A Not-Terribly-Significant Hand in a $3/$5 Cash Game

I was in a $3/$5 No-Limit game earlier today. I'd been playing a tight game at a loose table, and had worked my $500 stack up to around $700 in two hours of play -- a pretty decent win rate. Then, this hand came up.

I was in the big blind. Action uncharacteristically folded all the way to a player in late position, who limped in for $5. He was a very poor player; he nearly qualified as a calling station. He was playing way too many hands, and generally playing them far too passively to walk away a winner in this game. Everyone else folded to the small blind, who called. I looked down at Queen of diamonds/Three of clubs; a truly dreadful hand. Since folding unfortunately wasn't an option, I merely checked and we went to the flop.

The dealer spread the Ace of clubs, Queen of hearts, Seven of diamonds; so I'd flopped middle pair. The small blind checked. I also checked, allowing the late position player to maintain his momentum. He didn't disappoint, putting out a $15 continuation bet. The small blind folded, and it was back to me.

I gave the matter some thought. Although it was possible that my opponent had paired the Ace, I felt that if he HAD an Ace, he would have come in for a raise preflop rather than just limp in. I'd seen him raise preflop before, so I knew it was the type of play he did. If I couldn't put him on an Ace, I had to call the flop bet. So I did.

The turn brought the Six of hearts. I checked again. The villain put out a $20 bet. I felt I was in the same situation as the previous street, so I called again.

The river was the Ace of spades. I checked again; villain put out $25. It was time for me to think it through some more.

First of all, with two aces on the board, it was now even LESS likely that my opponent also held an ace. There just aren't that many in the deck overall. And his river bet was ridiculously small, given the size of the pot at this point ($85). I was pretty certain now that I held the best hand.

I wondered about maybe putting out a value raise, but this brought its own complications. There's an important concept about river raises: You need to ask yourself, What are the chances my hand is good on those occasions when he CALLS? With this board, I lose to an Ace (of course), Kings, sets, and pretty much any Queen, since my kicker wouldn't play. If I raised, would he call with any hand that I beat? I couldn't imagine that he would. He would call whenever I'm beat, and fold whenever I'm not. So a raise wouldn't really accomplish anything.

I called, and showed my Queen-no-kicker. Villain showed Jack of clubs/Ten of clubs, and I pulled in the pot.

The Weirdest Hand I’ve Ever Played

I’ve been coming out to Pendleton’s poker tournaments for a few years now, off and on They’re among my favorite to play. I’ve even blogged about them before. So I thought I’d discuss a very weird hand I played here yesterday – probably my weirdest tournament hands ever. It essentially propelled me all the way to the final table.

The Wildhorse Casino hosts three big tournament series each year (in April, July, and November), called either the “Poker Round-Up” or the “Poker Rodeo”, depending on the time of the year. They are, without a doubt, the premier poker event in the Northwest, and hundreds of players descend on this tiny town from as far away as Reno, San Francisco, and Seattle.

Although I’ve been to plenty of the Spring and Fall events over the past several years, this is the first time I’ve gone to their Summer event. It’s a much smaller scale, and the crowd (I’ve discovered) is much more local … and, more importantly, less-skilled.

This particular tournament (“Event #1”) started with each player getting 10,000 in chips. Each level lasted thirty minutes, and there was a break every three levels. During the first three levels, nothing very significant happened at my table. I won some small pots and lost some small pots, and headed into the first break with a stack slightly below the 10k I started with. No big deal; during those early levels that sort of deficit isn’t too difficult to recover from.

Once I got back from break, though, I went on a massive heater. With levels at 100/200 with a 25 ante, the player under the gun raised to 600. It was folded all the way around to me in the big blind. I had a decent enough hand: 9c 9s. It’s certainly worth playing, and since I was already getting a discount (being in the blind), I tossed 400 in for a call.

The flop was absolutely perfect: Ah Kd 9d. I had a set on a board that almost certainly hit her hand. I checked, preparing a check raise. But I didn’t get the chance, because she pushed all-in! I happily called, saw that she held Ah Jd, and won the pot when the rest of the board cards bricked. Since I had her covered (slightly), she was out of the tournament … and I was nearly doubled-up. Sweet.

A few hands later, a player under-the-gun shoved his small stack. I was in the cutoff with (déjà vu!) 9c 9h, and called. It was heads up. He showed Ac Kh, the board didn’t help, and I’d busted my second victim in less than one button orbit.

