If we choose larger bets to maintain the effectiveness and profitability that a half pot bet has, we are committing ourselves a lot more by the river, and thus our river bet is losing some utility. We also lose the ability to raise preflop and continue on all 3 streets. We lose some ability to 3bet the "standard" raises which are generally smaller than the tapering strategy raise and are generally under 3 big blinds at most stages. We also lose the ability to raise on other streets and maintain the full aresenel of moves on every additional street as we decrease our stack size relative to the blinds.
Tapering is a concept that EXTENDS utility longer on in the tournament. Those with an edge that can play larger pots will have more chips for longer allowing them to keep playing slightly larger bets until their opponent's effective stack force them to play for less.Even then, as the blinds rise, tapering maintains full utility even as the blinds rise to where everyone becomes shorter stacked as even with smaller raises, the implied odds aren't there for opponents to call, and the risk management and stack preservation makes it difficult to even call a smaller bet.
However, tapering doesn't extend utility forever. Eventually there is a tradeoff regardless of the choice you make. 20-35 big blinds is really where that tradeoff occurs.
Option 1 is limp in to preserve utility on the flop. Limping adds the "last one in" advantage with 20-40 big blinds and under where you can shove rather than get shoved on and have no fold equity and only the equity of your hand, and where folding to an all in shove over your limp would represent a very small percentage of your stack. Limping strong invites multiple callers and isolation raises which requires you to have a range that contains enough drawing hands that play well multiway in your range, and enough strong hands that you are willing to 3bet shove for value or as bluff. Your strong limps offer opponents with small pairs the implied odds to setmine when you are strong. However, you maintain the ability to setmine vs someone who limped first or only made a small raise or when there are multiway pots and play drawing "implied odds" type of hands like suited connectors and suited aces that otherwise would lose their implied odds to be playable. It requires a very different logic to playing out of position such as frequently leading out small on draws as well as strong bets with a smaller than normal bet. You want to lead out weak often enough with strength as well so if you get played back you can shove, and so you aren't too predictable, but you also want people to just call often enough that they allow you to create the pot odds such that if they bet it, you would get the right price to call. You can use board texture to overbet the pot on later streets, and use information on wet, boards with say ten or jack high to follow up with a bigger bluff on the turn since they probably would have raised to prevent a difficult decision on the turn.
The real drawback becomes "forking your range" or "forking your strength/weakness". This means that your opponents can typically tell by how you acted preflop (raise or a limp) what you have. This forces you to always limp, or be slightly more predictable about what you have, or to complicate things by SOMETIMES limping with hands you would raise and vise versa. If you are able to limp raise often enough, you probably cannot raise during that period without making it easier for opponents to read your hands, so you'd have to pretty much always limp which certainly loses a lot of opportunity preflop and on the flop when you get multiple opponents as you cannot as easily buy pots with aggression. So limping usually switches mentality to playing for value rather than playing to steal, unless you can limp raise often enough to where you are restealing. The limp raise doesn't have to occur nearly as often for it to be more profitable since it's like a 3bet in that it wins more chips.
A limp in the middle and later stages effectively plays like a raise and a few callers in the earlier stages in that you need stronger hands to continue or draws to strong hands, and good implied odds hands in your range as opposed to the AJ,KT,QT,J9 and Qx suited type of hands.
Option 2 is to just bet less than half the pot and taper down to a minraise. A minraise is okay even though they will defend more, but betting less than half the pot is certainly questionable.
Option 3 is to remove the all in river pot sized bet and instead just have stack sizes where a shove might only be half the pot on the river, and all 3bet pots will be all in or effectively playing all in on the flop.
Option 4 is just to accept the lost utility, mostly play as normal, but plan to get the money in on earlier streets and readjust your bet sizes and hand strength accordingly. Since you are trying to get the money in earlier, slightly larger bet sizes now might also become acceptable again, and the hand ranges should reflect this.
So there could be a phase where you REVERSE taper and instead inflate the bet size again to make it more challenging to players who are unprepared for this style and also to take a higher risk/higher reward line since the bigger risk will soon become not taking one.
If you are going to play draws they will probably be the all in semibluffs as described in the nutball supersystem. This also means you will not be floating on marginal hands or checking to induce bets very often. You are reraising to get the money in or folding, or checking to give up if you don't improve. If you float it's only on small bet sizes and you'll probably be shoving in on the turn if you detect weakness.
