Townsend range calculations article question

[Danastasio1]

A good friend of mine from my home game emailed me this article the other week by Brian Townsend.

From Cardplayer Vol.20/No.9:

Poker in all forms is a simple math game. You have a hand and your opponents have a range of hands. You then make a decision based on their range versus your holding as to whether to call, fold, or raise. You determine this by looking at the equity, or how often you win the hand, against the size of the pot to determine your best action. In no-limit hold'em, when facing a pot-size bet on the turn, generally if you have greater than 50 percent equity in the pot, you should raise. If your equity is between 33 percent and 49 percent, and no fold equity exists, you should call. If your equity is less than 33 percent and no implied odds exist, you should fold. This is a simplistic model, but a good place to start when learning beginning range calculations.

The best players in the world have an intuition about hand ranges that comes from playing hundreds of thousands of hands. They intuitively know if they should raise, call, or fold. Although it comes naturally to some, there are exercises you can do to improve your analysis of your opponents' possible holdings. In order to be a winning player, you need to be able to determine not only your opponents' likely range of hands, but what your equity, or chance to win, is against their range. For the sake of equity calculations in this column, I have used the PokerStove software, which can be found at PokerStove.com.

Let's look at the following example to show us how an opponent's range of hands drastically affects the proper decision. You are on the button with the Ah Jh and raise three times the big blind (BB) and are called by the player in the big blind. The flop comes 10h 7h 3s. It is checked, and you bet 6.5 times the size of the big blind (the size of the pot) and are raised all in for another 45 big blinds. The decision to call or fold is rather simple if you can put your opponent on a range of hands. To begin, let's say we know that the villain is an extremely tight player and will do this only with a set.

Using PokerStove to calculate the equity, against this player we have .265 equity in the pot, or we will win the pot 26.5 percent of the time. So, our expected value, or how much we expect to win on average, of calling is: EV = [(1 - equity in the pot)x(bet to call)] + [(equity in pot)x(pot size)]. So, in this case, our EV = [(.735)x(-38.5 BB)] + [(.265)x(58 BB)] = -13 BB. So, with a tight opponent, we should fold our nut-flush draw because our expected value of calling is negative. This means that we don't have the pots odds to call his raise.

Now, instead of being up against a very tight opponent, we are up against a reasonably tight player who will do this with a much wider range, including top pair. Against this range (sets, top pair, and overpairs), we have much better equity, 46 percent. Now our expected value is: EV = [(.54)x(-38.5 BB)] + [(.46)x(58 BB)] = 6 BB. In this case, against the reasonably tight player, we gain six big blinds by calling, though a raise won't be profitable (assuming we had more money), since our equity is less than 50 percent.

In the last case, let's look at a hyperaggressive maniac. Again, using PokerStove and giving him a range of any pair, any draw, overpairs, sets, and bluffs, our equity really improves. In this case, we have 73 percent equity against his range of hands. Now, our EV = [(.27)x(-38.5 BB)] + [(.73)x(58 BB)] = 32 BB. So, a call is profitable. An interesting thing has happened in this last case. We have greater than 50 percent equity against the maniac's range, so instead of calling, we should reraise if we both have more chips left.

I used these three cases to show how equity and range calculations can be used when learning a new game to help with the thought process. This approach can be used when learning any form of poker, whether it is no-limit hold'em, pot-limit hold'em, or stud eight-or-better. Learning to accurately put players on hand ranges and apply them to equity calculations is one of the building blocks to becoming a successful high-stakes poker player.
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My question is when Townsend talks about the "interesting case" vs a hyperaggressive maniac, is he implying a standard reraise or a raise based on effective stack sizes? I realize this may seem like a simple question, but I've read a lot about playing against LAGs, and I'm seeing that there's a lot of very specific ideas on the matter.

[GittyUP]

[ QUOTE ]
Let's look at the following example to show us how an opponent's range of hands drastically affects the proper decision. You are on the button with the Ah Jh and raise three times the big blind (BB) and are called by the player in the big blind. The flop comes 10h 7h 3s. It is checked, and you bet 6.5 times the size of the big blind (the size of the pot) and are raised all in for another 45 big blinds. The decision to call or fold is rather simple if you can put your opponent on a range of hands.

[/ QUOTE ]

I think he forgot his example was a C/R all in. But if the C/R wasn't an allin and the villain was hyperaggressive then a reraise would be the right move.

EDIT: I think I misuderstood your question. If you think you have over 50% equity then a reraise obviously is the right move. In his example the villain reraised to 45BB which any reraise might as well be AI if playing for 100BB-150BB effective stacks.

Now if the villain is hyperaggressive and both of you are deep stacked this is a bit more complicated and isn't so easy. If you already decided you have over 50% equity (easier said then done) then a raise is always the correct move if you are going to showdown. This becomes complicated if your raise still leaves a decent amount behind.
Example:
Effective stacks 300BB
Say in the above example you reraise to 130BB, villain just calls.
Pot=~260BB
You have to have a plan here depending on turn card.
If blank then...(will villain donk bet?) are we checking to river? are we calling any shove?
If I hit then...most likely value bet accordingly

Deep stacked here I think I would most likely just call the 45BB even if I am sure I have over 50% equity.

[rufus]

[ QUOTE ]

Deep stacked here I think I would most likely just call the 45BB even if I am sure I have over 50% equity.

[/ QUOTE ]

It depends on situation. It's possible to have scenarios (primarily draw hands) where the all-in equity is much higher than the expected equity on the turn. Consider, for example, a draw with 17 outs. All-in gets you about 60%, but you've only got a 36% chance to hit on the turn, and if you miss a 37% chance on the river. A maniac can push you out of the pot on the turn if you just call.

Now, in the example there is equity from pairing the ace, hitting the flush, and the backdoor straight, but missing the turn is unlikely to push the equity below 50% -- but it's still better to get the money in on the flop. Stack sizes should be considered, but all-in is certainly a reasonable option here at just about any stack size, and the best choice for smaller ones.

Notably, this issue of getting pushed out is a real concern in the middle case where the showdown equity is 46% - most of which is coming from the 13 outs to hit the flush, pair the ace, or hit the back-door straight. If the villain fires the other barrel on the turn provided the board doesn't show a third heart or pair the ace, you might not even see the river, and this can bring the effective equity down to around 23% depending on stack sizes. As a consequence, this second scenario is (depending on stack sizes) a good situation to consider going all in.

[Danastasio1]

Interesting, thanks fellas. In depth replies are always appreciated.

[GittyUP]

[ QUOTE ]
It's possible to have scenarios (primarily draw hands) where the all-in equity is much higher than the expected equity on the turn. Consider, for example, a draw with 17 outs. All-in gets you about 60%, but you've only got a 36% chance to hit on the turn, and if you miss a 37% chance on the river. A maniac can push you out of the pot on the turn if you just call.


[/ QUOTE ]

This is very true but again we have to make sure we actually have +50% equity to shove 300bb deep. Also against a hyper maniac sometimes its better to let him hang himself on later streets after we actually do hit then to shove 300bbs with the possibility of being somewhere in the range of 40%-60% equity.

Also consider that fact that he is hypermaniac but not necessarily dumb. He may check raise with a weak hand but wont call a shove for 300bb with a weak hand. Only call with a legit hand like a set in which we are behind or flipping in most cases.

Again I think there can be case made for a reraise to 130bb (with intention of calling shove) in order to take back initiative and let us see a free river. I think this and calling flop raise are almost equal IMO but shoving is bad with 300bbs.

EDIT: In all examples I am talking about big drawing hands with a lot of equity rather then made hands. (OESFD or Gutshot+FD+pair etc)