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HOLDEM RISK MANAGEMENT Book 1 1
HOLD’EM RISK
MANAGEMENT
Book 1: Theory
How to manage variance
in No-Limit Hold’em
Ken Cote
© 2020
Is it too late
to re-think
common
poker math
or the
paradigms
of current
hold’em
strategies?
2 HOLDEM RISK MANAGEMENT Book 1
HOLD’EM RISK MANAGEMENT
Book 1: Theory
By Ken Cote
MCE Excerpt Edition
Copyright © 2020
All rights reserved. No part of this publication may be reproduced, or
transmitted in any form or by any means, without prior written permission of
the publisher or the author.
To request use of any part of this book in any way, or to order your own copy,
contact the author at: [email protected]
HOLDEM RISK MANAGEMENT Book 1 3
Pot Odds and MCE “Pot odds” don’t sound like a subject that belongs in an EV chapter, but since
pot odds are a decision making concept, I think they fit well here. To use pot
odds, we are simply comparing our current equity with the equity needed to
make a call. Pot odds and the pot odds equity are concepts familiar to most
poker players and have already been briefly discussed. Minimum Call Equity
(MCE) is a new value that combines the InvestEV concepts and the pot odds
equity to arrive at a profitable “minimum call equity”. Remember that the pot
odds equity is a 0EV result for the current decision, which we have already
agreed is “just not good enough” and is not profitable by itself.
“Simply calculating pot odds to measure if a call is likely profitable or not, is
like crossing the road while looking straight ahead. We won't see the
danger coming down the line (i.e. post flop playability).” 1
The author of this quote didn’t take his thought process all the way to imply an
MCE concept, but he may have had it in mind. The playability (equity
realization) portion of this is very important to understand.
Getting good odds is what allows us to play lesser hands and to play our draws.
When we have good odds, we are able to take on more risk by calling with
more speculative hands. We all choose how good our odds need to be in order
for us to make a bet or call a bet. This is the “skill” element that is involved in
poker. If we don’t like our odds, we simply fold before committing any chips
and wait for better odds. The subtle thing about chasing the odds in poker is
that we may have to do it multiple times in a single hand. If we choose to
chase the odds on the flop, we may have to chase again on the turn and again
on the river.
MCE is taking the break-even discussion one step further, to arrive at a
profitable line, rather than the pot odds equity which stops at a 0EV play. By
shifting our strategy to utilizing the MCE number, we can now address the
entire hand and its profitability. Here are the two formulas together:
POE = ourcall / ( pot + bet + calls + ourcall )
(the result is the minimum equity to achieve 0EV)
MCE = ( ourcall + invested ) / ( pot + bet + calls + ourcall )
(the result will be the minimum equity to achieve InvestEV)
1 https://pokernerve.com/equity-realization/
4 HOLDEM RISK MANAGEMENT Book 1
Theoretically, we can use simple pot odds equity for our initial investment in a
hand (i.e. pre-flop), and then use MCE for all of our subsequent decisions.
Since we haven’t invested any chips yet, the pot odds equity does the job for
our initial investment. 0EV is sufficient when we have not made an investment
yet. The easier plan is to use MCE for all situations. When we have 0 invested,
we simply plug in 0.0 in the “invested” parameter and we end up in the same
place using a single formula. Of course things change a little when we happen
to be in the blinds. With the current pot odds equity strategy, we would always
claim a discount when we have to call from the blinds, giving us the ability to
call a little wider. But using pot odds equity is still a 0EV strategy, even with the
blinds discount. If we want to include the blinds in our InvestEV strategy, then
we should use the new MCE formula in the blinds as well. These two charts
show the initial voluntary investment story with and without antes. (POE = pot
odds equity.)
This is another paradigm shift for the poker community. If we look carefully at
the BB call equity using POE and the BB call equity using the MCE break-even
equity, we will notice that in order for the BB to not lose chips in the hand, they
actually need more call equity, not less call equity, than a non-blind player.
This is a complete reversal from what the poker community has shared with us.
The reason is that the SB and BB will actually win fewer chips than the non-
blind player can win, meaning their stack can’t grow as much. This new “a-ha”
moment is easily validated if we look at the story from the perspective of our
beginning and ending stack, rather than from the perspective of simply calling
the bet or not. We need to know what we are trying to accomplish: do we
want to manage our stack or do we want to manage our current action? This
Figure Error! No text of specified style in document.-21
HOLDEM RISK MANAGEMENT Book 1 5
tells us that the math behind the common very wide big blind calling ranges is
flawed, and that the big blind truly needs a tighter calling range than everyone
else, because they can’t win as much. I will discuss this and some other
idiosyncrasies of playing from the binds a little later.
