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“Don’t Believe Everything You Have Read”

I am not referring here to the simple probability of your making a hand, but about the odds of your winning and losing money in a given hand. Remember that we keep score in poker by counting out money at the end of the session, not by the number of winning hands we make.


        The pot is $100 and you face a bet of $100. Thus the pot now stand at $200, and you are receiving 2-1 for your money. It is sixth street in seven card stud poker, or there is one card to come in Omaha. In both cases it will be about 4-1 against your making a flush. Thus you shouldn’t call heads-up. But several books suggest that, if there are players yet to come, then you can include the implication that they will call if you co. Thus, if you think two are going to call, now you have 4-1 for your money. This is absolute nonsense. Each of these players may pass, they may call, or they may raise. You do not know what is in their minds.

         Correctly, the tern “implied odds” refers to the amount of money extra to that already in the pot you are likely to win if you make your draw. Here is a good example from Omaha. Your hand is A-10-2-2. The board is K-Q-7-2. In other words, you have hit the mystery trips on fourth street. The pot is $1000, you are last to speak, and the only other player bets $1000, having led out on the flop. You will win with eight hearts, one deuce, and certainly not lose the pot with a jack. Thus you have 12 outs. But you can only see eight cards, and are assuming the opposition has three kings. Thus you win only with 12 cards in 42. This is worse than 2 to 1; in fact 2.5 to 1. If a flush comes, you cannot expect to be paid off. If a jack comes, you may split the pot. If not, there is a very fair chance he will came out betting, or check and call your bet, thinking you are bluffing. If the fourth deuce comes, not only is he going to come out betting, but he is going to stand a raise and may even reraise. Passing this hand would be madness. Strangely enough, from your viewpoint, it is better if he has trips rather than two pair, if you intend to pass a bet at the river if the board blanks. This is because you have a much better chance of being paid off if you hit the nuts. By the way, if the board blanks or pairs and he checks, do not assume your trips are winning and automatically bet. He may be lurking in the grass.


This concept of implied odds is a sufficiently important poker concept for us to take another example. In hold’em you have 10-8. The board is 9-6-2-K. You have three nut outs and a further nine hearts which may also be winning. Facing a near pot-size bet, you must assess the likelihood of your being called if you make the hand. Certainly the odds are inadequate on their own.
         It is always an advantage to act last in such cases. You are far more likely to be called if you are you are last to speak rather than if you must come out betting. In addition, what are you going to do if a heart arrives at the river and he bets out? Your flush is not the biggest.

         Sometimes in poker games you must play intelligently after all the cards have been dealt in order to receive the implied odds you imagined existed. e.g. at Omaha, you hold A-Q-Q-10 and the flop comes J-6-2. John is to speak before you, and Ann after. The pot stands at $100. John checks; you bet the pot with an overpair and the nut flush-draw. Ann calls, as does John. The board now brings (J-6-2) 8. The pot is $400. John checks, you bet $300, and Ann raises $1000. John calls. What is going on, and do you have value for a call? John’s holding is a mystery, but Ann presumably has trips. You must pay $1000 to win $3300. It is most unlikely neither has your cards, and certainly a queen may not win you the pot. In fact, it may prove to be a trouble card. They will probably both pass if a non-pairing flush card arrives. However, you may do very nicely if a nine comes up. 

       The last card is the (J-6-2-8) 9, making you the nut straight. Now John bets $2000. This small amount is disappointing. The correct play is just to call. Now Ann may call without any straight, because she can gain $8300 out there for just $2000. The fact we know trips is worthless is irrelevant. If you were to raise, John, an intelligent player who may be bluffing, will only call if he is sharing the pot or possibly if he has the under-straight. You must normally be content with $2000. Time and again I have seen players raise in this situation. What they hope to gain out of it, I cannot imagine. By the way, similarly if you are in John’s position, it is better to come out betting than to trap. If the nest player is doing his job and has the same straight, he will just smooth-call and hope to gain money from losing callers. If you check and the second player bets, the sandwiched player may be more likely to pass, fearing the possibility of a raise from you. 
       I was rather dismissive of making assumptions about how players yet to act will behave. Sometimes a reasonable assessment can be made, as in the following hand I played in Las Vegas in February, 1994. At pot limit Omaha poker the first player to speak bet, the second raised the pot, and I called with 9-8-7-5. Three more players called. The first player now raised the pot all-in for $2000. The second player called for $500. I had bundles left but none of the three following players had more than $2000; in fact two had less. I correctly assumed the first player had aces. Whether I had adequate odds is unknown to me. But I surmised, once I called, they would follow suit, rather like lemmings. I had my implied odds. Thus I called, the others went all-in, and I won the pot. I wonder if the hand would have been so memorable had another player scooped the pool?


