Morton’s theorem is a poker principle articulated by Andy Morton. It states that in multiway pots, a player’s expectation may be maximised by an opponent making a correct decision.
The most common application of Morton’s theorem occurs when one player holds the best hand, but there are two or more opponents on draws. In this case, the player with the best hand might make more money in the long run when an opponent folds to a bet, even if that opponent is folding correctly and would be making a personal mistake to call the bet. This type of situation is sometimes referred to as implicit collusion.
Morton’s theorem should be contrasted with the fundamental theorem of poker, which states that you want your opponents to make decisions which minimise their own expectation. The discrepancy between the two “theorems” occurs because of the presence of more than one opponent. Whereas the fundamental theorem always applies heads-up (one opponent), it does not always apply in multiway pots. The scope of Morton’s theorem in multiway situations is a subject of controversy. For example, Morton himself expresses the belief that the fundamental theorem rarely applies to multiway situations.
An example
The following example is credited to Morton, who first posted on rec.gambling.poker. (Some numbers have been changed to allow for complete information, see below.)
Suppose in holdem you hold A♦K♣ and the flop is K♠9♥3♥, giving you top pair with best kicker. When the betting on the flop is complete, you have two opponents remaining, one of whom you know has the nut flush draw (say A♥T♥, giving him 9 outs) and one of whom you believe holds second pair with random kicker (say Q♣9♣, 4 outs), leaving you with all the remaining cards in the deck as your outs. The turn card is an apparent blank (say 6♦) and say the pot size at that point is P, expressed in big bets.
When you bet the turn player A, holding the flush draw, is sure to call and is almost certainly getting the correct pot odds to call your bet. Once player A calls, player B must decide whether to call or fold. To figure out which action player B should choose, calculate his expectation in each case. This depends on the number of cards among the remaining 42 that will give him the best hand, and the size of the pot when he is deciding. (Here, as in arguments involving the fundamental theorem, we assume that each player has complete information of their opponents’ cards.)
E( player B | folding ) = 0
Player B doesn’t win or lose anything by folding. When calling, he wins the pot 4/42 of the time, and loses one big bet the remainder of the time. Setting these two expectations equal to each other and solving for P lets us determine the pot-size at which he is indifferent to calling or folding:
E( player B | folding ) = E( player B | calling )
When the pot is larger than this, player B should chase you; otherwise, it’s in B’s best interest to fold.
To figure out which action on player B’s part you would prefer, calculate your expectation the same way
Your expectation depends in each case on the size of the pot (in other words, the pot odds B is getting when considering his call.) Setting these two equal lets us calculate the pot-size P where you are indifferent whether B calls or folds:
E( you | B calls ) = E( you | B folds )
When the pot is smaller than this, you profit when player B is chasing, but when the pot is larger than this, your expectation is higher when B folds instead of chasing.
In this case, there is a range of pot-sizes where it’s correct for B to fold, and you make more money when he does so than when he incorrectly chases. You can see this graphically below
|
B SHOULD FOLD | B SHOULD CALL
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v
|
YOU WANT B TO CALL| YOU WANT B TO FOLD
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v
+---+---+---+---+---+---+---+---+---> pot-size P in big bets
0 1 2 3 4 5 6 7 8
XXXXXXXXXX
^
"PARADOXICAL REGION"
The range of pot sizes marked with the X’s is where you want your opponent to fold correctly, because you lose expectation when he calls incorrectly.
A. Bet What this basically says is, “I made something on the flop” or, “the flop doesn’t scare me”. Of course, if a pair of Aces came on the flop you’re going to probably scare off everyone, (except a player who holds an Ace) because raisers – particularly those in Early Position – are perceived as holding a hand like A-K, A-Q, etc. If the flop is more like 2, 7, 9 “rainbow” (unsuited) and you bet, you’re basically saying that you aren’t afraid of that flop because you have an over-pair (10-10 or higher in this case). Nobody’s really going to believe you flopped a set (Trips) or a Straight draw if you raised in EP, because very few players raise with 2-2, 7-7, 9-9 or J-8 from there.
