This question was posted in response to my analysis of a hand in which the Hero had to make a decision, for most if not all of his stack, with pocket Jacks facing an early position raise, a call, and a re-raise all-in in front of him. I wanted to write a thorough response and so saved it for a mailbag post.
Q: I have been a regular in small to mid and occasionally high-stakes MTT’s on Stars. The ranges for open-shoving, reshoving and calling that I was taught (by a very strong and respected HSMTT crusher) are miles wider than the ranges that most regulars consider to be correct. Only recently have I discovered, through many threads and posts like this (about hands I wouldn’t have thought even a second about) how wide this disparity is. Despite what should then be a massive hole in my game, I have continued to have a strong winning record over good samples especially in turbos where this sort of leak should see me be destroyed.
It seems to me then that there may be situations where despite the concept of tournament life, there may be value to taking neutral or even -EV gambles for huge stacks. It seems pretty obvious to me that even if Hero has a skill edge over the field, a 20 BB stack doesn’t give much room to exploit that skill edge; in weak tourneys like this stealing lots of pots and chipping up gradually is tough because players call raises too wide creating spots that will become awkward with the 20 BB stack. In tough tourneys too, a 20 BB stack gives you no “skill advantage” because with that stack, there is limited room to exploit whatever few mistakes people may make.
It’s just my intuition and I don’t know how to research to verify this, but I am pretty confident Andre Coimbra with 12k chips 33% of the time would have a higher ROI from this point than him with 4k chips 100% of the time.
A: It sounds like you’re talking about two different senses of the word “correct” here, and I want to address both. First there’s correct in the sense of +EV, that perhaps many people including myself underestimate how wide jamming ranges can be. That’s very possibly true, and I don’t claim to be an expert in that area – that’s a big part of why I wanted to work out the math here.
As for whether it’s correct to take neutral or -EV gambles to get a big stack, I don’t see how it can be. A big stack is valuable primarily for its buffer effect, meaning that it makes it possible for you to take some losses without getting eliminated. Obviously risking loss/elimination in order to acquire those chips directly undercuts that value.
It’s true that certain plays become available to you as a big stack that you wouldn’t otherwise have. This may be because you can make +EV plays at other deep stacks, such as 5-betting or 3-barreling, that require a lot of stack depth. Or it may be because you can “afford” to gamble in spots you otherwise couldn’t. This latter point is a direct function of the fact that each of your chips is worth less when you have a lot of them than when you don’t, so I don’t think that helps your case any.
I’ll admit that the former of these points is theoretically possible, but in practice I doubt those situations arise much. A short stacked player actually has an intrinsic advantage when everyone else at the table is deep. This is because they are all playing deep-stacked poker against each other, which often means playing more speculative hands that don’t have great pre-flop all-in equity. A short stack can exercise the tremendously powerful pre-flop shove, precluding any possibility of a rebluff, to either pick up a good-sized pot with no showdown or get it in good with a lot of dead money in the pot. Really the only drawback of a shortstack is the heightened risk of elimination – otherwise it’s nearly always advantageous vis-a-vis several big stacks. So I don’t see a lot of merit in heightening your risk of elimination in order to acquire a big stack.
The only time I’d seriously consider knowingly making a -EV play is when I feel that if I don’t, I’ll be forced to do something even more -EV later. The best example of this, which I believe comes from David Sklansky, would involve being UTG with a slightly better than average hand and an extremely short stack. Shoving may be -EV, but it will probably be less -EV than posting 50% of your stack blind on the next hand and being forced to go with a random hand.
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Dont have much time here right now but I constantly hear about Pros who make -EV plays in tournament because they are ‘going for the win, not the cash’. Maybe this is due to my ‘over’ viewing of WSOP ME/WPT TV coverage. Is shoving AK PF early in tournaments really a +EV event … Pros seem to love that hand regardless of the situation.
