[A Beginner's Guide to Poker] Poker odds and outts explained in simple terms!

What are Outs?

Outs are the cards needed to complete a strong hand.

Knowing the number of outs allows you to roughly estimate your chances of completing a strong hand and, consequently, your odds of winning at showdown.

Let’s consider how to count outs through specific examples.

Number of Outs

Flop

Suppose you are in the BB position holding ❤7❤6 and your opponent has ♣A ♠K.

On the flop, ❤8 ❤9 ♠A are dealt. You are currently losing. You check, and your opponent goes all-in. In this situation, where you’re losing but can win if you hit your outs, should you call?

What cards do you need to draw to win? Drawing a 5 or T will make a straight, and drawing a ♥ will make a flush, allowing you to win. There are 8 outs for 5 and T, and 7 more outs for ♥ (excluding ♥5 and ♥T), totaling 15 outs.

Your Outs

How to Calculate Winning Odds

Knowing the number of outs, you can estimate your winning odds. The formula is: Winning Odds = Number of Outs × Number of Remaining Betting Rounds × 2

This formula can roughly calculate the winning odds, assuming 50 cards in a deck and approximating the probability of drawing the desired card as 2% (1/50). The actual odds are a bit lower than the calculated figure, so keep that in mind.

Now, let’s consider the detailed method of calculation. If complex formulas are not your forte, it’s okay to remember the above formula and skip this part.

Detailed Method for Calculating Winning Odds

You have 15 outs. There are 47 unseen cards left in the deck, and you see 5 cards, so the probability of drawing an out next is “15/47”. Conversely, the probability of not drawing an out is “32/47”.

If you don’t draw an out on the first card, calculate the odds for the next card. There are 46 cards left, still wanting one of the 15, so the odds are 15/46. Thus, the probability of not drawing an out in two draws is “32/47 × 31/46 = 992/2162”, and the probability of drawing an out in either of the two cards is “1 - 992/2162 = 1170/2162”.

Therefore, with 15 outs, the odds of drawing an out by the river are about 54% (≈ 1170/2162), indicating you should call. However, calculating this during play is challenging.

So in practice, remember the formula: “Number of Outs × Number of Remaining Betting Rounds × 2”. With 15 outs: Odds for 1 betting round = “15 × 1 × 2 = 30%” Odds for 2 betting rounds = “15 × 2 × 2 = 60%” You might notice these are a bit higher. Remember to adjust the figure slightly downward.

What are Odds?

Odds refer to the ratio of the return you get when you win against the risk you take. Matching odds means the return is proportionate to the risk taken. In other words, odds are about “how much you put in and how much you get back.”

Important elements in considering odds are:

• The amount of chips needed to call (Risk)
• The amount of chips you can win (Return)

The odds of calling someone’s bet can be calculated using this formula:

Odds
= Total pot chip amount / Amount of chips needed to call

For example, if you put in 100 chips and get back 700 when you win, the odds are 7 to 1. In this game, if you can win with a probability higher than 1/7 (≈14%), you should continue. The threshold (required winning rate) for continuing the play is calculated as:

Threshold (%) = (Amount of chips needed to call × 100) / Total pot chip amount

If your “hand’s winning rate” is above the threshold, the call is profitable; if it’s below, it’s not profitable. The former is referred to as “matching odds,” and the latter as “odds not matching.”

• Matching Odds

= “Hand’s Winning Rate” > “Threshold”

• Odds Not Matching

= “Hand’s Winning Rate” < “Threshold”

“Hand’s Winning Rate” can be calculated from the number of outs, and “Threshold” can be calculated from the odds.

Specific Method for Calculating Odds

For example, suppose there’s 10,000 in the pot, and your opponent goes all-in for 5,000. If you also put in 5,000 to call, the total chip amount becomes 20,000. Thus, you’re risking 5,000 for a return of 20,000.
Hence, the “Odds” and “Threshold” are: Odds = 20,000 / 5,000 = 4
Threshold = 5,000 × 100 / 20,000 = 25%
The “Threshold” is 25%, so if you have a drawing hand, and the “Winning Rate” calculated from your outs exceeds 25%, the call is profitable.

Such a situation is called “matching odds”; if the winning rate is insufficient, it’s called “odds not matching”. Especially in river bets and all-in situations, calculating odds and outs is essential.

Summary

This chapter explained odds and outs. In actual play, not only “winning odds at showdown” but also the probability of the opponent folding to your bet should be considered, making calculations complex. However, understanding odds and outs significantly improves your poker skills.

To summarize the important formulas:

• Winning Rate = Number of Outs × Number of Remaining Betting Rounds × 2
• Threshold (%) = (Amount of chips needed to call × 100) / Total pot chip amount
• Matching Odds

= “Hand’s Winning Rate” > “Threshold”

• Odds Not Matching

= “Hand’s Winning Rate” < “Threshold”

Odds and outs are simple numerical games. Let’s logically consider our actions based on these calculations.