-calling hand. I think slow-played nut flushes will be a tangible chunk of O’Dwyer’s value betting range on the river. When I have the Ad, I know he can’t have the nuts, which means I have a good bluff-catcher. I doubt a pair of Aces would be ahead of O’Dwyer’s calling range at all, but even if it were, I still think it would play more profitably as a check-call than an extremely thin value bet.

Alex: Anything else you’d like to add or holes you’d like to poke in my thinking?

All of my analysis here has essentially ignored the fact that we’re in a tournament. I have no idea how many spots paid or to what extent either of these players believed he had an edge over the remaining field. Those factors could have a significant influence on how this hand plays out – specifically, both players would likely be disinclined from all of their thinnest plays, whether those are bluffs, value bets, or calls – but I think the hand is plenty interesting to analyze without taking any of that into account.

Alex Weldon (@benefactumgames) is a freelance writer, game designer and semipro poker player from Montreal, Quebec, Canada.