At this point, I definitely had some chirping chips. I started stealing some small pots and leaning on my opponents with big bets, and built my stack up to around 60k – around three times the average stack size at the time.

Then, the big hand came up. I mean, big big hand.

With levels at 400/800 and 100 ante, the player second to act (UTG+1) opened with a raise to around 1800. Action folded to a lady in middle position who had a short stack. She pushed all-in for about 10,000. The next player to act was a rather unsophisticated player on my right (late position, or “LP”). He thought and thought for a long time, and then called. I was next up, on the button. I looked down at Ad Kh and thought about how to play it:

·       If one of my opponents had either Aces or Kings, my hand is in very bad shape. Against any other pair, my odds are just slightly under 50/50. And against any hand that’s not a pair, my chances of winning start at around 60% and go up from there.

·       I didn’t put the guy on my right on Aces or Kings. He was having a tough time deciding what to do, and I thought it was because he had a hand other than those.

·       The lady who shoved? It was very possible that she had one of those pairs. But if so, and if she wins, I’m only out around 10k and still have a monstrously huge stack to keep playing with.

·       What about the opener? He was a young kid who’d just lost a pot earlier. Was he on tilt? Was he any good? I had a really tough time reading him. I had to make my decision without having much input there.

Although I briefly considered it, I decided that I wasn’t going to fold. It came down to whether I should just call, or re-raise and try to isolate one of the other two players. I didn’t see any advantage to isolating; I kind of wanted the guy on my right in the hand so I could win a post-flop side pot if in fact the shover did have Aces or Kings. So, I just called.

Next up was the player in the small blind. He also shoved, but since he only had around 8k he was all-in for less. He seemed a bit resigned at this point, and I thought he wasn’t particularly enthusiastic with his hand.

Action went back to the original raiser, who was now facing a re-raise to around 10k. He decided to shove himself, which was around 25k.

Now, back to the guy on my right. He had the UTG+1 player covered, but not by much. He hemmed and hawed for a long time, and then called the re-raise.

I was next up, to call the 25k re-raise. Wow, a lot of action in this hand! I figured I was probably beat somewhere along the line, but maybe I could still snag a side pot. I went ahead and re-shoved myself, hoping at least I could get the guy on my right to call. Since he was already nearly all-in, it wasn’t much more for him, so he called off.

It took probably three minutes for the dealer to assemble the three side pots! So, in total, we were fighting over four total pots:

·       The main pot held around 40k, and all five players were in that one.

·       The first side pot had around 8k, and everybody except the small blind were in that one.

·       The second side pot had around 45k, and the UTG+1, LP player, and I were in that one.

·       The final side pot had maybe 5k, and only me and the LP guy were in that one.

Then, we all turned over our cards. Here’s what we all held (in order of smallest to largest stacks):

·       The shortest stack, the small blind, had Tc Ts.

·       The lady who went all-in had Ks Kc. She was looking very happy.

·       The UTG+1 player had As Qc. He was drawing nearly dead.

·       The LP guy on my right had 8h 8c.

·       And me, your humble hero, with Ad Kh.

The board cards came out 6d 5c 9d. The guy with eights now had a straight draw. The turn was the 3h. Even at that point, except for the UTG+1 player we were all still alive for the main pot. Then, the dealer gave us the river.

It was the Ace of Hearts.

I’d won it all. Every chip. I was completely stunned. I could barely move. I’d knocked out four players in one hand. I suddenly had over 100k in chips sitting in front of me. I didn’t even have enough room to stack them all. Since there were only five players still at our table, they had to suspend play until they could fill it back up (which was very fortunate, because it gave me a chance to start the epic job of stacking all those chips). Ultimately, the TD bought two racks of my smallest chip denominations (the 100s) and brought over some 5k chips – which weren’t even supposed to be in play until after the next break!

Anyhow, I rode that massive chip advantage all the way to the final table. I think I played above average, but (as you can see) I also got hit by the deck pretty hard. But that’s how you win tournaments. Or, at least in my case, run really really deep in them!