Option 5 is to be anticipatory. Rather than WAIT until this moment comes, prior to the blinds rising, more liberally seek out all in situations and more aggressive plays in anticipation of losing that utility such that you maintain the ability to steal at a lower risk for longer if your aggressive stage is successful. So in the 25-35 or even 30-40 big blind range, you are willing to flip or even take the worst of it with pot odds or if you are a utility theorist, you might not even need a +EV decision to get it all in, you just need to be close enough to where you can make up for it later due to your extra utility when you otherwise would have been in the 10-20 big blind range that may last for a few levels.
Option 6 is to just completely change styles entirely. For example potentially open shove or check raise shove flops for large overbets as somewhat alluded to in the option 4. You might have a mixture of semibluffs and made hands and maybe more pure bluffs an extremely low percentage of the time. Then continuing for larger bets with the intention of shoving the turn with some top pair hands and possibly some gutshot draws that improve to 15 outs by picking up a flush and double gutshot on the turn and perhaps some bottom or middle pair hands that improve or see a scarecard on the turn. Your hand range may also change dramatically and possibly your bet sizing.
Option 7 is to change hand selection and criteria for a "stacking off hand" since you won't have that extra river to worry about or draw to so draws decrease in value if semibluffing is not profitable. Medium strength hands decrease in value unless opponents are making too many "hero calls" and medium strength hands aren't really worth stacking off except for top pair weaker kicker and top pair now goes up in strength. To really understand how your hand values should change, you need to use the rule of 3 and 6 and 5 and 10 and/or understand stack to pot ratios as described in Professional No Limit Hold Em Volume I and how commitment threshold of hands should change against different types of opponents based upon SPR..
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I believe the theoretically equilibrium shoving bluff to balance your nut hands is if you have a made hand 2% of the time, you might overbet shove for 5x pot 0.33% of all flops (1/pot size +1 times the made hand). And your semibluffs should on average break even to force opponent to widen his calling range. Or you might just include some of the more longshot semibluff hands on very rare frequency. This system was partially explained in nutball supersystem. I haven't really used it, but maybe I should. It requires some serious planning if you want to get the bet sizing and math right and definately is a high varience strategy that could get you back into the "full utility" zone. But in tournaments the ICM is really weird since if opponents obey the ICM they should really make big folds, which makes it profitable to more liberally push. But if they don't do as they should and you know it, you shouldn't be so aggressive and should have a much higher made hand to semibluff shove rate and eliminate a lot of the worst semibluffs and instead play those passively/cautiously.
You could argue you no longer need that full pot sized bullet all in on the river, but it's nice to have the flexibility to bet for value. Also, opponents have the power to eliminate all your utility by 3betting and effectively committing you to the all in.
Aside from this, being able to get the full value of 100 big blinds is usually going to result in a higher BB per hour rate if you are a skilled player, as well as present situations where you can play with greater implied odds if you choose to never have a preflop opening raise over 3.5 big blinds. With these implied odds more hands become playable for longer and there's added value early that gets lost as your chipstack declines.
It's not real easy to draw a clear line in the sand of where the benefits of getting more chips are large enough that it's worth accepting a lower bubble factor or even gambling with the worst of it in order to preserve the utility over multiple blind levels and parlay it into more chips in the future. I don't know what option is best and at what stage. You can also argue that the gains of utility are not sufficient enough to outway the opportunity to find a very profitable spot in the future while maintaining a large probability of survival and chance to make money by folding, as well as the possible opportunity in the future to get isolated heads up for more than a triple up after loose action and a big isolation reraise which may have a better probability of getting you back in it with more chips anyways.
Nevertheless, we can see that "utility theory" has a clear argument for consideration.
If I had to describe where I think Utility Theory takes place, it's where you have 25-35 big blinds, and as low as 15 if the situation dictates it. The odds to eliminate a very skilled opponent seated to your left, or a very loose, aggressive opponent to your left at a table where they are very passive and loose preflop and tight postflop do not have to be very high for you to be able to make up for it in future steal opportunities. Your chances of advancing deep will have to go through that player as you will probably not be able to outchip him by waiting for a hand, and if he won't let you steal your fair share of pots, you will be forced to bet a parlay with MULTIPLE all ins.
However, if you go after this guy and can cripple his utility or go bust, you immediately end the need to make multiple all ins as you have a high probability of being able to just accumulate chips and keep up with the rising blinds without a lot of risk to your tournament life aside from the initial all in.
Exceptions aside, anywhere from 5-15 and possibly as high as 25, I think "opportunity cost of better opportunities" is greater than utility gained by doubling up. So really in the 15-25 range there is a pretty big overlap between two schools of thought. I hope to cover "opportunity cost of survival" in a future post.
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