Scientific Tapering

Many players who have played tons of tournaments noticed their results improve by tapering. What that means is as the tournament goes deeper on bet sizes that may have started at anywhere from 3 to 6 big blinds decline to a minraise gradually over time. As the average stack tends to decline in terms of big blinds while increasing in absolute terms, risking larger and larger percentage wise

I don't think most of them know why this is good other than they are risking less to acheive the same results while players become increasingly tight to preserve their survival.

However, there's a very good reason we should want to taper more so by our stack sizes and why opponents should be less and less willing to call based upon their own stack sizes as bets increase proportional to their stack size.

Tournaments are about long term survival. People can talk all they want about expected value, but the longer the tournament goes on, the more even the best tournament players will get eliminated if they don't manage their risk.

You actually gain more by risking less at least in terms of long term growth rate. Not only that, but you gain a better growth rate to volatility ratio the less you risk. Some amount of volatility is unavoiadable so I'm not going to advise folding aces preflop to an all in, but if you had a choice of risking 65% of your chips on aces or 100% you'd be better off risking 65%. If you are a 60% favorite you may be better off risking something like 25%. Perhaps even risking less than this is better because there isn't a huge reason to try to squeeze out a slightly larger growth rate in exchange for volatility when you cannot safely move down in stakes or reduce the risk after a loss and the rising blinds virtually ensures that volatility will require an increased risk of elimination.

The question is, is it better to triple your stack with minimal volatility and be forced to go all in some point after that, or is it better to quadruple it some percentage of the time at risk of being forced to go all in much earlier and possibly bust a higher percentage of the time... and if you quintuple it successfully you have better hands to choose from and more chips when you ultimately do risk it all and successfully win.

I'm not totally sure what the answer is. From my own experience and observations and math I do believe that there is tremendous value in growing your chips in absolute terms for a long time. Although I'm uncertain at which point and under what exact conditions you should be willing to risk it all, I can tell you that passing up edges for a very big chance of applying your skill in small pots and resulting in a very low volatility and high probability growth of chips is useful.

I also believe knowing how to continue to grow chips even as your stack size goes smaller is very important. For me when I get around 20 big blinds I no longer am effectively still able to accumulate chips at the same rate and the fewer chips I have below 20, the lower my rate goes. And then at some point as an extreme short stack my ability to accumulate chips actually goes up because at some point my opponents are a lever to scare away other opponents and I can triple up or quadruple up while being headsup to see 5 cards while my other opponents may only see their preflop holdings or a flop before being chased away. Additionally, as a short stack pushing with far more hands becomes profitable. Folding may give up missed opportunity to have positive EV, however folding has an increased chance of survival and increased chance of being dealt a situation that is even more EV due to stack sizes. I will get called by multiple players with a premium hand and that can propel me from 4 big blinds to say 15 really quickly without risking too great of a chance of survival.

Well I'm not sure it's a good move to put yourself in a situation where you are chronically short stacked even knowing eventually everyone will be relatively short stacked, so it's hard for me to say if it's better to be liberally willing to risk an all in while you still have hchips relative to the blinds so that you can gain utility in being able to accumulate chips instead of dipping below 20 big blinds and slowly and steadily having to resort to increased desperation, or if it's better to play the shovecharts, or if it's better to play super nitty.

But I do know that it does pay to find ways to continue to accumulate chips and give yourself more ability to withstand or limit chip volatility as the tournament progresses and that will hopefully allow you to maintain a comfortable stack without additional risk.

That being said, here are a few decisions determined by the kelly criterion calculator. Note that betting 2 times the kelly or half of the listed amounts when I suggest tapering is not the end of rht e world if doing so increases EV at the expense of  but betting more than twice that

 Under 70 big blinds you should reduce to minbet with under half pot
 35-60BBs - check for pot control... 2 streets of value plus .40 pot bets when you are 60% to win
[down to 50 big blinds 1/3rd pot bet can get 3 streets of value.]
[down to 25 big blinds 1/3rd pot 2 streets of value is still 1 kelly.]
[down to 11.96 big blinds we can minbet plus a 1/3rd pot once (about a min bet again)]

This is all assuming calls and a 60% chance of winning. Reality will have different plans, particularly when we aim for only one single bet.

Obviously there is little we can do to protect our hands against raises aside from risking more than the kelly and risking all of our chips potentially. You can't avoid the risk and you should be aware of how having to reduce bet size reduces your win rate in BB/100.