B. Check This says, “I missed on the flop” or, “I hit a monster and want you to stay in.” If a pair of Aces come on the flop and you check, almost everyone will check behind you. The likely exceptions are those who have an Ace or those players who like to steal pots when a pair flops. If the flop is more like 2, 7, 9 rainbow, most players really will believe you missed the flop and they’ll feel safer in betting their hand.
C. Check, then call any bet made In this situation, you’re basically saying, “I have a good hand – probably a Straight or Flush draw or two-pair – and want to see if I can improve” or, “I have two over-cards and am (stupidly) trying to catch one of them.” Those who bet after you checked typically have one of four situations: they’re also on a draw (in which case their bet is a “semi-bluff”), have an over-pair (or two over-cards), they made something on the flop (perhaps Trips) or they’re just flat-out bluffing. If the flop is such that it’s “coordinated”, like 8, 9, 10 rainbow then they could be betting a set or a Straight – lots of people will call an opening raise with hands like 8-8 or J-Qs and so forth. Your call is saying that you either missed the fact that Trips or a Straight is out there or they don’t bother you. By just calling, you can be pretty sure that the original bettor will bet into you on the Turn if he really does have a hand and the card doesn’t appear to help you. If s/he somehow puts you on a draw, then you could very well face a huge bet because your opponent (if s/he’s smart) will want to make your draw too expensive to be a proper play. Hopefully you’ll recall that you need pot odds of at least 6 to 1 for an inside Straight draw, 3.3 to 1 for Straight and 3 to 1 for a Flush draw. Of course, if the bettor checks on the turn, it could be a good indication of a bluff, but it’s also a sign that s/he has hand that’s so strong (like a Full House), s/he wants you to “catch up.”
D. Check, then raise any bet made In my not-so-humble opinion, this is the strongest play of all. It says, “I trapped you” or, “Your hand doesn’t scare me.” It also might be saying, “I’m bluffing”, but few players will read that into your actions. You can pretty much count on the fact that anyone on a draw will fold when you do that, unless the pot odds are enormous at this point. You can also pretty much expect some players – usually those trying to “buy” the pot or those with a good, solid hand – to go all-in here. Whether or not you should call obviously depends upon what you hold, and the pot odds being offered. I love to check-raise, but actually use it sparingly because while you’ll win more hands with it, you won’t necessarily earn more $$$ by using it.
Okay, let’s discuss situation # 2 where you entered the pot with a raise, all the others either folded or called, the flop comes and a player acting before you bets. Besides folding, you can choose to:
While it’s best to memorize this chart, until you do just print it out and have it near you when you’re playing. You can see that as the higher card goes down in rank, the spread between it and the lower card gets tighter. That’s mainly because the only hope you have with a starting hand like 7-6o is to make a Straight and more Straights can be made when there are fewer “gaps” to deal with. For those of you who are Video Poker players, you know exactly what I mean; in fact, I found my experience at playing VP very helpful in recognizing playable situations.
Now look at the minimum hands for the mighty Ace. If the lower card is of any rank and is suited, the hand is playable, but if it’s unsuited, it should be no lower than a 10. As you’ll find out, most players will cling to A-xo until the bitter end. And you’ll most certainly lose some nice hands to something like A-6o, but in the long run, it shouldn’t be played. To draw an analogy to Blackjack one more time, folding A-6o is like hitting A-7 versus a dealer’s 9; not everyone does it, even though it’s the proper play. It may not “feel” right, but you’ll make more $$$ in the long run if you’ll do it. Math does not have room for “feelings”. Cold, perhaps but that’s how it is.
Pairs: No pairs are listed on here because all of them are playable at one time or another. Just remember that this list (and the pairs) is not a license to play these hands at any time, under any set of circumstances. For example, you’d be crazy to play 10-7s in an early position after 3 players have raised behind you. As I said earlier, this list is as much about what not to play as it is about what’s playable. So stop calling with those Q-3s hands and be patient until I show you the entire matrix. That will incorporate this list and the pairs into a complete strategy that takes into consideration your position, how many bets you have to call and so on. In the meantime, I have some homework for you and that’ll wrap it up.