Maximum Value at a Short-Stacked Cash Game

The $2/$5 No-Limit cash game at Snoqualmie has one very interesting anomaly: The maximum buy-in is limited to only $300. This has implications for how one should play this game. For example, say you’re on the button at a full ring game. A player in middle position raises to $15. Action folds to you, and you look down at 97s. If effective stacks were, say, $1000, this hand would definitely be worth playing (and might even merit a re-raise). But with only $300 behind, this hand hits the muck. There just isn’t enough implied odds to make such a speculative holding worthwhile.

Given that context, the following hand came up, and I’m pretty sure I got maximum value from it.

The player under-the-gun raised to $15. By the time action got to me in the small blind, three callers had come along for the ride. This, by the way, is another hallmark of this game; lots of preflop limpers and callers, which again has implications for how one should play certain hands.

I looked down at AcQc – a premium hand for this situation, for sure. I saw that there was $67 in dead money in the pot, and decided that was a big enough number of chips to try to take right there. I also realized that if anyone called (and the initial caller was the one most likely to do so), my hand had plenty of post-flop equity to continue on with. I decided to raise to $80. The big blind folded, and action returned to the preflop raiser.

I could tell from his reaction that he thought I was just trying to steal the pot. As the table sheriff, he wasn’t going to let me get away with it. He smooth called; everyone else folded, and we took the flop heads-up.

The flop came 4c 2c 7d. So I had flopped the nut flush draw; a backdoor draw to the idiot end of a straight; and I had two overcards. Overall, I was likely way ahead. Even if my opponent had something like pocket tens or Jacks, I was over 50% to win. Only a flopped set had me in trouble. If ever a flop called out for a c-bet, this was it.

I checked.

In doing so, I tried to look as weak and as disappointed as I could. After all, my opponent appeared convinced that I was merely on a steal; I was hoping that by feigning weakness I could induce him to bluff. And he did.

He pushed all-in, which (given the starting stacks) was only around $200. I nearly beat him into the pot, and immediately flipped my hand face-up for all to see. No slow-rolling for me!

The dealer completed the board with the 5h and the 2d. In other words, I had completely missed everything, and ended the hand with a measly Ace-high.

My opponent looked at the board, and slowly mucked his hand. My Ace-high was winner. I can only assume that he had a hand like King/Queen or King/Jack – hands far too weak to open under the gun, at least for me.

If I’d bet the flop with a c-bet, I’m pretty sure he’d wiggled off the hook. But my weak check gave him the green light to try to push me off the hand. Sadly for him, I had the near nuts. I wasn’t going anywhere.

Heartland Poker Tour Seniors Event Championship

That’s my ending chipstack … how it looked after I knocked out the #3 player on the way to heads-up. My JsJc held up against her Ad7h. At that point, both the last remaining player (Gregg) and I had roughly the same size stack (around 1.3 million), so we agreed to a 50/50 chop. I actually had just a little bit more than he did, so I became listed as the champion for that event. The tournament had 173 players; paid 18; and cost $200 to enter. Gregg and I walked away with a little over $6500 each. Hmm, $500+ per hour for twelve hours’ work? Not bad I’d say.

I think I got the better end of that bargain. Gregg had been running over every table he’d played at – including mine early on, before I was mercifully moved away – and I wasn’t eager to play heads-up against him. Although the two of us butted heads infrequently, the number of hands he won against me and the number I won against him were about the same. I’m probably the only one who could say that about him, and he’s probably the only one who could say the same thing about me. So a 50/50 chop seemed like an appropriate way to wind up the game.

I don’t really have a narrative for this entry beyond what I’ve said above, so I’ll just post some random, admittedly rather jumbled comments.

·       It seemed like there were a lot of women players at this event, and most of them were pretty good. Every table I was at, including the final table, had three or four ladies at it.

·       I spent a LOT of time as the chip leader at whichever table I was at. When I wasn’t leading, I was nearly always above average stack. It wasn’t the result of very many big hands (although I certainly did have many big hands). It was more the result of just slow, steady, consistent grinding. I think I was only all-in twice, and both times early on in the tournament.

·       One time I went all-in against another player who had me just barely covered. I won the hand, and he was down to a single chip!

·       I think I knocked out around ten players overall, which is a lot. I knocked out three players in one hand, taking KK against AQ, QQ, and 66.

