Tuesday, July 21, 2015

Tapering

Tapering is a concept that means over time you lower the size of your bets. It was given this label by Dutch Boyd in a pokerclinic and on his twitch stream. The concept was not invented by him but he deserves credit for going into details. He inspired me to go deeper into this concept.

The reason this is effective is because as the blinds get higher, the % of risk you are taking declines. In order to do well in tournaments, you want to extract a skill edge and accumulate chips without risking your tournament life if possible. Also, opponents become more willing to fold rather than defend their blind because even if they are getting the pot odds to call, they don't have as good as implied odds, and it simply risks a lot of chip volatility for just a small edge that it may be better to give it up.

Whether or not that is true shouldn't effect the decision to raise; As long as our opponents believe it's correct to fold or feel they should fold, raising smaller becomes more correct preflop

Of course spots will come up that you will learn to accept because otherwise you will be more likely to become short stacked and forced to move all in anyways, so at some point it's worth doubling up to prolong your desperation later and finish deeper.

With a smaller raise size you are getting better odds on steal attempts and can open with more hands and defend more often if you have the stack to.

I'm always looking for new wrinkles in my game so what I actually want to do is consider tapering POSTFLOP as well.

Ed Miller on continuation bets gave me food for thought about not Cbetting and checking behind based more on flop and entire hand range strength vs that flop, and less about your specific hand so he deserves credit for some of the nuances about what situations are less necessary to Cbet.

So I'm experimenting with introducing an entire tournament plan.

1)Start out with 4.5x preflop. Since you are risking 4.5 to get 1.5, you need to have a better hand or optimal opponents can exploit you. Assume opponents defend to force bluffs to break even, plus some bluffs, plus some of those defending hands are calls. So opponents collectively should have a 75% chance that their hand is best. Determine what hands have value over this range and multiply that hand range by 4 and this is your opening range.
2)Since opponents are not optimal early they will probably call more often which means you want to extract more value postflop but also that you will have to be more picky. Rather than be too picky about what hands you Cbet with, look more about position and flop texture with some slight adjustments to not bet a few middle strength hands and draws with showdown value that may get action from worse hands only after checking and to give up on the worst of hands with no pair, no draw, no backdoor draw.
3)IN position: bet all flops except check most paired flops, check all Ace high flops and King high flops check all but the wettest Queen high flops and check only the driest of Jack high flops. Only check dry ten high flops when you have two overcards as well as sets, twopair and some overpair and some backdoor draws.
Out of position: Out of position you actually want to bet the flops above that you check plus all jack and ten high flops and the wettest 9 high flops.
4)Bet sizing - Since out of position you will be firing two bullets more often when you bet, you want to bet smaller amounts, but it still needs to be large enough. Over half the pot is fine early on. In position you will be betting pot sized bets.

Later on this will invert. Early on you are going against weaker players so you probably want to build up a big pot since you are starting with a better hand. Later on you won't have deep enough stacks to fire multiple bullets out of position and you will be betting more often in position and it won't require as much to take it down and you will be tending to bet with more hands and want a better price on bluffs.


1) 4.5 BB opening hand range (adjusted for implied odds) no antes
8    99+,AK+,ATs+KQs+,QJs,JTs,T9s,98s,87s,76s,65s
7    88+,AK+,A9s+KJs+,QJs+,JTs,T9s,98s,87s,76s,65s,54s
6    66+,AQ+,A9s+KJs+,QJs+,JTs,T9s,98s,87s,76s,65s,54s
5    44+,AQ+,A9s+,KTs+,QJs+,JTs,T9s,98s,87s,76s,65s,54s
4    22+,AJ+,A8s+,K9s+,Q9s+,J9s,T9s,98s,87s,76s,65s,54s
3    22+,AJ+,A2s+,KQ+,K8s+,Q8s+,J8s+,T7s+,97s,87s,76s,65s,54s
2    22+,AT+,A2s+,KQ,QJ,JT,T9,98,87,76,65,K9s+,Q8s+,J8s+,T8s+,97s+,86s+,76s,65s,54s
1 22+,A2+,K5+,Q8+,J8+,T7+,96+,86+,75+,64+,54,A2s+,K2s+,Q2s,J7s,T6s+,95s+,85s+,74s+,63s+,53s+,43s

