Basic Draw Poker – Lesson #6: Probability

The next important part of draw poker strategy is understanding the probability of drawing different combinations when you replace cards. It is unlikely that a thinking player will enter the game only with high cards hoping for more reliable combination after cards replacement. All probabilities are against that.
When you replace 4 cards and keep an ace, you can very often form a strong pair but in most cases wins the player who already has a pair. His chances to form higher combination like two pairs or four of a kind are equal to your chances to get a second ace, therefore, he has greater chances to beat you. Thus, your opponent is already one step ahead. From time to time you will be able to compensate that but in most cases you will be late. Comparison of the probability of any combination and the pot odds will give you the mathematical feasibility of your bets. In case you have 4 cards to a flush and the probability of forming it is 1 to 4, you can enter the game when the pot odds are more than 4 to 1. In such cases, theoretically, you are going to lose 4 times a bet and in one case you are going to win the pot (which will be more than 4 of your bets).

By making “right” replacements you increase your chances to improving your initial combinations but in doing so you will show your opponents the true value of your cards. Here you have another secret strategic weapon: to bluff or to improve.
The table below will show you the probability to form any combination by drawing different number of cards. Based on that data, you can make several important conclusions. Never try to play three cards to a straight or a flush. Chances to get two cards of one suit in order to form a flush are 1 to 24. Never try to form an inside straight. If you decided to enter the game with high cards only, pretend that you have a pair, two pairs or better combination i.e. draw 2 or 4 cards or don’t draw any. If you bluff successfully, you will get an instant profit but in case it was revealed, perhaps your sacrifice will pay off in the future since your opponents may answer your bets with weak hands (thinking that you again enter the game with weak cards). As we already know, having an ace and replacing 4 cards is not the best decision.

Initial combination Draws Combination Probability
A pair

3

Two pairs

Three of a kind

Full house

Four of a kind

Other

1 to 5

1 to 8

1 to 97

1 to 359

1 to 2,5

A pair with ace kicker

2

Aces up

Another 2 pairs

Three of a kind

Full house

Four of a kind

Other

1 to 7,5

1 to 17

1 to 12

1 to 119

1 to 1080

1 to 3

Two pairs

1

Full house

Other

1 to 11

1 to 11

Three of a kind

2

Full house

Four of a kind

Other

1 to 15,5

1 to 22,5

1 to 8,5

Three of a kind and a kicker

1

Full house

Four of a kind

Other

1 to 14,7

1 to 46

1 to 11

4 to a straight

1

Straight 1 to 5
4 to inside straight

1

Straight 1 to 11
4 to a flush

1

Flush 1 to 4,2
4 to an open end straight flush

1

Straight flush

Other

1 to 22,5

1 to 2

4 to an inside straight flush

1

Straight flush

Other

1 to 46

1 to 3

Aces

4

A pair of Aces

Aces up

1 to 3

1 to 14

In case you have a pair, in most cases you should replace 3 cards. If you replace only 2 cards, your chances to form better combination will drastically decrease. But that can make your opponents fold or place small bets during the next betting round. In order to be successful, you should not use this strategic move very often. Usually this type of replacement is called advertise and not bluff (showing that you don’t necessarily have three of a kind when you replace 2 cards). But next time when you actually get three cards of one rank, and replace two cards, your opponents will decide that you are bluffing, they will not fold and they will continue placing bets and answer to your raises. If you have two pairs, you should replace one card. The probability to form a full house is not big (it is 1 to 11) but there is still a chance. The only other option you have is not to replace a card. A tactical move like this requires certain experience. Two pairs is considered a strong combination i.e. winning combination and if you decide to bluff, in this case you may decrease your profit – the players with lower combinations will simply fold. If you have two low pairs and your opponent has replaced one card i.e. there is a possibility for him to have two higher pairs, you may refuse to draw. It is very likely that in this case, your bluff will reduce your losses – in the next betting round your opponent most likely will not dare to open the game and will check, and you will not have to make a losing choice i.e. to call or to fold.

If you have three of a kind, you can replace one or two cards. The probability to form four of a kind in both cases is very small but the probability to form a full house is the same. If you replace two cards and till then you played absolutely “honest”, you will show your opponents the true value of your cards and that most likely will make them fold which will be not very good for you, since it will reduce your profit. In case you had previously made 2 cards replacement with a pair or other combination, and your opponents understood that you were bluffing, the latter replacement won’t make them confident that you really have strong hand. In this case to replace one card is also a good move since you show your opponents that you have two pairs or you are very close to form a straight or a flush which very often can bring you higher profit. You don’t need to replace any cards when you have 3 cards of one rank since you are already winning and your bluff will just decrease your profit or you are going to lose it at all. If you have 4 cards of one rank, you need to replace one card for sure. If you refuse to replace a card, most probably you won’t be able to make the profit, which promises one of the highest poker combinations.

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