Strip poker is a variant of the card game of poker, in which the rules require players to remove articles of clothing in response to various events.
Rules
The game can be played based on any variety of poker, with the same number of players, dealing and betting rules, etc. There are a number of ways in which the rules can then be developed into strip poker. For example, at the end of each hand:
The player with the worst hand must remove a piece of their clothing; or
The player who loses the most money in that round must remove one; or
The player with the best hand may remove it from them; or
The player with the best hand may choose which player must lose an article; or
All players except the winner of the hand lose an article. Note that this makes for an extremely brief game, unless fully-nude players are required to perform some action when they lose a hand, in which case it may even continue after all players are nude.
Alternatively, whenever a player runs out of chips, they must trade a piece of clothing for a new (usually fixed) number of chips.
If players are then allowed to “buy back” clothing when they have won more chips, this can result in a zero-sum game, where there is no long-term net loss of clothing. (With two people, this will have the consequence that only one of them is missing clothing.) (Note that “buying back” may be disallowed, so that the aggregate nudity is always increasing.)
As a further variant, players who have lost all of their clothing, achieving nudity, must perform sex acts.
Popularity
There are no known professional associations. The U.S. TV show Strip Poker is in fact a general knowledge quiz, albeit one where contestants take (some of) their clothes off; though it involves cards in poker hands, the resemblance to the actual game is distant.
The prefix “strip” can be added on to a game title with a subsequent nudity-inducing adaptation of the rules (examples: strip Candyland, strip chess, strip solitaire).
While a popular subject for pornographic fantasy and video games, genuine research into strip poker as a form of sexuality is lacking. The element of risk and of (mock) coercion fits in with a general sexual approach of domination and submission and/or humiliation.
Strip poker and other sexual games can occur:
as part of a mature sexual relationship, where the objective is to provide variety alongside intercourse (possibly introducing more adventurous/deviant forms of intercourse)
as a ritual of courtship (in some circumstances it may be more acceptable for partners to enter intimate situations as part of a game)
as recreation amongst adults with no intention to move towards sexual intercourse
as part of a pornographic display (whether as part of prostitution or not) which combines sexual titillation with the normal interest of seeing a game played
as a party game for youth
as the basis of television game shows such as Räsypokka (Finland - 2002) and Strip! (Germany – 1999)
If you’re following my recommendations on starting hands at no-limit Hold’em (NLHE), then you’re entering the pot with a raise probably 90% of the time. In this lesson, I want to discuss what to do when you’ve done that and several other players call to see the flop. If you think about it, the possibilities are fairly limited, so let me list them and discuss each one in order. If you have raised, a lot of what will happen on the flop really depends upon what position you’re in; a raise from under-the-gun (UTG) is usually perceived as being stronger than one from the Button, for example. Of course, none of what I’m going to cover will apply to each and every hand, but generally it’ll happen enough to allow us to draw some conclusions.
Please note that what I’m talking about here is the time when you enter the pot at a full or nearly-full table (7-10 players) with a raise and all of the other players either fold or just call. Situations where you raise and are re-raised are basically covered by the Starting Hands Matrix and I’ll discuss them somewhere in the future; for now let’s stick with the basic concept. If you raise and all of the other players fold or call, there are two primary situations you’ll encounter when the flop is dealt:
Situation #1. Everyone checks to you and you:
A. Bet
B. Check
C. Check, then call any bet made
D. Check, then raise any bet madeSituation #2. A player ahead of you bets into the flop and you:
A. Fold
B. Call
C. Raise
As you undoubtedly know, the vast majority of the time the other players will check to the raiser – it’s done so often that the saying is a part of poker lore. How you play your hand at that point “talks” to the other players and you need to remember that you might want to “say” something different, which is what we call a bluff.
