A poker “tie” or “chop” is a situation where two or more players have the same winning hand at showdown. The chips are divided equally among the winners. Often the relevance of chopping is overlooked, and the associated maths is almost never discussed.

Let’s clarify a few key points regarding poker ties.

## 1. HOW DOES THE POSSIBILITY OF POKER TIES TO OUR EQUITY?

If we divided the probability of chopping by two, it tells us the poker equity increase we gain - given that we might sometimes win half the pot. If a particular hand will chop 10% of the time, this translates to 5% pot equity.

Sometimes players are taught that “pot-equity” describes a “hand’s chance to win at showdown if all players agree to check down”. This teaching is only partly true, however. For example, imagine we hit the same straight as our opponent on the flop, and neither of us has redraws. An equity calculator will tell us that we have 50% equity. Does this mean we can expect to win the pot 50% of the time? Absolutely not. In fact, we can never win.

100% probability of chopping results in 50% pot equity.

## 2. WHAT POT-ODDS DO WE NEED TO BLUFF-CATCH PLAYING THE BOARD?

Firstly, what do we mean by the “term bluff-catching with the board”? Imagine our opponent bets into us on a 6c7c8h9hTd board where we hold 2s3s (in No Limit Hold’em)In some senses, we have nothing, but technically we have a straight since we can formulate a five-card hand entirely using all five community cards (playing the board). So, long as our opponent doesn’t have some type of Jx holding, we are guaranteed to chop.

If we imagine our opponent is betting half-pot, we’d ordinarily need to be good 25% of the time to have a pot-odds call. This formula would be assuming we win the entire pot. Here we are in a situation where if our bluffcatch is correct, we will win half the pot.

If the payout is half the size, it’s logical to assume that our price needs to be twice as good. If we’d ordinarily need to be good 25% of the time based on pot-odds, we’ll need to be good 50% of the time - if we are purely calling for the chop.

## 3. POKER TIES AND MINIMISING RAKE

If we are confident that our opponent has the same nuts as us, it might be correct to limit the amount we put into the pot. Mis-playing in these spots can result in unnecessary losses due to rake.

Imagine the following NLHE scenario,

Board: QsTsKd5cJd

Without being overly specific about the action here, we should be able to see that we have the nuts. There is four-to-straight already on the board, so any Ace has the broadway straight.

Imagine we bet the river and our deep-stacked opponent makes a huge raise. We have the nuts, we should reraise, right? Possibly not, it depends on whether villain can ever raise with a Nine (or worse). In most cases, villain will also have an Ace, and so we will chop the pot. They could, of course, be bluffing with some frequency, but re-raising doesn’t usually achieve too much in this instance since villain can never call our raise with air.

In fact, the only thing that raising will achieve is to ensure both players pay more rake in the case of a tie. A good player will hence just call against the raise with the nuts if they have a high degree of certainty that his opponent is never raising a worse hand for value.

## 4. POKER TIES AND MUTUALLY ASSURED DESTRUCTION

Let’s run a quick thought experiment on the above example. Imagine we were playing a million big blinds deep and decided to re-raise all-in. Should our opponent call? Not without thinking carefully about the rake and rake caps. The call with the nuts could end up being more expensive than simply folding.

Unfortunately, it is almost impossible to leverage this type of information to our advantage, because it’s rare that players are good enough to fold the nuts, even if it’s warranted. And, of course, if our opponent calls, we’ll both get killed by the rake - hence, mutually-assured destruction!

The same type of issues might occur on textures where the board holds the nuts. Imagine the runout is TJQKA in a dry pot (hardly any chips in the middle). Good players will not bet in this spot, after all, what’s the point? Everyone is chopping, so why pay more rake than we need to? A good way to become unpopular very fast might be to start making huge all-in over-shoves in these spots. While undoubtedly a legal option, this type of bet is considered downright unethical by most players.

The interesting thing here is that if villain is good enough to realise that calling is costlier than folding (due to rake), shoving all-in is the correct play for us! Villain makes the correct fold, and we win a pot we should have otherwise chopped.

We face two huge problems though -

1. Most villains cannot be relied upon to find the best play and fold the nuts.

2. Although our opponent can never win money in this spot, they can at the very least ensure that we both lose a big chunk by calling (mutually-assured destruction). Of course, this doesn’t make sense in terms of villain’s EV, but perhaps villain is simply spiteful.

Besides, us knowing that villain will make the minus-EV call creates a disincentive for us to try and pick up the pot in the future. Those interested in game theory might appreciate the similarities between this model and that of prisoner’s dilemma.

## 5. WHEN A POKER TIE IS NOT A POKER TIE

Of course, in some cases, our problem might be a case of getting to grips with basic hand reading. It’s possible for two players to have the “same hand” but it does not result in a poker-tie due to our kicker etc.

For example, if two players have a pair of Kings, we look at the next highest card (the kicker) to see who wins.

The following table is a quick reminder of how to differentiate between poker hands that might appear the same.

 Type of Hand Ranking In Case of Tie Royal Flush All Equal Impossible in most variants such as NLHE. Always chop otherwise (i.e. in Stud) Straight Flush Higher straight-flush wins. Impossible in most variants such as NLHE. Always chop otherwise (i.e. in Stud) Quads Rank of the quads is highest. The fifth card is the “kicker” which determines the winner. Full House Rank of the three-of-a-kind is highest. Always tie (if of same rank). Flush Rank of the highest flush card. Impossible in most variants such as NLHE. Always chop otherwise (i.e. in Stud) Straight Higher straight wins. Always tie (if of same rank). Three-of-a-Kind Rank of the three-of-a-kind is highest. This hand has two kickers. Highest kicker wins. If highest kicker ties, highest second kicker wins. Two Pair Rank of the highest pair is highest. Highest kicker wins. One Pair Rank of the pair is highest. This hand has three kickers. Highest kicker wins. If highest kicker ties, second kicker wins. If second kicker ties third kicker wins etc. High Card Rank of the high-card is highest. If high card is tied, second card is considered, then third, then fourth, then fifth.

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