# Equity – Fully explained

## Definition of pot equity

Pot equity refers to the odds that a particular hand (or range of hands) will win, given the hand(s)/range(s) held by opponent(s), AFTER the river card is dealt.

Equity is usually expressed as a percentage, but can also be expressed as a ratio. It is important to note that the equity of a hand will usually go up or down as the hand progresses. If you have ever watched poker on television, and see a percentage shown next to a player’s hole cards, this indicates the player’s current equity in the hand. Quickly combining equity calculations, with pot odds calculations, is an important skill to have.

• Let’s say we are playing \$2/\$5, and it is folded to the cutoff who is holding KdKc. The cutoff (who has \$500 in his stack) opens to \$20. The button (who covers the cut-off), who has AhAs, 3-bets to \$60. It is folded to the cut-off, who 4-bets to \$200. The button goes all-in for \$500, and the cut-off quickly calls.
• Just before the flop is dealt the CO with KdKc has 18.74% equity, whilst the button with AhAs has around 81.26% equity.
• The exact suits each player is holding can impact these percentages.
• If any other player has folded an A or K, this does NOT matter as we cannot know they have done this (you should note if you watch poker on television, the equities shown usually take account of the cards folded by other players where they are known).
• If however, one or more cards are accidentally exposed by the dealer or another player (which does happen from time to time in live poker), this will have to be taken into consideration in your equity calculations.
• If the flop comes Ks Qd Js, equities change considerably.
• The CO’s KdKc has 75.96% equity, whilst the button’s AhAs has 24.04% equity.
• CO has a set, but button is looking to hit one of the 4 remaining tens in the deck (which would make him a straight), or one of the 2 remaining aces in the deck (for a higher set than his opponent). That’s 6 direct outs to improve.
• Of course, even if button makes a straight on the turn, cutoff can still win the hand if the board pairs on the river (giving him a full house). If the button makes either a straight or higher set on the turn, cutoff can still win if the river is the last king in the deck (the case king) which will give him quads. That is to say, your equity is diluted.
• Button also has backdoor outs (and thus, backdoor equity in this hand). Backdoor equity/outs means that he will need 2 running cards (i.e. both the turn and river) to be useful if he is to win the hand. In this example, two more spades (as long as the board does not pair, which would give CO a full house) would win button the hand.

Equity can be calculated as:

• Hand v Hand
• Estimates for Hand v Hand equity, can be easily memorized
• For example, an overpair usually has around 80% equity, versus an underpair
• Two overcards usually have around 45% equity, versus an underpair
• Hand v Range
• i.e. What is the equity of your known hand (e.g AhKs) vs the range of hands you have assigned your opponent (e.g AA, KK, QQ, AK)?
• Range v Range
• i.e. What is the equity of the range of hands you would normally hold following a sequence of actions, versus the range of hands you put you opponent on?

In terms of poker strategy, you will usually be thinking either in terms of hand v range equity, or range v range equity. Hand v Range and Range v Range equity, can be calculated instantly from the table using an equity calculator. There are many good pieces of software, available on a variety of platforms, that are totally free to use. The best way to get a feel for Hand v Range, and Range v Range equity is to perform these calculations regularly using software – you will start to notice patterns or get a feel for the likely equities in a variety of situations, so you can estimate these accurately at the table when a similar spot comes up.

### Hot and cold equity

When we say that AA has around 80% equity versus KK which has around 20% equity, we are talking about ‘hot and cold’ equity.

Hands with the most hot and cold equity, are not necessarily the best hands to be playing. Clearly A7o has more equity then KQs – if you could get all the money in with A7o knowing your opponent had KQs, in a heads up scenario preflop, clearly you would want to do so. In real life, you are unlikely to know what hand your opponent has – instead you can only put them on a range of possible hands. In a 9 handed poker game, with deep stacks, you will almost certainly be folding A7o preflop, unless it is unopened to you on the button or you get to check your bb (or you are getting a good price to continue in the bb). You will however likely be at least thinking about playing KQs from all positions.

### Retained equity

We prefer hands that will retain their equity versus the hands our opponents ranges for continuing in the hand (whether they do so by raising, betting, or calling). Being ahead in equity terms of hands our opponent will likely be folding before showdown (be it preflop, on the flop, turn, or river), don’t help us.