“The end depends upon the beginning.” I heard that line in a movie recently and it certainly applies to Hold ‘em poker, although that’s not what the movie was about. At best, it’s extremely difficult to make a comeback if you enter the pot of a Hold ‘em game with a bad hand. I see it all the time and it happens, I guess, because so many people feel about poker like they do about Blackjack; “it’s all luck, anyway, so what’s the difference?” Well, if you’ve studied my Blackjack lessons the least little bit, you know it’s not “all luck” by a long shot. Sure, there is a luck factor that we cannot deny (I prefer to call it “variance”) but making the mathematically proper play for each and every hand goes a long way toward reducing the luck factor in Blackjack and that’s what we call playing Basic Strategy. Unfortunately, playing Basic Strategy alone will not give you an edge over the casino – which is why my Blackjack lessons also teach you how to count the cards – but the proper Basic Strategy for a given set of rules in a Blackjack game will reduce the casino’s edge over you to a minimum; generally 0.5% or even less.
Hold ‘em poker also has a “basic strategy” and it begins with the first two cards you’re dealt in the game, your “pocket” or “hole” cards. (I suppose that “pocket” cards is more the poker expression, so I’ll try to use that when I’m talking about a player’s two face-down cards in a Hold ‘em game, but forgive me now and then when I lapse into calling them “hole” cards). Anyway, it’s easy to imagine that if you were always dealt a pair of “pocket” Aces, you would win tons of $$$ at Hold ‘em. Of course, it wouldn’t be long before no one would play against you, but you get the idea. Great cards in the pocket are the start of a great hand. In poker, as in Blackjack, great hands win most of the time. Not all of the time, mind you, just most of the time. We don’t always win with a hand of 20 versus a dealer’s 6 in Blackjack, nor will we always win with AA (“pocket rockets” in poker slang) in Hold ‘em, but it’s still a good way to start.
So, how do you make sure you have a good start for a Hold ‘em poker hand? Well, that’s the beauty of the game of poker. If you don’t like your first two cards, you throw them away! It’s somewhat like the surrender rule in Blackjack, except it doesn’t cost as much. If you’re familiar with surrender, you can stop the play by giving up half your bet and, if surrender is allowed in the casino where you’re playing, you should do it whenever the mathematics say you’ll win less than 50% of the time. But 50% is a fairly steep price to pay for getting out of the hand. However in poker, it’s not nearly that much. In most poker games with 8 to 10 players, you’ll have to post a “small blind” and “big blind” bet only about once every 8-10 hands. All of the other hands you’ll get cost you nothing to throw away, so in, say, a $10/$20 game with a $5 small blind bet and a $10 big blind bet, it’ll cost you only $15 for each “round” of 8-10 hands to toss them. That’s a little more that $1.50 per hand and, with a $10 minimum bet per round, the percentage is only 15-20% if you always fold. It would be stupid to always fold, of course, but I want to contrast this with surrender in Blackjack where it would cost you 50% of your total bets if you always did it.
The point I’m trying to make here is that you do not have to play poor cards in a Hold ‘em poker game, but most beginners do. The wise player enters the pot on his or her own terms or s/he simply doesn’t play. This takes a certain amount of patience that many beginners seem to lack (“Hell, I’m here to play Hold ‘em poker, not Fold ‘em poker”) and you can take advantage of that. Just as it takes patience for the count in a 6-deck Blackjack game to get into positive territory, so it is with Hold ‘em. Good pocket cards don’t come along on every deal, so you’ve got to fold a lot if you expect to make any $$$ from this game. There’s no arguing that the game of Hold ‘em poker is much more complicated than the game of Blackjack, but both use decks of 52 cards and both are subject to mathematical analysis, so it’s actually possible for us to determine which sets of pocket cards are worth playing and which are not.
There are actually EV tables that show the long term statistical results of Hold’em hands. Another site has a copy of this chart, where it ranks poker hands by EV. This gives a numerical value to each hand combination, that easily shows the good vs bad poker hands.
