Split trips

With split trips the high card content of your starting hand, as well as the size of the third flopped card and your position, should dictate your course of action. Thus, if the first three cards on the board are 7♥-7♠-J♣ and you hold T♦-9♦-8♠-7♣ and you are the first to act, you should bet. You are basically asking the other players whether you possess the best hand or not. When your bet is raised, you are entitled to assume that the answer is no, in which case you should discard your cards, especially if another contestant flat calls the re-raise.

You have not got a card higher than the Ten and in all probability with more than two opponents somebody has the house of Jacks. However, if you are holding A♥-Q♠-T♥-7♣, and the flop is T♣-T♦-6♠, your response to that answer may be different if the pot odds are favourable. In late position, you should obviously bet if everybody checks to you but when an opponent bets before you, then you must raise; you have nine outs to win or share the pot.

Against a skilful opponent you must exercise caution if you do not flop the full house in these situations. I remember a hand that cost me more than it should have. I was in late position holding A ♣-K♦-Q♣-T♠ and the flop was K♠-K♥-J♦. A good player came out betting and I raised him. He called my raise. The turn card was the T♦which gave me a house of Kings over Tens. He checked and I duly made a bet. He flat called. The fifth card was a blank. He checked again and of course I happily made another bet, which he raised. By then there was so much money in the pot I had to call his raise.

Needless to say, he showed me A♠-K♣-J♠-9♦. He did not re-raise my original raise because he knew that only three cards (three Queens) could take the pot away from him and as you know the overall probability for that to happen is 12% (15:2 against). I should have checked on the river card because I had the second-best hand.

2.3 Flushes

As I have said before, flush draws are my favourite. The probability of completing the flush on the turn or the river cards is 20% (4:1 against)

74 T HE S CIENCE OF P OKER

and in limit games the pot usually offers better odds. When the flop offers a flush draw only, do not take part in the action unless you are aiming for the Ace and sometimes the King-high flush. Lower flush draws must not be your only targets; they may win the pot if you backdoor them.

Frequently one or two of the cards to complete the flush must be discounted because they may improve your opponents’ hands. I will explain this in the following example.

Suppose you held K♠-J♠-T♥-4♦ and a rock raised before the flop. The raise was called by five contestants including yourself. You know the rock must be holding two Aces, otherwise he would not have raised from early position. The dealer flops A♠-6♠-5♣ and the raiser comes out betting. What are your chances of winning the pot with the flush draw? Since you know the rock is betting with trip Aces, your outs on the turn are in fact eight not nine, because the Five of spades will complete the house of Aces. Even if the turn card gives you a flush, the rock still has a 22% chance of winning the pot on the river. That means you should reduce your eight outs for the turn by roughly 20%. If the turn card is a blank, say, 9♦, your outs on the river are seven, because the 9♠ and the 5♠ will give the rock the best hand. Thus, you are 11:2 against on both the turn and river.

To make life easy for yourself, when you put one of your opponents on trips and you are drawing for the nut flush, assume that you have seven outs working for you on the turn and the river. Your decision to call his bet, therefore, must be guided by how the probability of completing the flush draw compares with the pot odds. Your overall chance of winning is in fact about 28% (5:2 against); this was confirmed by a computer simulation whose results will be presented in the section concerned with straights.

The table below shows the results of a number of computer simulations on K♠-J♠-T♥-4♦. The hand was played against seven to three opponents sharing A♠-6♠-5♣ as the flop.

Starting cards: K♠-J♠-T♥-4♦

Flop: A♠-6♠-5♣

T HE F LOP

Number of opponents Win-rate

7 28.0

6 30.0

5 31.5

4 33.5

3 35.6

Table 1: The % win-rate of flush draws

The table reveals that the number of outs for a flush draw against seven opponents is seven (28 ÷ 4 = 7), not nine, because almost certainly at least one or two would have flopped two pairs and/or trips. As the number of opponents decreases, the chances of flopping trips and two pairs diminish;

thus against five or four, the win-rate of the flush draw increases to numbers compatible with eight outs. Against three rivals the number of outs becomes nine.

In general, it is sound practice to assume that the flush draw has seven outs when more than four opponents are competing to win the pot. I recommend seven for the turn card to allow for losing to a full house if the fifth card pairs the board and seven for the river card. With three or less, it is usually safe to assume the usual nine outs. Of course, if you put one of your rivals on trips, then the flush draw has seven outs no matter how many players are contesting the pot.