        Again, this is badly misunderstood in pot-limit or no-limit. You hold (A K) 2 9 in seven card stud. There are no other hearts on board. It is checked to you. You bet, and Harry (a vigorous player whom you know stylistically has at least two pair and is locked in to the bitter end) raises the pot-size of $100. It is now going to cost you $100 to win $200. We know it is about even money to make a flush in the next three cards. But are your money odds truly 2-1? If you call, the pot is now #300. You haven’t made the flush and he bets out $300. You call. The pot is $900. If you decide to call on sixth street, despite not improving, you will have wagered $1300 to win $1400. This is not quite the 2-1 you had in mind. If you raise on fourth street and the two of you get all-in, then you will be receiving only slightly better than even money, as already shown.
       Here is a paradox. Had you taken him all-in on fourth poker street, then your odds were reasonable. If you call on fourth street, setting your mind to call on fifth and sixth, unless he breaks out into an open pair; then on sixth street it is a mistake to call. You are a 4-1  underdog. Yet, you have avoided the full house disaster until seventh street. My was going all-in okay and playing along all wrong?

       If you have an extremely live four-flush and he has two pair, what are the true odds against winning the pot from fourth street? Although two pair have only four improving cards and are thus nearly 10-1 on each card, overall they are only about 3-1 against filling up. Thus they hit 25% of the time. You can only win 75% of the hands, and this reduces you winning hands to 40%, a 3-2 dog. Let us hope this explodes the myth that you should pour your money in on fourth street with a four-flush. Once you fear two pair, or the dreaded trips, you should switch off.
       Four cards to an up-and-down straight has eight outs rather than the nine of a flush and, what’s more, is a lower-ranking hand. However, it has one great advantage over a flush-draw. If you make it on fifth or sixth street, you are much more likely to be called. Your implied odds are enormous.

       In both hold-em poker and Omaha poker, you are approximately a 7-4 dog to make a flush with two cards to come. With a board such as 8-4-2 and you holding A-J, you may well also win with an ace or jack. In Omaha, if you hold A-A-Q-7, you should fear that an ace will give you a loser. If the heart pairs the board, you will be traumatized by the fear of a full house, which is why we recommend only thinking in terms of nut outs in that game.


       The “reverse implied odds” is the amount of money lost that result from completing a draw, yet failing to win the pot because the opponent either has or makes a better hand. Here is an example. A grand is in the pot. You hold (K 2) 9 2 J 4 at seven stud. Your opponent has (??) A 9 3 7. He check-raised you on fifth street and bets $1000 on sixth street. You have seen.

       Clearly you have only 9 outs from 40 cards, and thus the bare odds are inadequate. The implied odds must be considered. Let us assume he will check on the river, irrespective of his holding. Provided he has at least aces up, the typical player will call your river bet. Thus you determine not to bluff at all. If you call, 31 hands out of 40 you lose $1000 (-$31,000). On the other nine hands, you make the flush and bet $3000 (+$45,000). This seems quite a juicy price. But he has 4 chances in 40 of making a full house. In that case, which arises statistically on one of the hands where you make the flush eight hands, winning $5000 on each (+$40,000). One hand you lose an extra $3000 (-4, 000). Thus your implied win for this hand is not $45,000, but $36,000. This is a very healthy 12.5% and certainly cannot be passed up. Of course, in real life he doesn’t invariably call. But on the other hand, you don’t invariably pass his check-raise.
       This type of reasoning is hardly ever relevant in limit poker. You invariably have adequate odds for your money for such a draw. In no-limit, with the added potential of being able to bet more than the pot, the implied odds really blossom.

       In Omaha, the “reverse implied odds” are a major consideration when you have called a couple of players to make a straight with two cards to come and there is a two-flush on the board. You may well make your straight and yet be beaten either by a full or flush. In lowball draw, you must consider the reversal very seriously. You cannot pass all your drawing hands, and if you await a draw to the stone-cold nuts, the antes will swallow you up. In London lowball, you must never call a pot bet in order to make a hand such an 8 low, where the opponent may be holding an apparent 9 or 10 low, but is drawing under you to make a 7. Only in hold’em is the reversal relatively less importance, because so many pots there are won by less than the maximum possible hand.


       There is another factor at work when we take a wide view of the term “implied odds.” Certain steamers figures to go on tilt if they lose a big pot. Hitting a longshot against them like a middle-pin straight may send them over the moon. Here is a hand where the tilt factor was taken into account.
       At Omaha, Stewart Q-Q 9-8. Flop Q-3-3. Chris Bjorn led out, Stewart called, and Jimmy raised. Chris passed and Stewart called. On fourth street, Stewart checked, Jimmy bet, and Stewart called. At the river Stewart checked and Jimmy bet. There was 30K in the pot. Stewart had discounted Chris’s bet as a herring, and knew Jimmy might have 3-3. Anyway, he raised the remaining 5K and Jimmy called, showing down the quads. Stewart’s sole reason for raising was that Jimmy would have gone on tilt in a big way had he lost the pot, perhaps blowing another 50K. Divided among the other five players at the table, that comes to 10K for Stewart. Thus he had 3-1 for his extra 5K, not mere even money.




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