Let me give you a crystal clear example: Which pocket pair do you think will win more, KK or 22? Hopefully the answer is obvious. A pair of deuces can be beat by any other pair out there but a pair of Kings can only be beaten by a pair of Aces. Of course, both are beat by two-pair, a set of Trips, etc. so a pair of anything isn’t necessarily an automatic winner when all five community cards have been dealt. But it’s actually fairly easy to determine which pocket cards will win in the long run and which won’t. It’s not exactly like determining how much we’ll make with a 20 versus a dealer’s 6 in Blackjack, because your position at the poker table, the cards that come on the flop, the turn and the river (Unfamiliar with these terms? See lesson 1.), the other players’ cards, how much is in the pot and a variety of other factors will ultimately determine the value of a starting hand.
But, believe it or not, we can assign some average values to all of those variables and come up with a nice list of playable pocket cards, which I’ll present below.
But before I do that, let me explain my “grand scheme” here. What I intend to ultimately present to you is a Hold ‘em Poker Basic Strategy Matrix, which is very much like the matrix I use in teaching Basic Strategy for Blackjack. But the Hold ‘em matrix is going to be a bit more complicated because it will take into consideration your position at the table, the number of players that called the bet before you, any raises, etc. Complicated? Yes. But remember that I’m teaching you how to play Hold ‘em poker at online poker rooms, so you won’t have to memorize anything! Just print out what I show you and keep it by your computer as you play. Of course, if you are willing to do some memorizing, then the process of evaluating a hand will proceed more quickly, plus you might want to use this information in a brick-and-mortar casino where using a “cheat sheet” may not be appropriate.
Like any other matrix, mine will be built in layers that hopefully have some sort of rhyme and reason about them. But I definitely know where to start and that is to give you a list of the minimum hands you should play. What I mean by that is this: Your pocket cards can only be one of three types: pairs, suited cards or unsuited cards. Obviously pairs cannot be suited; there is only one King of spades in a deck; get two King of spades as pocket cards and there’s a definite problem. Back in the Old West, you’d probably get shot for that. But to continue along, besides pairs (cards of equal “rank” but different suit), you can get suited cards (different rank but same “suit”) or unsuited cards (different suit, different rank) and that’s it. Within all of those various permutations of cards, there are 1326 different two-card combinations that can make up the pocket cards in a Hold ‘em game. Play long enough and you’ll get all of them, but there are only about 250 or so that you should bet on. Except for the pairs, each set has one card that is higher in rank than the other and that’s what forms the basis for my minimum starting hand list. For example, you might be dealt 10c7d (10 of clubs, 7 of diamonds) so the first thing you do is look at the card of the highest rank, which is the 10 of clubs. If the lower card of the two is equal to or higher than the minimum I list, the hand may be played. I say “may” because as we go along, you’ll see that your position at the table, the number of raises you may have to call, etc., will all have an effect on whether or not you play the hand. But if the lower card of the two is outside the “minimum”, you’ll just fold the hand, regardless. So, I guess this isn’t so much a list of hands to play as much as a list of hands to not play.
Let me amplify my example with the 10c7d hand. The absolute minimum hand you should play where the 10 is the high card is 10-7s. This means “10, 7 suited”; in other words, the two are of the same suit, like spades, hearts, diamonds or clubs. Remember that this is the minimum hand, so it’s okay to play 10-8s or 10-9s, because they are “above” a 10-7s. What about a 10-Jack, you ask? Well, that falls under the Jacks hands, because we always work off the higher card, so don’t get confused. Okay, what about 10 and something unsuited? The minimum hand there is 10-8o (10, 8 offsuit). I’m using a small “o” to represent unsuited (“off-suit”) only because that’s the way it’s done by most poker writers. I think it should be “u”, but they got here before me, so I’ll do it their way. Okay, so now we know that the minimum hand with a high card of 10 where the cards are not suited is 10, 8. This means it’s okay to play 10-9o, but not 10-7o. The cards would have to be suited for that. Obviously, 10-5, either suited or unsuited is outside the range, so it should never be played, period.