·       Early in the tournament, I raised in middle position with A9o. It folded to the small blind, who had a somewhat short stack, and he shoved. After thinking it over for a while, I called (it wasn’t that many more chips). He showed 4h2h. My Ace held up, and he was busted. The guy sitting next to me, who was pretty much a jerk, said, “When did Ace/Nine become a raising hand?” I said, “The same day Four/Deuce became a shoving hand.” He had a lot more commentary on how badly I was playing overall. I just said, “Yes, you’re right, I am a really bad player.” He busted out soon afterwards.

·       I did not deliver a single bad beat the entire tournament. That is astonishing. Every time I won a hand at showdown, it was because it started out being the better hand (at least post-flop). I certainly suffered some soul-crushing bad beats myself though! Once my Aces were cracked on the river for two pair (we were all-in on the turn). Another time, my Ace/King was beat by Ace/Six when my opponent rivered a Ten-high straight. This was by the same lady that went all the way to #3 (who I busted later). But I had so many chips that I was able to survive both of these setbacks.

·       Another notable hand happened at the final table. This player with a very swingy playing style (she was always involved in massive pots with marginal hands, which she sometimes won) went all-in in early position. I was in late position with Aces and called. (There's no better feeling than when someone shoves into your Aces.) She had AQo and busted. What made this hand notable (to me) is that I think it was a mistake for her to shove with Ace/Queen offsuit. First of all, she just had way too many chips. A smaller raise would have made more sense, and been appropriate. But also, AQo just isn’t a good shoving hand from early position at a full table, unless you are desperately short-stacked. Again, she should have just raised.

·       When facing all-in bets, I folded 55 twice, 99, and AQo. The AQ fold was against the same player who busted #3; I was probably actually ahead of her range but didn’t want to get involved. The very next hand, I shoved with AJo and won. The point here is that you need a much better hand to call a shove than you do to shove yourself.

After I won (it was around 1am), I was so excited that I couldn’t sleep. This morning, I’m exhausted. I have another tournament that starts in a couple of hours though, and I really want to play it, so hopefully I can keep it together long enough to run well. It should only go about three or four hours, so I should be okay.

That Was One Weird Hand

I recently played a session of $3/$5 no-limit at Muckleshoot, and ended up winning a hand I had no business winning (and, arguably, no business being in). It ended in a most bizarre way; providing me with an experience I’d never had before.

I was on the button in this hand. By the time action got to me, there were four limpers. I looked down to see 4h4d, the hand nicknamed “Barack Obama” (since he is the 44^th President). There were a few ways I could play this hand:

·       I could fold. However, even though this is such a small pair, I just couldn’t bring myself to make such a wimpy play. The opportunity to flop a set and double my chipstack (or more) was just too enticing.

·       A raise might be in order. However it would probably have to be on the order of a $35-$40 raise to clear away the deadwood, and from playing at this table I realized I wouldn’t be able to shake all of my opponents. A low pair is good for winning a pot preflop; but once the board cards start coming one generally loses.

·       I decided to go with the third option; the smooth call. This gave me the chance for a big score, while risking a minimum of chips.

Action moved on to the small blind. He actually DID take the opportunity to raise, to $40. He was a younger guy; extremely aggressive, but no maniac. It was tough having him on my left, and I knew whenever he was in a hand I would need to be extremely alert.

The big blind folded, and all the limpers called (this was precisely why I had decided not to raise). By the time action got back to me, there was a little over $200 in the pot, and I was being asked to commit another $35. I found these odds irresistible; and as I was closing the action, I decided to call.

The flop came Qh As Qd. At that point, I was done with my hand. I had failed to flop my set, and with such a dangerous board I just wanted to move on to the next hand. However, everyone mysteriously checked this flop; so I checked as well and bought a free card on the turn.

As an aside, the only opponent I was really paying attention to was the preflop raiser on my left, who was the first to act. When he checked the flop, I took all the hands which had an Ace or a Queen out of his range. Given his terrible position and such a dangerous board, I would have expected him to bet these hands if he had them (I know I certainly would have). When he didn’t, I realized he didn’t have those hands.

Things got worse on the turn, with the Jd coming. But once again, it was checked all the way around. I decided to remove Jacks and King/Ten from my opponent’s range, as these are hands he would be obliged to bet with such a scary board and myriad opponents.

The river card was the Jh. Now, the preflop aggressor suddenly came alive, betting $60 into this pot of nearly $250. All the field insta-folded, except for me. I decided to think it over for a bit.

