HOLD’EM RISK

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]


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/

https://pokernerve.com/equity-realization/


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


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


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


– 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.


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


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.

HOLD’EM RISK

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