I tend to agree with your thoughts above. I think we may have even somewhat discussed the potential differences between Pros and Ams in tournament play in the past regarding using the ‘edge’ that an Am is not going to reload (cash) or have the opportunity to play in multiple tournaments and thus is less willing to put large portions of their stacks at risk for fear of busting/not cashing. (Not the same situation as JJ hand)
As far as a logical view point of ‘why would you ever do a -EV act’? Then of course we dont ever want to do anything but +EV actions. But when your ‘attitude’ about the event as a whole is ‘win or walk’ then you can ‘see’ where a -EV action gets this person to their ‘goal’ of a better position to win or walk away. This certainly could be seen a weakness in their overall game, but when they have the bankroll to back it up … ????
answer20, what you’re doing is taking opportunity costs into account. If said pro could be playing online earning 1000$ per hour, then a win-or-bust attitude suddenly seems worthwhile at the tournament: So, for example, suppose we have 1000$ in equity for the tournament, and we face a 50-50 decision which if we win leaves us with 1800$ in equity, but if we lose it busts us out. In isolation, this is a -EV gamble. But if we realize that when we bust out we’re winning another 1000$ on average instead of the time we would expect to be playing the tournament, then it becomes a 50-50 wager for either 1800$ or 1000$, thus this wager becomes a +EV move with expected gain of 400$.
One could ask why the pro would be playing this tournament in the first place, if it’s so far from being worth her time. Maybe the pro is giving extra value to winning a bracelet or something. The “sentimental value” could still be added to the value of the first prize, but this can still result in a situation like above (especially if the pro is facing a very close decision, or if she found herself with a short stack).
Also, about the blog post itself, I found it odd that the un-named questioner says that “even if Hero has a skill edge over the field, a 20 BB stack doesn’t give much room to exploit that skill edge”. I suck at tournaments myself (partly for this reason) but it seems to me that there are sizable communities of poker players that have significant skill edge with short stacks. Indeed, I doubt hyper-turbo players find such stack sizes awkward, seeing as that’s the stack size they play most of the time (correct me if I’m wrong). For all I know, a skilled hyper-turbo player has as much of an edge playing a 20BB stack as a seasoned tournament player has playing a 40BB stack; but, again, correct me if that’s clearly not the case.
There’s a book Poker Tournament Formula (and PTF2, http://www.pokertournamentformula.com/). The author is a former professional blackjack player that brings a unique mathematical perspective. One of the things he does that I haven’t seen elsewhere is quantify a tournaments skill level by it’s speed (how many hands played between rounds), how quickly the blinds escalate, and of course starting stack size. So a hyperturbo would have a skill factor of 3 and the WSOP Main Event would be 50 (just to illustrate, I don’t know the actual numbers). I seen discussions on these things, but I haven’t seen an actual number with all of these factors in the equation.
Anyway he talks about a concept called chip utility. If you are a skilled player the more chips you have the more profitable moves you can make, and the more skilled you are (compared to your competition) the more that utility is worth. It’s kind of like in Monopoly if you have %50 of the cash in play your odds of winning over the rest of the field are much greater than %50 because of how much more utility you have than anyone else. So basically his argument is the more chips you have the more your stack is worth (the opposite of ICM which states the more chips you have the less each chip is worth). He also quantifies utility and shows you how to take it into consideration when calculation pot odds.
Personally I think he makes a good argument. I think there is both a cash value (ICM) and a utility value in your stack. However I’m not completely sold on the strategies in his book so I can’t really recommend them for that reason alone. But I feel his unique mathematical perspective on things like tournament speed, risk or ruin, and of course chip utility is worth the price of his book (especially the $10 kindle version).
Does he also discuss the utility of a short stack? I find that this is vastly underappreciated.
With a short stack you don’t have too much utility. You may be getting other players to play sub optimally, but that’s not the same as chip utility. You only have a few moves, mainly the open and the jam, and you’re risking a lot when you use them (basically your tournament life). When you have a large stack you have many moves available to you, and even in the case of a small effective stack the same moves cost very little in comparison. And lets say you make a loose, -EV call and lose as a big stack. Now no one will bluff you. So even though you took a %5 hit to your stack your utility actually increases because you effectively took away a weapon of everyone else at the table. Theoretically the higher the stakes (i.e. life changing money jumps) the more utility you have. The more skilled other player are at using what utility they do have (i.e. a perfect ICM shove game) the less utility you have.