I had already removed so many hands from my opponent’s range, what was left for him to value bet on this river? Pocket Kings? I suppose a monster hand such as quad Queens or Aces full. Or perhaps I had my ranging wrong; but I really didn’t think so. Aside from Kings, I couldn’t put him on a hand that beat the board. And his bet was so small, it was hard to take seriously as a value bet. So I called.

Almost immediately, a number of things happened in somewhat rapid succession:

1.       My opponent said, “You’re good,” and picked up his cards, preparing to helicopter them into the muck.

2.       I turned my pocket fours face up.

3.       My opponent mucked his hand, and the dealer immediately buried it.

4.       I said, “I play the board.”

5.       The dealer pushed me the entire pot.

6.       My opponent realized he’d mucked a tying hand.

And that, boys and girls, is how I won a pot of nearly $400 that I never should have.

The only thing that made this experience better was what actually happened: My opponent started to berate me for my call, enumerating all of the winning hands he could have had (which also happened to be all the hands I had removed from his range as the hand played out). The only reply I gave was, “I know. I’m a really bad player.” And I have all of your chips. It took me three hands to stack them all.

How a Poker Player Thinks

I’ve been spending this week playing at the Ameristar in St. Louis. I’ve been playing nearly all of the Heartland Poker Tour events (including the Main Event), but also plenty of cash games. These games are among the juiciest I’ve ever seen. Outside of Aruba and the Florida rooms, I can’t recall anyplace I’ve played where the chips came so easy. Here’s one hand as an example:

This was a 1/3 game. Having started with $300, I’d been able to grind it up to around $400 after a half-hour ($395 to be precise – see below to learn how I came to know that).  Lots of limping taking place; it wasn’t at all uncommon for six players to see a flop. This isn’t to say there wasn’t ANY preflop raising; on two occasions someone raised $100 into a pot with a few limpers. Both times, after everyone folded, they tabled pocket Kings face-up. Everybody respectfully and solemnly congratulated the winner on their immense skill and judgment for how they avoided a potentially dangerous flop. I felt like congratulating them on winning the absolute smallest amount of money humanly possible with poker’s second-best starting hand.

The following hand happened while I was in middle position. By the time action got to me, we’d seen two limpers (including the older player on my right). I looked down to see pocket nines, and raised to $15. I’d been raising every pot I entered regardless of the number of limpers, which threw some of the other players off since it was so unusual. Not that it made that much difference; my preflop raises didn’t get much respect, and I knew I’d have to trust my post-flop game to be successful in this room.

My raise got cold-called in two spots behind me. The small blind folded; big blind called; and the first limper also called. Now action was on the player to my right. To recap: Four players plus me, with one left to act.

Suddenly, this player shoved all-in; nearly a $400 re-raise.

My first instinct was to fold. After all, pocket nines generally don’t play well in a hand that’s been three-bet preflop. But I decided to give the matter a bit more thought. I asked myself, what hand would someone limp/shove with … that could beat pocket nines?

We’ve already established that folks will raise preflop with premium hands at this table. This means that my opponent probably didn’t have Aces, Kings, Queens, or Jacks, because he would have raised with them himself. Maybe even Tens. So what hand would he reraise-shove with? Let’s say Tens, Nines, Eights, Sevens, and maybe Sixes. Against this range, 99 is a 65/35 winner. So I should call.

Let’s add a few more hands to his range. Assuming he’d also raise AK and AQ, that removes those hands from his range. So maybe AJs and ATs … KQs, QJs, and JTs. I can’t think of any other reasonable possibilities, and even these might be stretching it. But even so, I’m still 60/40 against this range.

Again, the key for me was his limp/shove, and what preflop raises tended to mean at this table. If he’d raised a reasonable amount himself preflop, I’d have just called (and given the exact flop, bluffed if checked to or folded to a bet). If he’d three-bet a smaller amount, I might have folded. But his shove, paradoxically, just looked too weak, and WAY too polarizing.

I called.

Everyone else folded, so it was heads up. The board cards were KKQJ4 rainbow. I showed my 99; he showed 77; and since I had him outchipped by around $5 (that’s how I knew exactly how much I had above), he was completely felted. I stacked towers of chips, while he rebought.

THIS …. (drum roll) … IS THE HPT.