The antes plus escalating big blinds actually neutralizes the short stack somewhat. In other words, no matter how short stacked you get, you're never that many double ups pplus blinds and antes away from being back in it. Take having a single ante chip left when the antes are 1/3rd the small blind. If you win the hand, you go up to 9 ante chips which is 3 small blinds or 1.5 big blinds. If you go all in on the next hand, you get 1.5 small blinds in antes plus 1.5 by the small and big blind, plus at a minimum someone matches your 1.5 but let's say there is a raise and a 3bet and you call the 3bet and at some point everyone folds. 1.5+1.5+1.5+1.5+1.5. Now you have 7.5 big blinds
2 double ups from $25 in 75/150 with 25 antes and you have went from 25 to 1125.
Now blinds go up to 100/200 $25 ante. If you jam and everyone folds you pick up 500 to 1625. 2 double ups plus a jam from 25 to 1625.2. One more double up plus blinds and antes to 3750.4 and you have 18.752 big blinds.
If you say had AA with one preflop caller twice and jammed with AJ and then doubled up with KK you might be something like .8*.8*.7=44.8% to survive. A little less because no one called your jam with AJ. But a 44.8% chance of going from a single ante or 1/3rd of a big blind to 18 big blinds? I'm being a little generous, but it goes to show the point that being patient is more valuable than you think in an age when everyone else is shoving at equilibrium and everyone else is taking any plus EV spot not considering how much more plus EV it is to be so shortstacked loose tables can't properly defend from giving you a really good chance of getting paid off and then they're playing for a side pot.

This is not even to suggest passing up +EV spots is the right move but IF you can reliably gain chips even as the blinds rise, even going card dead for a very long extended period of time at a wildly loose table shouldn't force you to do something out of desperation necessarily. The edge in reliably being able to multiply your stack to later stages of the tournament is worth a lot

The probability of getting dealt JJ+ or AK at least once in X number of hands is about 1-(.967^X). So if you have 30 hands left, you have about a 63.5% chance of getting it. I would play slightly more hands and you will if you constantly adjust based upon your hands left but you may find more favorable spots to attempt a steal such as having AQ on the button when it folds to you or AJs or TT. Those hands are outside of the range I listed, but the spot is better since you will be jamming and since it folds to you indicating no one prior to you had a hand and thus you only have to be better than 2 opponents, not the normal full 9.

When you are deep in the money and especially near the final table and folding up a few spots counts and you ultimately only really need to survive one or maybe two all ins to fold your way to say 5th, I personally want to be very selective rather than pushing earlier and hoping I get enough chips to give me the breathing room to push with a few more and eventually get caught and have to win as an underdog.

Minraise and willing to fold is acceptable if your odds of winning are great enough down to like 10 big blinds and really 5 at risk of insane volatility.  But I'd only do that in a spot where I've waited 30 hands without playing and maybe I'm in early or mid position with ace rag. I have a blocker to ace combinations and I plan to fold and my opponents probably will have an ace or a big pair. If it fails at say 7 big blinds I may have to call off my tournament life from the small blind or maybe I'll get a walk or maybe I'll check see a flop and be able to get my money in good or maybe I will live to see another rotation, but I want a good chance of buying an extra rotation as 10 hands is a big deal. In 10 hands I have a 28.5% chance of picking up JJ+ or AK and a 43.5% chance of TT+,AJs+,AQo+

People who think this is a bad idea say something like, but then the blinds will go up. I want them to go up right before I get a hand, especially if the antes go up. That means I get a much better payout on the money, especially if you measuredd by big blinds at the prior level. I'd rather them go up right before I get the hand than right after. I also want them to go up right after I paid the big blind as that is 9 hands at increased rate of earnings if I get a hand


I do recognize that there is a really long shot opportunity to win from being very short stacked, but if I survive 80% of the time to very deep in the tournament and then get it all in with aces or at least a premium hand where I'm 70% vs the calling range Then I've got a really, really good chance to make it very, very deep and with a little luck I can still win a very high percentage of the time despite having say a field of 1,000 players.

But perhaps I'm better off getting my money in with the worst of it early on enough to parlay that into a big stack but not too early. I think to win tournaments without large risk of elimination you have to have at least some stage during the ante phases where you are able to steal a lot of pots repeatedly. So taking a risk at 20 big blinds in order to double up may be worth jamming even lighter than the push/fold charts with the idea being that if you get lucky and win when called or get lucky and face opponents that fold too often such that they make your weak shoves profitable when it shouldn't be then you might just get ahold of a lot of chips with a reputation of not being afraid to risk it all (thus opponents are unlikely to try to steal from you too much. and you may influence them to tighten up more. so One lucky win with a negative EV strategy overall and if you can gain a huge edge afterwards and gain a lot of utility and have one shot to get chips and if so now by tapering you can

Tournament Planning 2

A more thorough way to plan tournament strategy around the blind structure is to factor in more or less your entire strategy. You may prefer to have a goal to make the final table and from there just use ICM. ICM is terrible for entire tournaments but when you have 5 big blinds and everyone is short stacked (5-10 big blinds) it's all in or fold anyways. Skill may exist but it is really limited. Skilled players might fold a bit more or recognize when jamming slightly wider or slightly less often is better based upon how opponent's are playing and how well they know ICM shoves based upon payout structure.
Say a tournament has 500 hands until 5 handed. You can determine this by the following calculation
1)Number of entrants times average chips per player (starting stack plus add on plus rebuys per person) equals total chips in play.
2)Total chips in play divided by 5 players equals average stack at that stage.
3)average stack at that stage divided by the average number of big blinds like 10 equals the rough approximate blind
That equals the rough estimate of what the big blind is with 5 players left.
Once you know at what blind level, you simply need to know an estimate of hands per blind level. Usually live play is around 30 hands per hour and online is around 100 hands per hour. In other words 30 hands per 60 minutes or 1 hand every 2 minutes( 0.5 hands per minute) live and 100 hands per 60 minutes or 1.667 hands per minute. So if there are 30 minute blind levels live it is about 15 hands per blind level. So 15 times the number of blind levels until the big blind is where you anticipate 5 handed let's say 34 times 15=510 hands per tournament of this nature.

