Calculating Pot Odds Quickly and Accurately

Have you ever had a tough time figuring out what the odds of making your hand really are?  Poker math can be tough, but only if you let it be.  There are a few rules that you can apply to make the math in poker VERY easy.

When facing a bet in No Limit Hold’em, or any poker game for that matter, you use pot odds to help you make certain decisions. This article will focus on situations where you are facing a bet on the Flop or Turn and are certain you need to improve to win the pot. Once you know how many outs you have and compare your “card odds” to your “pot odds”, you can then determine if it’s profitable for you to draw to the best hand.

Common Scenario

In a game of .10/.25 No Limit Hold’em you have the Kh and the 9h on a flop of Ah 4h Jd. The pot has $2.50 and you need to call a bet of .50 to see the Turn card. You have a draw to the Nut Flush which currently represents the best possible hand for this board. If the board pairs, you could potentially be drawing dead to a Full House. What you need to do now is determine if the pot is offering you the correct odds to draw to your flush.

The “Hard” Way

I use the word “hard” loosely as this is straight forward math and not too difficult. But when you are just starting out and are in the heat of the moment, or even multi-tabling, then you may find the following math cumbersome or time consuming to do in the short timeframe you have to make your decision.

Pot Odds: (total pot $):(call $)

You need to call .50 to win a $2.50 pot. This is represented as: 2.50:0.50 or 5:1 odds. (Divide 2.50 by .50 to get 5:1).

Card Odds: (cards left – outs):(outs)

To determine the odds against you hitting your flush card on the Turn is quite simple. Since there are 13 cards of each suit (13 hearts, spades, diamonds, and clubs), and 4 are already accounted for (the 2 in your hand and the two on the board)) then there are only 9 cards of those 47 remaining cards that will make your hand, whereas there are 38 cards that are another suit, and will not. So using the formula above we get 47-9:9 or 38:9 or 4.22:1 (Divide 38 by 9 to get 4.22:1).

In this case, the pot is offering you 5:1 odds and the odds against you hitting your hand are 4.22:1. Where the pot odds are greater than the card odds, you call.

An Easier Way

The Rule of 4 and the Rule of 2
There is a concept known as the Rule of 4 and the Rule of 2 which states that when you are facing an all in with two cards to come (all in on the flop) then you multiply your outs by 4 to get your approximate percentage chance of making your hand. If you want to know the percentage chance of making your hand on the next card, whether it’s the turn or the river card) you would instead multiply your outs by 2 then add 2.

This rough approximation is not without its shortcomings. When using the Rule of 4, the percentage chance becomes really unreliable with 10 outs or more. For instance: with 15 outs, the Rule of 4 gives you a 60% chance of making your hand when it is actually more like 54%.

To follow our example above we would multiply our outs (9) by 2 (plus 2when you have 8 or more outs) to get 20% to make our flush on the very next card. The bet we need to call, when represented as a percentage of the pot, is 20%. Based on this, our percentage odds to make the hand equal the odds offered by the pot so we call.

A Hybrid Approach: Mixing Solomon’s Rule and the Rule of Two

Solomon’s Rule: When Facing an All In on Flop
A more accurate way to estimate your percentage chance of making your hand when facing an all in on the flop is by using Solomon’s Rule. To use it, multiply the number of outs by 4 then subtract the number of outs in excess of 8. In the 15 out example above, Solomon’s Rule would be: ( 15 * 4 ) – ( 15 – 8 ) = 53%.

Rule of Two: When Facing a Bet on Turn OR River
The Rule of Two will be accurate enough to use when you want to determine your percentage chance of making your hand on the next card. It is made more accurate by adding 2 to the product of (Outs * 2) when you have 8 or more outs. So if you have 15 outs on the flop again and would like to know your percentage chance of making your hand on the turn: (15 * 2) + 2 = 32%.

Again, to follow our example above, and use the modifier, we now see that the percentage chance of hitting our flush is 20% while our call is just 16% of the pot to be won. An easy call.

A Note about Implied Odds

The scenario above is pretty straight forward but it doesn’t take implied odds into consideration. Implied odds are the odds offered by the amount you have to call against the amount in the pot plus the amount one stands to gain from bets made on future streets. If your opponent is likely to invest more money in the pot when you do hit your flush, then the strict call/fold guidelines according to straight pot odds (direct odds) can be loosened.

Common Pots Odds

Here is a chart that includes the actual odds and percentages for 1 to 20 outs. The Rule of 2 and Solomon’s Rule have been included to show its effectiveness.

Related posts:

1. Pot Odds and Implied Odds
2. Bad Beats Happen, Deal with It!
3. Value betting the river