This article is being released in a series of three. Parts I-IV of this article can be found here.
Part V: Diminishing Marginal Value of New Chips
Another issue with cEV-based tournament analysis is that it rarely bothers to consider how truly important new chips are. For example, adding 5 big blinds to your stack when you have a 12 big blind stack can be the difference between eventually winning or losing a tournament; adding 5 big blinds to your stack when you have 100 big blinds usually isn’t worth any reasonable risk at all. The very important concept at work here is the diminishing utility value of tournament chips, or the fact that every additional chip added to your stack is less important than the previous one. In terms specific to our discussion, cEV becomes a less relevant factor of consideration the more your stack size increases.
As I mentioned, however, I’ll often hear students skimming over how strategically deep they are relative to the blinds and other stacks at the table, and ignoring how truly valuable the new chips actually are.
“Why are you 5b/calling 85 bb effective here?” I’ve once asked a student.
“Because he’s so aggressive that I’m a 54% edge over his range and I’ll show a profit,” he responds.
Even if you forget to consider the fact that with such a deep stack and his knowledge of the game, the student could just as easily out-play his opponents for a few levels and be essentially guaranteed a gradual double up; by his math the student is projected to be knocked out of the tournament a little less 46% of the time.[1] The other 54% of the time, he doubles his stack to approximately 170bb. In the early stages of a well-structured tournament, the true difference between 85 and 170bb is much less meaningful than the difference between 85 and 0bb.[2]
Although the above example is more extreme than most, it illustrates how diminishing marginal value of tournament chips – a central implication of tournament payout structures – is often ignored by many MTT players. The translation: your tournament life is usually more important than the size of your stack, especially as that stack increases in size.
Part VI: tEV Within Other Typical MTT Spots
Even if you don’t know it, tEV is an inherently crucial concept behind some of the basic MTT strategies you may already intuitively follow. For example, most MTT players know to play very precariously with 16-24bb stacks. They are mindful of the fact that their short-term goal is to double up, and if they bleed too many blinds from their stack first, their potential double up isn’t as worthwhile. Experienced players know that they can stretch their skill advantage over a table much further if they have a 48bb stack rather than a 32bb (or less) stack. [3] Thus, in some circumstances they may play much tighter with smaller-size stacks in hopes that a future double-up will give them a better stack to better outplay their table later.
Consider this fairly common MTT spot: with 20bb it’s unopened to you in the CO with 97o. The button and SB are both fairly passive and the BB either folds or defends, so on paper one would think you should be opening fairly wide here – by constantly defending and check/calling or check/folding too often, the BB makes your play sizably positive in terms of pure cEV long-run. But what about that one time every so often that the BB defends and actually flops something, or one of the other two opponents actually wake up with playable hands?
Although your play is probably positive when you’re adequately deep, at 20bb you expose yourself far too often in the interim to be opening as wide here. If, for example the BB defends, check/calls the flop, then musters up the courage to go with it on the turn, you may find yourself folding with 8-12bb left, and now needing a double up just to get back where you were beforehand. Although your play was positive, your stack is not deep enough to withstand negative swings for the times when it doesn’t work. In short, winning this pot is probably not as big a deal to you as losing it would be.
Had you passed on this marginally-positive cEV spot and found a double up to 40bb later, you would be better equipped to make more complex plays and take advantage of more spots like this one– a central component of increasing your tEV. This is one of many MTT situations in which short-run tEV and long-run cEV directly conflict with one another. While cEV analysis alone would direct you to raise and play the hand, your tEV might persuade you to fold.
Part VII: Online Hand History Example
When I won the Merge Sunday Major in 2011, I came into the final table ranked 7th in chips. The stacks at the table were mostly all very deep relative to the blinds and to be honest, most of my opponents were clearly not very experienced at all. Even better, most of the big stacks were to my immediate right, and the tighter players were to my immediate left. As you likely know by now, this is an incredibly favorable table draw for aggressive players to exploit. Thus, I assessed that the combination of my skill edge, table position, and the payout structure dictated that my tEV should heavily influence my decision-making process, meaning much more to me than the potential +cEV of adding chips to my stack.
Early on, I was fortunate to double my stack when KJ won against AQ all in preflop for about 15 big blinds each. Once my stack reached 30 big blinds, I was extremely careful to avoid any remotely excessive gambles. Six and seven-handed, I avoided most pre flop all-ins at all costs unless my reads on opponents told me otherwise, or my hand fell within an incredibly profitable range. This was because stack size dynamics (and my opponents’ relatively poor play) allowed me to mercilessly exploit spots with little or no resistance. My opponents were constantly defending their blinds versus my opens and subsequently check-folding to my continuation bets. Although calling all-in bets with a reasonable hand range was certainly +cEV, what was the point of risking a 20-30 big blind all-in without the absolute peak of my hand range if I was already picking up 6-8 big blinds per orbit? Whether I won the tournament quickly or it took me 7 hours, I didn’t much care – so long as I was still likely to win.
Undoubtedly, the strategy I employed here was the difference-maker in winning the tournament rather than risking a 6th or 7th place finish. My skill edge over the final table allowed me to systematically trim almost all my opponents’ stacks down to 12-15 bb before swinging for knockouts. Certainly, this final table scenario is a rarity at the higher stakes these days; however, it serves as an illustration of just how much your explicit awareness of tEV can translate into real money.[4]
Next week’s article will discuss a live hand example posted on the TPE forums by “calvin4140,” then wrap up the series by summarizing the main implications of tEV and how they can be implemented into your overall tournament strategy.
[1] This figure considers fold equity.
[2] This parallels almost perfectly with the economic theory of Diminishing Marginal Utility. Think of it in terms of income: a $5,000 raise is a big deal when you only make $17,000 a year. But if you were Bill Gates, a $5,000 raise is essentially meaningless.
[3] Recall: skill advantage/edge is a major component of one’s tEV.
[4] The difference between 6th place and 1st place in this tournament amounted to more than $16,000.