Once you know the number of hands, you can determine how many big blinds per blind level you need to win to avoid getting too short stacked. Your skill edge may diminish under 20 big blinds OR your risk will increase. I would prefer to raise more and take more risk unless I can coast into higher payouts if skill diminishes too much the blinds will catch you and then you have to get multiple double ups just to survive and resort to multiple all ins. If you take too much risk you may end up unnecessarily getting eliminated. There is a difficult balancing act.

Let's say for example you need to steal 3 times per blind level or win about 6.5 blinds per blind level on average whether that is one hand or 10 hands to avoid all ins. You can simply determine what hand range you need to play such that you have a more than 50% chance of getting this hand range 34 times or more.34 because 510/34=15. But with each hand you play you will have to gain 6.5 big blinds. Let's be honest that may be a little high so you will want to widen your range overall or be willing to risk all your chips a time or two or three with superior hands.

Unfortunately you may find out even if you execute this plan, you will spend about half the tournament between 15-20 big blinds.

If the goal is to avoid being all in, chances are this isn't a fast enough rate of chip accumulation given the higher variance that will occur in the 15-20 big blind range and the possibility for hands not coming as regularly, or earnings not maintaining a high enough rate... plus given the action before you act, you may prefer to fold. Foretunately the math is for more than 50% chance of 34 hands OR MORE so it allows us to fold a time or two and still have a good chance of doing very well with manageably limited risk.

But we can still use this hand range as a baseline and build a strategy around it.

So what is the hand range that in 510 hands we will get 34 times or more?
77+,AQo+,ATs+,KQs

Take a situation where it folds to you in Middle position and you raise with this range... We may want to be slightly tighter in early position and looser in late position and tighter when reraising. We also will want to look for any situation that has a better or similar low risk to high reward to a middle position raise equivalent to this.

I believe this strategy becomes most flawed in the ante stages and later on as it's lower risk to fight just a little harder to preserve chips to maintain a large enough stack to avoid anything that could even cause you to approach a stack where an all in may become necessary.

So how about this.

Pre ante stages: when it folds to you
Early position: raise 88+,AKo,AQs
Middle position: 77+,AQo+,ATs+,KQs
Late position:22+,AJo+,KQo,A2s+,[45s-KQs]
When facing a raise from
Early position: raise QQ+,call JJ, bluff raise AKs
Middle position:raise JJ+,call AKo,88-TT, bluff 22-77,AJo+, KQo,X9s (any 2 suits cards with low card 9 or higher)
Late position: raise 88+,AKo,AQs. Call 44-77,AJo,AQo,ATs,AJs,KJs+. Bluff X9o+,X6s+,Q2s+,K2s+,A2s+

Bluffs only done half the time or less unless there is knowledge that opponent folds too often.

Ante stages most people don't play enough hands in my opinion. There is math to back it up. Basically you will get the pot odds to call a raise. In this model the reason we become struggling to avoid all ins is because the blinds catch up to us and the antes are costly. Going card dead late has the most severe consequences and losing a hand or having to fold has greater consequences late.

So how do we adjust to the antes?
Early position: 55+,AQo+,AJs
Middle: 22+,AJo+,KQo,A8s+,K9s+,Q9s+J9s+,T8s+,97s+,76s,65s,54s
Late: 22+,A9o+,KTo+,QJo,JTo,T9o,A2s+,K2s+,Q8s+,J7s+,T6s,96s+,85s+,75s,64s+,54s

When faced with a raise in the ante stages every single hand in the "bluff" range you could call with, but I will say bluff with that range half the time and call the other half in the ante stages. The other details don't change because opponents don't adjust to the antes enough.

In addition, you are always looking for opportunity

For everything else keep risk mitigated to under 2x the Kelly bet such as a short stack jamming.


Adapting: Not every tournament will deliver enough hands and sometimes you may lose a big enough pot to where you are running way behind expectations. As you go below expectations I like to take additional risk (but calculated). If I haven't played a hand in 2 rotations I will raise any two halfway decent cards and if the blind steal fails I will be really cautious and usually check/fold as opposed to continuing. Save the cbets for playable hands. I also might minbet all 3 streets to virtually guarentee a call. This gives up a little bit of value and increases chance of suckouts for a high probability of decent chip accumulation. When you are barely hovering above 10 big blinds or even as you dip below 20 I think minbetting is a reasonable risk and giving up some value in exchange for a high probability of getting back in control is worth an increased chance of allowing a suckout as long as you can fold when they raise and adapt as needed.
Unless there is value from folding your way up a few blind levels, dont fear the all in, we strategize around it but if you are blinding down there, you need to take some chances to get back to manageable. I will usually minraise more frequently say around 7-16 big blinds or consider jamming after a few limpers or a small raise with a wider range.