Here is the dilemma:
Pot odds equity gives us the equity we need to call the current bet and
to break even on that bet. The net result is that we will play more
“lesser hands” in order to break-even with the bet we are facing. This
is a double edged sword if we are in the blinds, since our POE allows
us to call with even “lesser hands” than everyone else, spending even
more chips on worse hands.
MCE gives us the equity we need to call the current bet and to break
even for the entire hand. The net result is that we will not invest
additional chips without playing hands that have a reasonable
probability to get our initial investment back.
Once we have invested chips, then any subsequent raise or bet, now or on later
streets, should consider our previous investment. All previous investments are
treated alike. It is interesting to notice how much wider the “pot odds equity”
strategy is, than the profitable MCE strategy. Figure 5-22 shows the 0EV “pot
odds equity” strategy and the profitable MCE strategy, side by side, for post
flop decisions.
Figure Error! No text of specified style in document.-22
6 HOLDEM RISK MANAGEMENT Book 1
The pot odds equity strategy that ignores our current investment would have
us calling ½ pot bets with 25% equity. We would be investing more chips in a
bad investment. Yes, we will win some of these, but our EV says that our stack
will not break even by doing this over and over. To break-even, we are
generally going to need more than 40% equity to call almost any bet, while the
pot odds equity formula will almost never push our required call equity above
40%. This is a fairly significant impact of this break-even philosophy. Of course,
the chart confirms that our equity will always need to be larger in order to call
a larger bet, which has implications of its own.
The most interesting learning from this analysis is that if we have a previous
investment of 50% of the pot, then we must have >50% equity to be profitable,
no matter what the bet size is that we are facing. We may be able to take
down the pot with a bet, but this is a calling discussion, not a betting
discussion. Does this mean we always call a bet with 51% equity? Not exactly.
I would not propose a chart based decision process. We need player and board
context to make good decisions. We could calculate that a 44 pocket pair has
67% equity on a 23578 board. But if we really consider our opponents combos
that remain on the river, we are probably kidding ourselves if we believe we
will win 2 out of 3 hands in this spot. After removing some folded out hands
from our opponents range, we may be left with <20% equity. These formulas
and charts are valuable in context only, and only when used with the proper
perspective.
We need to talk a little more about the 50% MCE threshold when we have
invested 1/2 of the chips in the pot. In order to achieve 50% equity on the flop,
we really need at least a pair or more than 12 outs to a win to achieve 50%
equity. This has us folding a lot more hands than we might want. Of course if
we are the aggressor and are betting then we have fold equity on our side, and
we do not care about MCE, but our opponent does. Also, on the flop, unless
we are the BB, we probably invested less than ½ of the pot, but as the pot
grows on each street, we will likely have invested closer to 49% of the pot by
the river against a single opponent. This is where simply using 1/2pot
investment is a reasonable baseline simplification to use. It will never be worse
than this. Early streets and multi-way pots are when we will have invested
much less than ½ the pot.
I think we have now discovered why pot odds equity can lead us astray. MCE
gets us to a profitable EV. Pot odds equity does not. A 0EV strategy for betting
has the benefit of possible folds. A 0EV strategy for calling has no such benefit
HOLDEM RISK MANAGEMENT Book 1 7
– a call must win at showdown, and as we have seen, we can win at the
expected equity rate and still lose ground. We have been led astray too often
and were put in a position where we had no way to make up the difference.
Pre-flop play is especially vulnerable to this since we have to live with our pre-
flop decisions for the entire hand, and if our first decision is bad, the best we
can hope for is to get out of it cheaply. Each post-flop investment is a larger
sum of chips and hurts more than the first. If we use the same tool that was
responsible for the first bad decision, to make subsequent decisions then we
are merely compounding our problem. My opinion is that pot odds equity gave
us permission to continue in a hand, but it never told us whether we should
continue with the hand. Pot odds equity is one of those questions that could
only give us a “no” answer or a “maybe” answer. It should have never been
relied upon to arrive at a “yes” answer. For the “yes” answer we need more
information in context of the hand, the board and the opponents. MCE gets us
much closer to accomplishing this.