3bet 4x raiser (not properly adjusted to mix in calls and bluffs)
8) 3.53% TT+,AK
7) 4.03% 99+,AK
6) 4.68% 99+,AQ+
5) 5.59% 99+,AQ+,AJs+,KQs
4) 6.94% 99+,AQ+, ATs+,KTs+,QJs
3) 9.14% 77+,AJ+ATs+,KTs+,QTs+,JTs
2) 13.40% 44+,AJ+,KQ,A8s+,K9s+,Q9s+,J9s+,T9s
1) 25% 22+,A8+,KT+,QT+,JT+,A2s+,K7s+,Q9s+,J9s+,T8s+,98s,87s,76s


3xBB no antes opening range (adjusted for implied odds) no antes
8: JJ+,AK || 77-TT A9s+,KTs+,QTs+,[67s-KQs]
7: JJ+,AK,Aqs || 55-TT, A9s+,KTs+,QTs+,[67s-KQs]
6: JJ+,AQ+ || 33-TT, A4s+,KTs+,QTs+,[45s-KQs]
5: TT+,AQ+ || 22+,A4s+,K9s+,Q9s, [45s-KQs]
4: 99+,AQ+,AJs,KQs || 22-88, A2s+,K9s+,Q9s+, [64s-J9s]+,45s
3: 88+,AJ+,ATs,KQs || 22-77, KQ, A2s+,K9s+,Q9s+, [64s-J9s]+,45s
2: 66+,AT+,KQ,A9s,KJs+ || 22-77, [78-QJ], A2s+,K2s+,Q8s+, [53s-J9s]+
1: 44+,A7+,KT+,QJ,A2s+,K9s+,QTs+ || 22,33,A2-A6,k2-K9,Q8-QT,J7+,T7+,97+,[45o-87o], Q2s+,J7s+,T6s+,95s+,85s+,74s+,64s+,54s,43s

3bet 3x raiser (not properly adjusted to mix in calls and bluffs)
8 8.3% 88+, AJ+,ATs+,KTs+,QJs
7 9.43% 88+, AJ+, KQ, A9s+,KTs+,QJs,JTs
6 10.91% 66+, AJ+, KQ, A9s+,KTs+,QTs+,JTs,T9s
5 12.95% 66+, AJ+, KQ, A9s+,K9s+,Q9s+,J9s+,T8s+,98s,87s,76s,65s,54s
4 15.91% 66+, AJ+, KQ,QJ,JT, A8s+,KTs+,QTs+,J9s+,T8s+,97s+,87s,76s,65s,54s
3 20.63% 55+, AT+,KT+,QT+,JT,A7s+,KTs+,Q9s+,J9s+,T8s+,97s+,87s,76s,65s,54s
2 29.29% 22+, A9+,KT+,QT+,JT,T9,98,87,76,65,A2s+,K9s+,Q9s+,J9s+,T8s+,97s+,87s,76s,65s,54s
1 50% 22+,A2+,K4+, Q8+, J9+,T8+,98,A2s+,K2s+,Q2s+,J5s+,T6s+,96s+,85s+,75s,64s+,54s

Giving you a good idea of how to balance your ranges with help from Ed Miller in the book "the course" I came up with a few tweaks and the following ranges.

When facing tight raise
If you have QQ: if left card is black, 3bet, if left card is red, flat.
Otherwise:
3bet: AA,KK,[QQ],A5s,{T8s}
flat: 22-JJ,[QQ],AK,Ats+,Kts+,Qts+,{JTs,T9s,98s,87s,76s}
{only flat the suited connectors in position and only raise T8s in position}
When facing loose raise
3bet: QQ+,AK,A2s-A5s,{T9s,87s}
flat: 22-JJ,AQ,A6s+,KTs+,QTs+,JTs,{98s,76s}
{in position only, otherwise fold}

4bets:
When Facing a 3bet:
4bet:QQ+,AK+,AQs, A5s,T8s
flat:88-TT,[QQ],AQ,AJs,{AJo,ATs,KQs}

