Tuesday, July 14, 2015

Nutball Tournament System Preflop 2

The start of the nutball tournament system looked at the optimal preflop poker, and used roughly the same frequency of hands but adjusted the specific hands for implied odds, preferring hands that had drawing potential over hands that might run into kicker troubles even if these hands may not necessarily have the right showdown equity when the hands are simply checked to the river.

The concept is to be aggressive and either semibluff more or get paid off enough when you hit with these hands while avoiding kicker troubles to make up for the slight drawback of hands not being strong enough to have the equity when called preflop.

This is still somewhat approximate to "equilibrium" or GTO play preflop where we gain to the degree which opponents make a mistake, but we are not directly speculating or observing opponent's tendency and trying to capitalize off of them but instead recognizing the inherent benefit in real postflop poker that drawing hands have over weak kicker hands.

Not having to make a big call on the river with a top pair weak kicker hand is of large benefit. Sometimes you may hit your draw and bet it for value and sometimes you will represent your range that the board has hit and bluff the river.

Also of benefit is being able to profitably semibluff overbets in certain conditions to put opponent's all in by keeping in mind the semibluff chart shown below. The % to win is the probability you win when called and based on the multiple of pot you are giving a percentage chance you need all remaining opponents to fold in order to show a profit.

Due to the non-linearity of chips, you probably want to raise the standards to have opponents fold more often than this in tournaments.

This post will look at the conditions necessary to speculate profitably on when opponents left to act are too tight in the ante stages in order to loosen up your hand ranges even more.

If your raise range of any two vs calling range of opponents has zero equity when opponents don't fold, or opponents make a monster overbet shove when they do play, you can raise with any two if remaining players defend this often assuming you bet the amount in the pot:

8 players left: All opponents each must play 8.2996% of hands or less to a raise for steal to be profitable.
7: 9.43% of hands or less.
6: 10.91% of hands or less.
5: 12.95% of hands or less.
4: 15.91% of hands or less.
3: 20.63% of hands or less.
Button: Steal profitable if blinds play 29.29% of all hands or less.
Small blind: Steal profitable if opponent plays 50% of all hands or less.
Big blind: Opponent must fold 50% of the hands he completes with or more.

Fortunately, when opponent calls you still have two cards with potential, so you still have some equity when called. Assuming bets break even after the flop or it checks to the river, as long as you have more than 0% equity you can steal if opponent's defend more often.

So based upon the understanding that if it's automatically checked to the river and you are 20% to win when called (and all bets on and after flop break even), the preflop steal must succeed 35.56% of the time or more to profit.

Raise with any hand that has 20% equity if remaining opponents call/defend this often or less:

8    12.13% (remaining opponents on average play 22+,AJ+,ATs,KQ,KTs+,QJs or less)
7    13.73% (opponents play 22+,AT+,A9s,KQ,KTs+,QJs,JTs,T9s or less)
6    15.83%
5    18.70%
4    22.78%
3    29.16%
2    40.37%
1    64.44%

If you have 30% equity when called (and all bets on and after flop break even), steal must succeed only 3.333% of the time.

Raise with hand that has 30% equity if remaining opponents call this often or less:
Hand % of opponents needed given X players remaining:

8    34.64%
7    38.49%
6    43.27%
5    49.35%
4    57.27%
3    67.82%
2    81.74%
1    96.67%

If you have 33% equity and up you can raise with any two assuming you won't get raised and you won't get called by multiple opponents.

It shouldn't be that uncommon for a hand vs opponent's defending range to be around 30% equity if you take away some of the worst starting hands.

Of course, since opponents sometimes will raise you rather than call, you might argue that your steals need to succeed more often. But that isn't necessarily the case and here's why.... If opponent raises 6.25 big blinds, you only give up 2.5 every now and then but as long as you could come up with a hand to 4bet and take it down 18% of the time you could still break even when you are reraised. You might not quite that often if you are opening with a wide range, but it shouldn't be that far off. Since you will also often get the pot odds to call and implied odds to lose less than 2.5, you can 4bet even less often and be okay, but that assumes effective stacks aren't large enough to 5bet, or else the opponent can turn that on it's head and shove to gain back his edge. You also may be able to still continue in the hand often enough in some cases to profit or break even with a postflop advantage.

