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Thursday, 23 November 2017
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Preflop All-In Match-ups

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By Tony Guerrera

Anyone with a bit of tournament experience is highly familiar with the situation that occurs when players become short-stacked with respect to the blinds: people either go all-in or fold preflop. To play optimally in this dynamic, you need to know the winning percentages associated with individual hand match-ups (say AK vs. AJ). However, that’s not enough. From there, you need to figure out how to compare your hand against a distribution because you have to put your opponents on ranges of hands–the only time a range of hands can contain only one set of hole cards is if you have an extremely good read on someone (and with tournament preflop all-ins from short-stacks, such magical reads will happen rarely, if ever).

Types of Preflop All-in Match-ups Between Individual Hands

By accounting for connectivity and suitedness, it’s possible to come up with approximations to winning percentages that are usually good to within 1%. You should ultimately get to the point of being able to do such approximations at the table. However, we have to crawl before we can walk…it’s usually better to learn things gradually than to be bombarded with a flash flood of information.
With that in mind, the effects of connectivity and suitedness have been averaged, and all results are rounded to the nearest .05 to make the numbers easier to remember. While these might seem like significant simplifications, the numbers and methodology provided in this article will enable you to calculate your winning percentages to within 5%, and for most players, being within 5% should be more than good enough.

All-in Match-ups Involving Pocket Pairs

Type of Match-up

Example

P(Hand 1 Wins)

Overpair versus underpair

AA vs. TT

.80

Pocket Pair versus unpaired undercards

AA vs. 75

.85

Pocket pair versus a card of the same rank and an undercard

QQ vs. QJ

.90

Pocket pair versus an undercard and an overcard

QQ vs. AJ

.70

Pocket pair versus a card of the same rank and an overcard

JJ vs. AJ

.70

Pocket pair versus two overcards

JJ vs. AK

.55

 

All-in Match-ups Not Involving Pocket Pairs

Type of Match-Up

Example

P(Hand 1 Wins)

Two higher cards versus two lower cards

AK vs. QJ

.65

Alternating relative ranks

AJ vs. K9

.65

Tweener match-ups

A2 vs. 76

.60

Domination match-ups

AK vs. KQ

.75

 

Some exceptions exist, but generally, the absolute values of the cards don’t matter–only the type of match-up matters. Additionally, unless you have an underpair versus an overpair or no overcards against a pocket pair, you’ll never be worse than 25% (and usually, you won’t be worse than 30%). This surprises quite a few players who think that 23 would be much worse than 35% against AK.

Doing Analysis Against Distributions

Before reading on, make sure that you understand the discussion involving combinations in my Poker Helper article entitled “Basic Probability for Poker Players.” Understanding combinations is essential for evaluating how a specific set of hole cards will fare against a distribution.

Evaluating how your hand holds up against a distribution involves two steps. First, figure out your winning percentage against each hand in your opponent’s distribution. Second, take a weighted average of the winning percentages using the number of available combinations for each hand in your opponent’s distribution. When you’re at the table, the key to doing this process in your head is taking a series of smaller weighted averages as you go along. Below are a few examples, where the dialogue is an attempt at replicating what your thought process should be at the table.

1.) Assume you hold JJ, and you put an opponent on {AA-88, AK-AJ}.

Against the 18 AA-QQ combinations, I’m 20% to win. Against the 1 JJ combination, I’m 50% to win. And against the 18 TT-88 combinations, I’m 80% to win. Against these 37 combinations, I’m effectively 50% to win.

Meanwhile, against the 32 AK-AQ combinations, I’m 55% to win, and against the 8 AJ combinations, I’m 70% to win. The weighted average between 55% and 70% should be shifted heavily towards 55% since I’m 55% against 32 out of 40 combinations. Since 62.5% is halfway between 55% and 70%, I’m probably about 58% to win against AK-AJ.

I’m about 50% against 37 combinations and about 58% against 40 combinations. 37 and 40 are very close, so the weighted average should be very close to the unweighted average, meaning that I’m about 54% to win.

*Poker Stove reveals that the actual winning percentage is 53.61%.

2.) Assume you hold QJ, and you put your opponent on {AA-22, AK-A7}.

Against the 12 AA-KK combinations, I’m 15%. Against the 3 QQ combinations, I’m 10%. Against the 3 JJ combinations, I’m 30%. The 6 QQ-JJ combinations average out to 20%, and when averaged with the 12 AA-KK combinations, I should be around 16%. Meanwhile, against the 54 TT-22 combinations, I’m 45%. The unweighted average of 16% and 45% is about 30%, but since the TT-22 has three times as many combinations, I’m probably around 40% overall against the 72 pocket pair combinations.

Meanwhile, I’m 35% against the 16 AK combinations, 25% against the 24 AQ-AJ combinations, and 40% against the 64 AT-A7 combinations. The 64 AT-A7 combinations outweigh the 16 AK combinations by a factor of 4, meaning that the weighted average between them is something like 39%, which is close enough to be called 40% to make the math easier. These 80 combinations against which I’m 40% outweigh the 24 AQ-AJ combinations by a little more than a factor of 3, meaning that I’m probably somewhere around 37% against all the AK-A7 combinations. Since the AK-A7 outnumber the AA-22 combinations, it sees that a good estimate would be that I’m about 38% against {AA-22, AK-A7}.

*Poker Stove reveals that the actual winning percentage is 39.07%. Again, this is more than adequate enough for the purposes of an estimate such as this.

Estimates Are Usually More Than Enough

Even by doing rough estimates, we’re able to get winning percentages that are very close to the actual ones. When you’re at the table, you need to pay attention to your opponents constantly, so it’s not practical to put all your mental energy into making precise calculations. As long as you are able to make educated estimates on the fly, you’ll have numbers that are more than accurate enough with which to make profitable tournament decisions involving preflop all-in situations.

Tony Guerrera is the author of Killer Poker By The Numbers and co-author of Killer Poker Shorthanded (with John Vorhaus)

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