2.25xBB
Antes:
8: TT+,AQ+,Ajs | 22-88, A9s+,[45s-KQs]
7: TT+,AJ+,Ats+,KQs | 22-88, {A9s-J9s}+,[45s-KQs]
6: 88+,AJ+,Ats+,KQs | 22-88, A4s+,{A9s-J9s}+,[45s-KQs]
5: 77+,AT+,KQ,A7s+,KTs+ | 22+,[KQo-T9o],A2s+,K9s+,Q9s+,[64s-J9s]+,54s
4: 77+,A8+,KT+,A2s+,K9s+,QTs |22+,[45o-KQo],K7s+,Q8s+,J8s+,[53s-J9s]+,43s
3: 66+,A8+,KT+,A2s+,K9s+,QTs+ |22+,[45o-KQo],K4s+,Q8s+,J8s+,[53s-J9s]+,43s
2: 22+,A2+,k2+,Q2+,J5+,T7+,97+,86+,Q2s+,J2s+,T2s+,94s+,84s+,74s+,64s+,54s,43s
1: A2+,K2+,Q2+,J2+,T5+,96+,85+,75+,64+,54,T2s+,93s+,84s+,74s+,63s+,53s+,43s


3bet (not properly adjusted to mix in calls and bluffs)
8 8.3% 88+, AJ+,ATs+,KTs+,QJs
7 9.43% 88+, AJ+, KQ, A9s+,KTs+,QJs,JTs
6 10.91% 66+, AJ+, KQ, A9s+,KTs+,QTs+,JTs,T9s
5 12.95% 66+, AJ+, KQ, A9s+,K9s+,Q9s+,J9s+,T8s+,98s,87s,76s,65s,54s
4 15.91% 66+, AJ+, KQ,QJ,JT, A8s+,KTs+,QTs+,J9s+,T8s+,97s+,87s,76s,65s,54s
3 20.63% 55+, AT+,KT+,QT+,JT,A7s+,KTs+,Q9s+,J9s+,T8s+,97s+,87s,76s,65s,54s
2 29.29% 22+, A9+,KT+,QT+,JT,T9,98,87,76,65,A2s+,K9s+,Q9s+,J9s+,T8s+,97s+,87s,76s,65s,54s
1 50% 22+,A2+,K4+, Q8+, J9+,T8+,98,A2s+,K2s+,Q2s+,J5s+,T6s+,96s+,85s+,75s,64s+,54s

3bet or flat:
when facing tight raise
3bet: QQ+,AK,A2s-A5s,T9s,87s
flat: 22-JJ,AQ,A6s+,K9s+,Q9s+,J9s+,T8s+,98s,76s,65s,54s
when facing loose raise
3bet: TT+,AQ,AJs,A2s-A5s,T9s,98s,87s,76s,65s,54s
flat: 22-TT,AJ,KT+,QT+,JT,T9,98,87,76,65,54,A6s+,K9s+,Q9s+,J8s+,T8s,97s,86+,75s

When Facing a 3bet you might construct some balance like this as the "default" range with no information.
4bet:QQ-KK,[AA] AK+,AQs, A5s,T8s
flat:88-TT,[AA] AJ-AQ,ATs,KQs.
(or looser, but obviously this is more opponent dependent)

2x only needs to succeed 47% of the time. So opponents should raise to force you to break even so they need to raise 53% of the time collectively.
8 9%
7 10.2%
6 11.8%
5 14%
4 17.2%
3 22.23%
2 31.4%
1 53%

The shortcut is to increase this range by 50% since half the hands have value and then you want to open raise 3 times as often as you can bet for value.
8    13.50%
7    15.30%
6    17.70%
5    21.00%
4    25.80%
3    33.35%
2    47.10%
1    79.50%




When you get under 40BBs but especially under 30BBs, you do lose some utility in dealing with 3bets preflop and your "tapered" Cbets becomes less than half the pot which at some point may cause it to lose some effectiveness even though it doesn't need to succeed as often when it is smaller. The main reason being that opponents are more likely to see a showdown because they will widen their range some, even if they don't widen it "enough". Once they start seeing the hands that you show down you are much more likely to see opponents widen their range even more. Alternatively you must create suboptimal shoving stacks on the river, or potentially shove earlier than the river, or check more often. None of these options is ideal, but it's just the nature of most blind structures.