If a strong studied player opens in early position in a deep stacked live \$2/5 game, and it is folded to us on the button, would we rather have A9o or 87s. Clearly, A9o will have more hot and cold equity than 87s versus any reasonable range of hands we put our opponent on. However, A9o is almost certainly fold in this situation, however we will always be continuing (whether by calling, or 3-betting) with 87s.

## Outs

In the above example we talked about outs. In order to calculate your equity, when you think you are behind after any of the flop/turn/river have been dealt, it can be useful to think in terms of outs. Once you know how many outs you have it is easy to estimate your equity as we will show below. Outs are the number of cards remaining (i.e. that you know could still be dealt) that you think will give you the winning hand.

When you have a draw, and you think you will will have to hit your draw to improve, you will want to think about your outs

• If you have a flush draw, you have 9 outs to hit the flush draw
• For example if you hold KdTd and the flop is 9d5c2d, the following 9 cards will give you your flush: Ad, Qd, Jd, 8d, 7d, 5d, 6d, 4d, 3d.
• It is important to note you may have other outs too – if you think making a pair of kings might be enough to win the hand, then perhaps you have 3 further outs (Ks, Kh, Kc).
• You may also have backdoor outs (such as hitting a running straight, or running two pair, or trips). Note that, even if you hit your flush draw it might not be enough to win the hand (e.g. if your opponent held 99/55/22 on this flop, if the board pairs on the turn or river, you cannot win this hand unless you hit a running royal flush).
• A Straight draw that is open ended has 8 outs. A straight draw that is a double belly buster (e.g. if the flop is Tc9d6s, and you are playing Qd8d, you will make a straight with any J or 7) also has 8 outs.
• A Straight draw that is a gutshot (also known as an inside straight draw) has 4 outs.

### Not sure a card is an out?

Let’s say you are mainly going for a flush, as the example immediately above. However, you think making a pair of kings might also be enough to win the hand. However, you are not sure. How about counting either 2 or 1 (instead of all 3 remaining kings) as outs?

## Converting outs to equity quickly

### Rule of 2 & rule of 4

Rule of 2: After the turn has been dealt (i.e. there is 1 card to come), multiply your outs by 2 (i.e. count your outs, and double it), to get a fairly accurate estimate of your equity expressed as a percentage.

The reason this works is that there are 46 unknown cards on the river (52 cards in the decks – 2 in your hand – 3 on the flop – 1 on the turn). If it was 50 unknown cards, clearly to get a % you would multiply by 2 (as percentages represent the chance out of 100). With 46 unknown cards, you get a reasonable estimate, by multiplying by 2 (but clearly there is a small error).

Rule of 4: After the flop has been dealt (i.e. there are 2 cards to come), multiply your outs by 4 (i.e. count your outs, and double it twice), to get a fairly accurate estimate of your equity expressed as a percentage.

You have probably deduced why this works, after reading the above explanation. As you have 2 chances instead of 1 to hit your outs (i.e. both the turn, and the river), your equity approximately doubles. Again, this simplified rule has a degree of error (as there are 47 unknown cards on the turn, and 46 on the river, yet this formula is assuming there are 50 unknown cards on both the turn and river).

### Improving the rule of 2 or 4

We have shown you why the rule of 2 and rule of 4 produce good but not perfect estimates. To reduce absolute errors, we would suggest the following modifications, which are certainly not onerous to do at the table.

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– You can actually improve on the rule of 2, with almost no additional effort, just by adding 10% to your answer. So, if you had 7 outs, you would use the rule of 2 formula to estimate that you have 14% equity. Then you add 1.4% to this answer, giving you 15.4% equity.
– The rule of 4 is actually pretty accurate, until you have a larger number of outs. So we suggest you use the rule of 4 as is for 1-9 outs. If you have 10 or more out we suggest multiplying your outs by 3, and then adding 9. So, if you had 15 outs, you would do the following calculation in your head 15×3=45%, and then add 9%, giving you 54% equity.

By taking a few more seconds to do this, you will reduce your absolute errors in your equity calculations based on your outs. The more accurate your equity estimates, the better your decisions might be. Using these modified rules (which are still easy to perform on the table), means your equity calculations will a maximum absolute error of around 1% (provided you have accurately counted your outs).