If you are stealing and finding yourself able to accumulate chips gradually this way, you will likely need to cbet and then just be done with the hand a large percentage of the time when your opponent calls your cbet. If you do this, you will have low varience chip accumulation and you can pass up any all ins and theoretically still win the tournament. Mix that in with raising close to the optimal hand range with the antes which is actually fairly liberally, plus frequent cbetting while also knowing when to scale back and tighten up and you stand an excellent chance of accumulating a lot of chips at lower risk.

In theory if you can win an average of 3 times what's in the pot at low variance per rotation, you can win a tournament without ever being all in and you can maintain your big blinds in most structures.

In reality, you probably won't have quite that big of an edge and even if you do there will be enough variance where you will get short enough that you will have to be all in a few times. Nevertheless, if you can pass up race situations and accumulate chips for quite a long time and secure survival to stages in the tournament where steals are worth more, you should.

It's actually mathematically correct to pass up race situations for your entire stack even ignoring opportunity costs because opponents bennefit from every confrontation and you can literally make money by folding as a result of other people taking race situations when you are close enough to the bubble. This is much more prominent in THEORY the closer you get to the bubble. There are a lot of really odd things that happens as a result of this theory which requires a counter adjustment in my opinion that we will get to later.

In practice those with a skill edge able to accumulate chips actually have far more incentive to avoid the flips EARLY because of the opportunity cost to be able to build up a lot of chips over the course of the tournament.

On the opposite side of the spectrum is "utility" which states that the more chips you have, the greater edge you tend to have and the longer you can prolong variance that risks your tournament life. Because opponents are SUPPOSED to (in theory) avoid players with larger stacks, that creates an inherent advantage for having more chips that should according to this theory gain more respect as the opponents are supposed to avoid coinflips with those that can knock them out or significantly reduce their stack. Opponents should be less likely to bluff you knowing you can knock them out, less likely to try to force a race onto you, and you get the implied odds to see more flops, float more flops, double barrel without a huge hit if it fails and as a result, you can gain more chips per rotation.

But not so fast, the small stack still has the ability to be all in and double called with no individual fold equity while the others potentially can bet out a hand to force drawing hands that would have hit out. Or if you shove and someone calls and opponent tries to isolate, you might be tripling up and then some with only a single opponent to fade. Your equity goes up slightly as the short stack in some situations as you have the advantage of the last one in to shove. You certainly can make all in semibluffs on the flop for a slight overbet where your opponents cannot except vs shorter stacks like yourself when there are no other opponents in the hand. Additionally, opponents aren't worried about busting out in the earlier stages so much. It's when they invested some time into the tournament where this is prominent. Also if everyone else is shorter and moving all in preflop, there's not as much of an edge in having more chips as you might think, particularly when opponents don't understand or utilize ICM and thus don't respect your chip stack.

Even if you will have a pretty good probability of eventually having to take a coinflip, you still should often pass because you can get into plenty of coinflips later after you accumulate a lot more chips. THEN the utility can come into place later on when opponents are also scared of money bubble and final table bubble.

Plus there are plenty of unexploitable spots where you can shove and keep up with the blinds and have a low probability of being knocked out since opponents have to call AND win. They may call with a worse hand if they call too loosely or not call often enough if they call too tightly such that your odds of surviving an all in shove may be better than 50% even if when you do get called, you get called with the worst of it. Even multiple shoves all in will often give you a better chance of making money, and this is even more true when the blinds have risen.

PLUS if you establish a really tight image, and win a double up with a monster hand, you stand a greater chance of not getting called in the future when the blinds are perhap twice as large as they might be now which leads to a lot more profit as a result of that image following showing them a hand.

So tournaments are about chip accumulation and saying "no thanks" when you have a small edge especially early for all your chips or on the money bubble. There is a difference between a small edge and a slight favorite in a coinflip. If your pot odds are extremely large, you may have an edge while only being 40% to win. Take a straightflush draw where you actually move all in. Opponents will fold often enough to provide you with pretty good equity and you probably get the pot odds to call an all in for 2x pot or less, so shoving for that amount or less is a pretty big edge.

You can see Dutch Boyd put this concept to work in his twitch stream.

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