If you use seven outs to calculate the win-rate of the flush draw on the turn and the river, the probability of completing the flush on both the turn and the river is roughly 16% (11:2 against). Thus, if your chance to win depends mainly on the draw, at least two and preferably more players should be in the pot to get the maximum value for your hand. Of course, if the board is paired on the turn or the river, you must review your position.

2.4 Straights

Again, I shall restrict this section to the circumstances in which the number of outs of the straight draws, presented to you by the flop, should be reduced. Let us look at some examples.

76 T HE S CIENCE OF P OKER

Your starting cards are Q♦-J♠-T♥-9♦ and the flop is A♣-K♣-3♥.

To the unskilled player you have flopped a nine-card draw to the top straight (three Queens, three Jacks and three Tens). The truth is you have flopped a six-card draw because you do not really want to see Q♣, J♣, or T♣ on either the turn or the river. If you hit the straight on the turn, you may still lose the pot to the flush 20% of the time, or to a full house 22% of the time.

These facts reduce the overall probability of ending up with the best hand if you get the desired turn card. If the turn card does not give you the straight, then you will be victorious after the fifth card 13% of the time (about 13:2 against). Therefore, the above flop is not as good as many Omaha players think it is. It has an overall win-rate of about 17%. This is confirmed by the computer simulation described in the next paragraph.

The following three sets of specific starting cards and flop were dealt to three players.

Player 1: A♥-A♦-6♦-6♠

Player 2: Q♦-J♠-T♥-9♦ Flop: A♣-K♣-3♥

Player 3: 8♦-8♣-7♣-7♠

Thus, the flop gave Player 1 top trips, Player 2 a six-card draw to the best straight and Player 3 a flush draw (I chose an 8-high flush draw for convenience). The fourth and fifth cards were dealt over 10,000 times and the average win-rate of each contestant was recorded. The results of the simulations are listed below.

Player Flopped hand Win-rate

1 Trips 55.5

2 Straight draw 16.5

3 Flush draw 28.0

The flush draw had a win-rate of 28%. The straight draw against trips and a flush draw, however, managed a win-rate of only 16.5%.

I also performed two different computer simulations which were designed to measure the win-rate of Player 2 (Q♦-J♠-T♥-9♦) against six to two opponents holding randomly dealt starting cards. The first set of simulations had the flop A♣-K♣-3♥ as in the above example. The

T HE F LOP

second set, however, had a flop which contained K♠ instead of K♣.

Thus, the second simulations did not present a flush draw to any of the contestants, thereby giving Player 2 nine outs for the top straight. The results are presented in Table 2.

No. of opponents Flop is A♣♣♣♣♣-K♣♣♣♣♣-3♥♥♥♥♥ Flop is A♣♣♣♣-K♠♣ ♠♠♠♠-3♥♥♥♥♥

6 16.0 26.0

5 18.0 27.5

4 20.7 28.0

3 23.0 30.0

2 28.0 34.0

Table 2: The % win-rate of Q♦-J♠-T♥-9♦

Even with second flop, which did not include a flush draw on the flop, the win-rate of Player 2 was less than 36% (4 × 9 outs) though the win-rate approached its correct value against two opponents. The reason for this abnormality is the same as in the flush draw. If the turn card gives you the top straight, you could still lose the pot to a full house on the river.

If you flop a straight, you may still lose the pot. For example, you have K♥-J♠-9♠-8♣ and the flop is A♣-Q♦-T♥. Against five opponents the overall win-rate of the flopped straight is about 52%, and the pot will be shared with at least one of your opponents about 20% of the time. If you change the flopped T♥ with the T♦, the straight’s win-rate shrinks to 37%. Again the pot will be shared about 20% of the time the straight holds its grounds.

Guess who is the favourite when a flopped top straight is challenged by trips and a flush draw? The player holding the trips will win the booty just under 40% of the time, whereas the one defending the straight will celebrate about 32% of the pots. The flush draw will be fortunate about 28% of the time. Note that the win-rate of the flush draw is nearly as good as that of the made straight.

I am not against straights. They are good money earners but are fairly vulnerable, especially if there is a possible flush draw on the flop. The moral of the story is, ‘Straights have a high mortality rate in loose multi-handed games.’ I prefer flushes in such games; a flopped Ace-high flush

78 T HE S CIENCE OF P OKER

will sweep the money over 70% of the time, in a six-handed pot, whereas the flopped straight may scoop less than 35% of the pots.

Chapter Six