Your opponents can now open shove so you have to have a hand often enough to call off. If not, you are exploitable. This means that in order to prevent being exploitable you'd be forced to tighten your opening range up slightly or call off in situations even when the bubble factors likely will suggest otherwise, or just be exploitable until opponents prove that they are capable of exploiting. Neither option is particularly appealing, so while limping in also isn't particularly "optimal" either, you at least can do so in a defensible way, and use the advantage of being the last one in. Either you can "exploit the exploiters" who try to "punish the limpers" as well as those trapped behind by limp raise shoving more frequently,or at least frequently enough as part of your range to not be exploitable, or you can limp in with drawing hands and good multiway hands vs loose/weak-passive opponents. This allows you to use blocking bets to control the size of the bet in multiway action to both play more hands than you normally would and also reduce the volatility of your chip stack in exchange for possibly giving up some value in your ability to bluff and steal through bets and Cbets.

I can't say whether it's better to give up the value of raising in exchange for the utility of not allowing opponent a more optimal shoving opportunity. I can't say if gaining back the utility of a larger Cbet closer to half the pot or over half the pot is worth the lost value in limping. I can't say if the ability to limp-raise shove a more optimal stack or add more multiway playable hands and gain the implied odds is worth what you give up by limping.

I won't even argue against utility theory that getting your money in worse than ICM suggests order to make up for it due to additional utility gained due to a larger stack, more fear/fold equity, and the utility to play more streets at more optimal bet sizes. Any decision on "which is better" is speculative until I see someone prove otherwise. But you need to speculate based upon your own awareness of the opponents and your personal skillsets and observations as well as the stage in the tournament.

You should be aware of this and recognize that this stage is coming and be prepared to deal with it in whatever way works best for you given the stage in the tournament. Some might limp to preserve consistent betting throughout. Others might check more, others may give up after the Cbet and double barrel less. Others might get it all in on the turn more often for value, and some may even open shove far more liberally earlier than they're "supposed to", hoping to gain back what they're giving up in EV in the future due to larger bubble factors of opponents who face them and utility of Cbets and more streets in 3bet pots and such often enough to make up for it.

Just because you can play all streets for value, doesn't mean you need to bet every street. Particularly with marginal hands and shorter stacks preserving your tournament life and ability to accumulate chips at low variance is more important than maximizing value. Early in tournaments against looser players you are trying to get called and maximize value. Later on you are trying to get folds and maximize bluffing equity.

You also probably want to taper your 3bet sizes as well, But when there is a 3bet and you see a flop without a 4bet you probably will be getting your money in after 2 streets of betting instead of 3 so you can set up a shove to be around the pot by strategic 3bet sizes.


If you get too much below 30BBs a 3bet probably is all in (depending on the raiser's initial raise size and if the antes are involved), or at least is made with intention of calling an all in and probably getting it all in on the flop. At exactly 30BB, if your 3bet is less than 7.5BBs total you aren't necessarily committed if you have a small percentage of hands in the 3bet/fold to 4bet range.

I don't really see much value in minraising except to get opponent committed to calling all in but I'd rather just shove and try to take down the equity even if I had a real hand. Alternatively you could 3bet normal, be willing to call any all in and if opponent calls just have a shove or fold range with a high probability of shoving the flop.  Probably just calling or shoving is best below 30 BBs though and keep in mind calling is putting in more than 10% of your stack so you don't have very good implied odds. You shouldn't call unless you're ahead, and if you're ahead you're probably better shoving.

For this reason I don't know that raising preflop under 30BBs has all that much value unless opponents are folding too often and not shoving often enough and also calling sometimes when they should shove. But again, whether you bet, call, or shove or taper, any decision when you are under 30BBs gives up something. Getting above 30 may not gain it back either if most opponents are short stacked. It is probably just the nature of tournaments

Tapering The Flop
When you taper your bets on the flop you have to understand that larger bets are offering a worse price on your bluff attempts. Early on you are generally betting larger to isolate the fish. Even though your opponents are offered a worse price and should call less, the tendency for opponents to not properly adjust to bet size means that you should be more selective about how frequently you bet. You also don't need to bet as much to make as much. With the possibility of raises it won't take much to get full value out of your good hands anyways.

In position: Most flops that you are recommended to check, you can also call when faced with a bet rather than raise when you have a strong enough hand to continue when faced with a bet.

4.5xBB stage - Check Q high flops, King high flops and A high flops and paired flops. Check some dry Jack high flops. With few exception you will ALWAYS check these flops. You also will mix in some checks on dry Ten high flops provided you either have 2 overcards or a backdoor draw or flop an unbeatable nut hand like top set with no possible draws or a straight with outs to a flush redraw to beat a split. Half the time you will check overpairs, half the time you will bet. (left card red, bet, left card black, check) You will bet pure bluffs, medium strength hands.