I spent this past week in lovely Reno, Nevada playing my very first HPT tournament at the Grand Sierra. I’ve played here (and stayed here) before, done well, and had high hopes. Sadly, I finished out of the money, but it was a good experience nevertheless.

The Main Event was a $1650 buy-in, and the stars were definitely out. They had three starting flights, and I played the first one. The pros in the field included Howard “Tahoe” Andrew (on my left); Pendleton triple-crown winner Angela Jordison (on my right); Dutch Boyd; and 2015 November Niner Neil Blumenfield.

As is usually the case, my bust-out hand was rather inconsequential. I pushed AhQd against KK and lost. It was a previous hand which was actually the key hand. Losing it knocked my chipstack down to under 25BB, giving me considerably less maneuverability and preventing me from being a factor in the game.

With blinds of 250/500 and 50 ante, I was on the button and after several hours of solid grinding was one of the overall chip leaders with roughly 60k. The player under-the-gun limped in. He was a passive player, frequently limped, and quite honestly was what one would refer to as a calling station. He was way out of his league against these players, and if he hadn’t already hit a few miracle board cards he would have been long gone. As it was, he started the hand with around 40k in chips.

Cary Marshall was in middle position with the smallest stack at the table of around 10k, and he limped behind. He’s an older player; tighter than average and very tough. He had knocked me out of a previous tournament (which he went on to win), and I definitely did NOT like seeing him at my table. He’d lost a bunch of chips in a couple of bad beats, but I’d seen him grind it back up before and knew he was just as dangerous now as he was when he was chip leader.

The next player was Ian Steinman, a 25-year old pro from the Bay area. He had around 20k. He had a good, solid game; a bit on the loose side, but definitely good competition for this field. He thought about his action for a bit, and then raised it to 2.5k.

It folded to me, and I looked down to see AsKs. I thought carefully about what I wanted to do with this hand. Folding was out of the question. Should I raise to thin the field, or just call behind to see if I can encourage some additional players? AK suited plays well against many opponents, so I decided to just smooth-call and see if I could get more folks into the pot.

Everyone else folded back to the UTG limper, who also called (as I totally expected him to). Then Cary was next. He shoved all-in for a total of 10k. Ian thought about what do to next; it was pretty clear that he didn’t expect to see so much action on top of his raise. Finally, he folded. He told me later that he had Ace/Jack offsuit.

I was next, and once again I was facing the same question: Re-raise to (likely) get heads-up against Cary, or just call and let the UTG player tag along? I really felt that I had a premium holding, and getting as many chips as possible is so important in a tournament, so I went with the call. I felt that if I missed the flop completely, I could just release if I came under pressure. UTG called also, so it was three players to the flop (one all-in).

The flop came Kh 8d 3d. Immediately, UTG shoved all-in for his remaining chips (around 40k total). I knew instantly exactly what he had. When a player acts quickly, it almost always means that he is on a draw. If UTG had a set or some other big holding, he’d have thought about how to play it for a bit before acting. I was convinced that I was ahead, so I called without much delay.

Sure enough, UTG had 9d 6d. Cary had Kc Qs and was drawing nearly dead. I had a huge lock on the hand. The turn card was a brick, but the river was … another diamond. Cary was knocked out of the tournament and I lost over half of my chipstack and was nearly crippled.

I’ve given this hand quite a bit of thought, and here’s what I’ve concluded:

I really don’t like the way Cary played this hand. King/Queen offsuit is not a good preflop holding -- as this hand makes obvious; he was completely dominated. He hit top pair and was still behind. He should have folded and waited for another opportunity.

On the other hand, I really like Ian’s play. He took a stab at the pot with a good hand, and then released once he realized that he was beat. I can’t fault his play at all.

At first, I really didn’t like UTG’s flop shove. I thought it was way too spewy, and he’s only called when he’s behind, such as with this hand. But after thinking about it some more, maybe this judgment is a bit harsh. Although he’s behind, the pot is laying him pretty much the correct odds to make a play like this. I still think it goes against ICM strategy, but mathematically it’s not a disaster. On the other hand, deciding to play 9/6 suited under the gun is not the kind of thing I would do.

So that leaves my play. The only adjustment I could reasonably have made at some point pre-flop would have been to re-raise (or over-shove) rather than just call. But I think the preflop call, overall, is going to have a higher +EV than those alternatives. (At no time did I consider a fold.)