To me the concept of utility in a game theory is a lot like chaos theory, in that it is an complicated abstract mathematical concept that I may slightly begin to understand if someone else dumbs it down a lot first. So I don’t expect anyone to grasp the concept of chip utility from anything I write because I don’t fully understand it myself, and to try and argue that it’s a good idea sometimes to take -EV chip risks because the utility you gain might be worth it would be too ambitious for me. But I do find the concept interesting, and I do think there is value in trying to understand it.
Chip Utility – Simplified
I’ll start with a quick example. Consider a big stack at or near the bubble; This player can abuse all short stacks at this time with any two cards. In this case, his stack is providing him with great leverage, and thus, it has utility, aka, power. The power to damage, cripple, and/or end a player’s tournament life. The ev of his hands aren’t a factor.
Now take a player who has a modest, e.g., an avg. stack earlier in a tournament. He flops a gut shot draw with two other players in the hand, all having much larger stacks. Obviously, the goal is to increase your stack size. It gets checked back and the turn appears to be a brick. One of the players leads out and to call, even if you take into consideration that the third player makes the call, plus you calculate your implied odds, you’re still getting just 6:1 or 7:1, a clear fold – normally. However, if you call and hit your str8, and one of the other players calls off, your stack will now be well above average and with decent play will not only take you into the money but much deeper. You are also assigning a value on your time, i.e., you’re not spending the time to just min cash, but to go after the big money (whatever that may be for this tournament). This is the utility factor!
In the above illustration, the utility factor actually overrode the pot/implied odds factor of making the call for a gutshot straight.
Utility decisions are not made in a vacuum, nor are they to be made frequently. They are very situation dependent. They can often be equated to ICM decisions late in a tournament, whereas, betting or making a call to win a pot (or be in a hand in the first place) places you at greater risk (if you lose) than the value of the chips you gain – if you win the hand. (Think of ICM in sngs w/ 3 payouts or being a cl in a satty where you can fold your way to a seat; the gain from additional chips is a far greater risk.) In this case, utility is to not risk chips.
Utility strategy in a poker tournament is debatable, and as I recall, there were some interesting threads between Mason and Arnold (Snyder), the author), on 2+2.
There is also a very useful spreadsheet designed by a user named MathBoy (another high-staked AP) that calculated what is known as the Patience Factor. This is the main tenet of Arnold’s two books. The spreadsheet’s value is to assist in determining what are good tournaments to play – and those to avoid. Back when the books were written we knew less about overall structures and the value of time in them, than we we do today
Thanks for the explanation, TCP, but I must say that I disagree with both of those examples.
“Consider a big stack at or near the bubble; This player can abuse all short stacks at this time with any two cards. In this case, his stack is providing him with great leverage, and thus, it has utility, aka, power. The power to damage, cripple, and/or end a player’s tournament life. The ev of his hands aren’t a factor.”
This isn’t true. “Any two cards” is a tremendous overstatement, and to the extent that there is this bully effect, keep in mind two things:
1. It doesn’t require a “big stack” per se, just a larger one than the players you’re raising (and sometimes not even that).
2. One of the reasons a player with a larger stack can afford to play hands that shorter stacks can’t is that his chips are worth less than theirs.
“if you call and hit your str8, and one of the other players calls off, your stack will now be well above average and with decent play will not only take you into the money but much deeper.”
Again, not true. In a tournament that pays 10% of the field, the average stack when you make the money is 10x the starting stack. Doubling or even tripling up early doesn’t mean you can just coast into the money, let alone “much deeper”.
” You are also assigning a value on your time, i.e., you’re not spending the time to just min cash, but to go after the big money (whatever that may be for this tournament). ”
This is really a separate argument. There are plenty of reasons why you might not value your survival in a tournament, but that doesn’t mean that -EV plays improve your overall expectation IN THAT TOURNAMENT.
Here’s something to think about: if you make a -cEV play that somehow increases your $EV in a tournament, who does that $EV come from? $EV in a poker tournament is zero-sum, so if your expectation goes up, the expectation(s) of one or more of your opponents must go down. I would argue that when players A and B get all-in and A wins, A’s $EV is increased, but not by the full amount B’s $EV. Rather, A gets some large percentage of B’s $EV, but the remaining fraction of it is divided, not necessarily evenly, among all of the other players in the tournament. That’s because all of these players are now one step closer to cashing or moving up the pay ladder.