Like many poker strategies, MCE is most reliable when there is no more action
to take place. The river and all-in situations are great examples of this.
Additional cards muddle the equity story and additional action muddles the EV
story. But this isn’t unique to MCE; it is just the nature of elusive poker
certainty. If we are not guaranteed to see a showdown, then our equity
estimate is not guaranteed. This concept is also referred to as equity
realization. If we intend to utilize MCE during pre-flop, flop or turn play, we are
going to have to understand this concept well. If we somehow convince
ourselves that we have enough MCE to get to the flop with 72o, we will quickly
realize why 72o is unplayable. We may pair it and we might even hit a 3 of-a-
kind by the river, but we will have invested a ton to get here, with only 4%
likelihood. This is the essence of equity realization and is also why simply
playing using pot odds is insufficient, and can be downright dangerous. We
have to know the limits and applications for each tool we use. When we are
all-in, we will realize our full equity, every time - this provides insight into why
some shove/fold ranges are wider than normal.
MCE numbers are generally associated with calling decisions of a bet or a raise.
Of course, when we are betting, we should be aware of the odds we are giving
our opponents. Smaller bets give them better odds and allow them to properly
call with more speculative hands. Larger bets give them poorer odds and
require them to have better hands to call properly. Just like us, they also need
>50% equity if their investment in the pot was 50% of the pot, to play correctly.
8 HOLDEM RISK MANAGEMENT Book 1
Since an opponent can never have invested more than 50% of the pot, there is
no need to consider values any higher than this. We need to ensure we can see
all of these concepts from both our perspective and our opponents’
perspective. Of course, not all players understand what a proper call is, and
now that we have complicated the issue with MCE, we may not know what
they know or don’t know. Some players won’t care about the correct call, if
they are on an exploitative path to bet us off the hand later. Knowing our
opponent is the key to interpreting what their call may mean: it could mean
everything or it could mean nothing. But, with this new knowledge, we can
know that our ½ pot bet actually may require >42% equity to make the correct
call, and that any player still using >25% equity to make the call is actually
making a poker mistake. This tells me there are a lot more poker mistakes
being made than we used to think there were.
It should be clarified that much of this discussion was about no-limit hold’em,
where the bet sizes cause this issue. If we are playing limit poker, then we will
rarely be put in a position where we require large equity values. Each bet in a
limit game could be much less than 10% of the total pot. This allows much
lower equity requirements to call and results in many more multi-way pots.
The dynamics of a limit hold’em game are much different than what has been
described here. If you are playing in limit games, the concepts and formulas
will translate just fine, but the results and implications of the strategy will be
much different.
If you haven’t noticed yet, the MCE is able to easily dial in any equity
requirement for any EV we desire. We can substitute the “invest” value for an
“EVtarget” value to determine the minumun equity needed to achieve this
specific EV. This could be very powerful.
MCE = ( ourcall + Invest ) / ( pot + bet + calls + ourcall )
becomes
MCE = ( ourcall + targetEV ) / ( pot + bet + calls + ourcall )
MCE = ( ourcall + 0 ) / ( pot + bet + calls + ourcall ), this provides us the
minimum equity to break-even for the call only (same as POE)
MCE = ( ourcall + invest ) / ( pot + bet + calls + ourcall ), this provides
us the minimum equity to break-even for the hand
MCE = ( ourcall + 1/2pot ) / ( pot + bet + calls + ourcall ), this provides
us the minimum equity to have the same EV as our opponent
HOLDEM RISK MANAGEMENT Book 1 9
MCE = ( ourcall + pot ) / ( pot + bet + calls + ourcall ), this provides us
the minimum equity to ensure our opponent has 0EV
MCE’s primary purpose in life was to determine the minimum equity for true
break-even for our stack. It has far more to offer us, than just this one idea.
At the point of our decision, MCE provides solid information for a decision. If
we trust EV for every other decision, then we should trust the EV here. MCE is
a great tool to have in our tool box. We want to always use the right tool for
the right job, right? We need to know when to use them and how to use them
correctly. Misusing these tools or putting too much authority on their output,
could harm our game more than help it. I am hopeful that this has given us
something to think about next time we are determining our odds. This is all
about making very good decisions. Hopefully, I have adequately shown that an
MCE strategy is very robust and reliable.