3.5xBB stage - check ace high and king high flops and paired flops. Check only the dry Queen high flops. Treat some Jack high flops mostly like you treated Ten high flops in the 4.5x stage. Also check most of the worst hands in your range given the flop. For example, if you play any suited connectors, any pocket pair and AJ+,KQ,QJ on a QJ9 flop most suited connectors are probably bad enough to check and give up on. You can check the worst of your medium strengthed hands for stack preservation. If you have J8s or QT or T9 on JT4 board normally you'd bet, but you are almost never going to get a worse hand to fold, and a better hand will certainly call. This is a clear spot to check as NOW opponent on the turn may begin to think his T8 or 45 is good, and he may make the mistake of calling 98 after bricking thinking his 9s and 8s are live, plus he may plan on bluffing certain river cards because he thinks you are weaker. He may now call with ace high,22-99, A4, and any card he may pair on the turn. He may also try to bluff hands that he was willing to give up on. There's no value in betting those hands other than taking the equity that is in the pot. Remember, in this stage usually a check means weakness so a smart opponent will give you value after a check.

3xBB - Check all ace high flops, and some King high flops and paired flops with a single face card or paired face cards. In terms of hands in your range you check, occasionally check draws and medium strength hands only. You can semibluff if opponent shows weakness two streets in a row and still build up a big enough pot for the river if you hit either the turn or the river. Your weakest hands due to the decreased size can now be bluffed rather than given up on, and many times you will bet your longshot (4out draws) and monster (12+out draws).

2.25 or 2.5x stage - check ace high flops sometimes, check paired flops with one or two Ace or Kings in them. Occasionally check full house or better and usually check top pair, medium or weak kicker on dry board type of hands. You aren't necessarily doing this to reduce to 2 streets of value, but instead to get 2 streets of value more often and preserve your tournament life in the instance that you are up against top pair better kicker or better, while also getting 1 street of value more often as well by inducing bluffs and weak calls.

2xBB stage - Check paired flops with at least one ace or king in them, check dry ace flops with an additional face card. Rarely pass up an opportunity to bet since you are betting small and are getting a much better price on your bluffs. Since you have a wider range of hands preflop you must not slow play your hands or even your draws or you will be too predictable.

Short Stack Limp In or desperate stages where all ins will occur before the river - Shove 4out draws, any pair except for pocket pair lower than the 2nd highest flop card without at least a straight draw as well. Check double backdoor draws and strength and 6+out draws. Usually shove 8+ outs on turn if a shove on the turn card tells a believable story, and there are not river bluff cards to represent (such as more obvious draws or double flush draw boards when you picked up the back door flush draw). Also shove strength on turn and made draws. Always shove 14 outs on turn.

Checking draw heavy boards - When you are in position usually you shouldn't check draw heavy boards but if you are facing a good, tricky opponent or an unknown you may want to check the flop anyways when your hand has some showdown value to avoid complicating things

Tapering Out Of Position On The Flop:
Strong flops out of position are the opposite of strong hands in position. If a lot can change with a single card, it favors being in position typically. It's hard for position players to know where they're at and they have no idea what cards are scary for you. Firing two barrels or floating the flop out of position then checking and if they check betting the river makes it pretty easy to play since there's very few cards that opponent can probably hit after you call the flop that can make opponent feel confident about his hand if he doesn't have an ace.

4.5BB stage - Cbet paired flops and A high and King high flops only. Also some dry Q high flops when you have AK or paired your queens. Otherwise only bet or check raise your good hands.
3.5xBB stage - CBet paired flops, A high, King high, Queen high flops and two overcards on dry Jack high flops
3xBB stage - CBet paired flops, flops where J to A is the high card. Cbet T high flops when you have any piece of it or two overcards of any kind or middle pair. Also bet big draws and big hands and the worst of hands that have no shot at winning otherwise.
2.25-2.5x stage - CBet T high flops or higher. Cbet some dry 9 high flops.
2x stage - Cbet all flops where the lowest card is 7 or higher.
Multiway - Generally don't Cbet multiway but later on it's fine if you get 2 callers or less or 3 callers and are in position.

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