The gut shot example is a bit extreme. I dusted off my copy of PTF2 and Mr. Snyder talks about calling a check shove early in a fast moving tournament with a nut flush draw to win a pot of $2800 when it would have to be $3500 to be getting correct odds in a cash game. His reasoning is if he folds his utility would be crippled but if he calls and wins he’ll have full utility, and his chances of winning the tournament increase by more than the 2/1 pot odds he was getting. So he’s not saying ignore pot odds, he’s saying consider how a decision affects your utility.
“If you make a -cEV play that somehow increases your $EV in a tournament, who does that $EV come from?” – You are correct if you are assuming equal skill levels using ICM calculations. However if Vanessa Selbst accumulated a large stack early in a tournament everyone’s equity would be a little bit less than say if Darvin Moon accumulated the same stack in the same tournament. However I think everyone’s equity would be more equal whether it was Ms. Selbts or Mr. Moon with a short stack.
So let me ask you this: would you make a play that would be slightly -cEV that if you won you would increase you’re fold equity an average of 10% for every pot that you’re involved in until you reach the final table? Of course you would. You seem to acknowledge as much when you say “I’ll admit that the former of these points [move moves available with a big stack] is theoretically possible, but in practice I doubt those situations arise much”. So it seems to be a matter of degree. In Kill Everyone they use the term “fear equity” and that may be a part of what Snyder calls chip utility, but I think there is a little bit more to chip utility than that. The math will never be as neat and tidy as average fold equity increasing so we may never know for sure.
I think if you just use cEV you would be correct/optimal in almost all of your decisions, but I also don’t think you can accurately say that it’s never optimal to make a -cEV play with the exception of blinding out the next hand.
This whole “chip utility” discussion seems to assume that stacks are somewhat static, ie that short stacks stay short and big stacks stay big. It’s not like your options just vanish when you get short-stacked. You have new moves available to you that weren’t available before, and those new moves will often result in you doubling up, at which point that “chip utility” returns to you. So rather than deliberately making a -cEV play in hopes of getting a bigger stack that will enable you to do make certain plays, you can plan to accumulate chips through +cEV plays, with a backup plan of making even more +cEV moves if you start to get short.
Likewise, just because you get a big stack early doesn’t mean you’ll keep it. Especially in a badly structured tournament, blinds go up quickly, so whatever options are opened up for you as a result of winning a big pot aren’t going to stick around for all that long.
It’s true that having more chips tends to give you more options. I just think that making +cEV plays is the best way to get more chips. Although I can imagine hypothetical scenarios where -cEV plays can be +$EV, I’ll say the following:
1. I’ve never seen one in the million plus hands of tournament poker I’ve played. I’ve never even seen someone successfully present a non-hypothetical example of one.
2. The examples I have seen have turned out to rely on flawed assumptions about how to value stacks of various sizes.
This leads me to the following conclusions:
1. They are extremely rare, so much so that if you think you’ve spotted one in-game, you’re much more likely to be wrong than a genius. It’s even harder for me to imagine such an example arising from a case where you have to risk the last of your chips, as in the hand that sparked this discussion.
2. Trying to identify them is not a good use of your practice or playing time.
Chip Utility – Final Thoughts(?)
Let’s get this out of the way first: I agree 100% with your conclusions.
In my comments, I stated that utility is situation dependent. And I stand by that comment. I think chip utility has, when all is said and done, more to do with fast (serious donkaments) tournaments than anything else. Without taking the time to “dust off my PTF(s)” – I have better things to do with respect to my poker education, I believe that this is what Mason was actually referring to. (At the time, a lot of angst was taking place between Arnold and Mason, plus Radar O’Reilly – a modern and less than private tête-à-tête between poker and blackjack authorities, but I digress)
Sorry for the clutter. In today’s poker world, with edges as small as they are and the skill levels (ever rapidly) growing, there’s just no place for negative EV plays. So even though, conceptually – David Pham I believe, is a proponent of this – there’s some merit to it, your conclusions are spot on. GTO is a much better use of one’s study (and play) time.
On a different topic I’d like to thank you Andrew, for all your work. I am fortunate to have found your site some time ago, and have both learned from you and recommended this site and yours (and Nate’s) podcasts to many people