As you go through the list, keep in mind the rationale for most of these choices. Pairs can be improved in many ways and high pairs (Aces-Jacks) can often win on their own. Two suited cards of different rank can win by turning into a Flush, a Straight or a Straight Flush, or by improving to Two-Pair, Trips, etc. Two pocket cards of different rank and suit are not likely to turn into a Flush, and while they might make Two-pair, Trips, etc., they’ll most likely either make a single Pair or, if all goes well, a Straight. Generally you’ll see that the “bottom” card is at or near the low end of a Straight Flush for the higher card. For example, the minimum hand for a Queen is Q-8s (Queen, 8 suited) because the 8 is the lowest card that will make a Straight or Straight Flush with a Queen. If the Queen and the other card are not suited, the minimum hand is Q-9o. This makes sense, because you’re giving up some “flush power” with this hand; it’ll take four cards of whatever suit the Queen is in to make a Flush and somebody else may have the King or Ace and beat you. Just so we’re clear on this, if the higher card is a Queen and the lower card is of the same suit, Queen-8 is the minimum hand which means it’s okay to play the hand with a suited 9 or 10, also. But if you have, say, a suited 7 (or lower) with the Queen, the hand should be folded. If they’re offsuit, then a 9 is as low as you should go; not even an 8 should be played, let alone a 7 or lower.
Make sense? I hope so, but if not, don’t hesitate to e-mail me your questions. I always answer my mail personally and I try to do it within 2-3 days at the most. You’ll find my address at the end of the lesson.
Okay, so here’s my list of minimum starting hands. Remember that s = suited and o = offsuit or unsuited. Oh, yeah “x” means any card. By the way, this list is for Limit Hold ‘em; No-limit starting hands would be quite a bit different.
All casinos and many home games play poker by what are called table stakes rules, which state that each player starts each deal with a certain stake, and plays that deal with that stake. He may not remove money from the table or add money from his pocket during the play of a hand. Nor is a player allowed to hide the amount of his stake from other players; he must disclose the amount when asked. This requires some special rules to handle the case when a player is faced with a bet that he cannot call with his available stake.
For example, look at the hand of A-Qo (remember, “s” is suited and “o” is off suit). If you’re in Early Position (see Lesson 11 for the various position designations), you should raise with A-Qo. Now, look at the * (asterisk) next to most of the starting hands, including A-Qo. Down at the bottom, you’ll see this note: * = fold if a player before you raises preflop. So, if the UTG were to raise and you’re next to play, you fold with A-Qo or any other hand marked with an asterisk. About 90% of the time you’ll be either raising or folding. If you’ve read many books on no-limit Hold ‘em, you’ll often see the words “raise or fold” and it’s good advice. Also note that most of the hands have a “Fold” designation in the Early Position column. It means just that; you don’t limp and you certainly don’t raise in EP with A-Jo, you simply throw it away. About the only time you’ll call in EP is when you have 9-9 to Q-Q and the pot’s been raised in front of you. Those hands are just too good to fold, but they’re not strong enough to re-raise.
Let’s continue with A-Qo. If you’re in Middle Position and no one has raised ahead of you, (which would cause you to fold), you’ll raise with A-Qo. If one or more players have limped, you’ll still raise, but you should raise more than the standard 3 times the big blind, which is why I say, “Raise should be 3-4x Big Blind” in a note at the bottom of the matrix. You’ll fold if someone (anyone) re-raises after you. It’s tough to do, I know, but it’ll be the correct play the vast majority of the time. Oh, sure, you’ll get some player who will re-raise with A-10s every now and then, but most of the time you’ll lose if you call the re-raise. If you’re in Late Position, you should raise with A-Qo, assuming no one has raised in front of you (in which case you’d fold), but call if someone now re-raises you. Because the re-raise might come from an early position limper, you might wonder why you’d call and it all has to do with position. You’ll most likely be last to act for the rest of the hand, so it’s profitable to see the flop, then make a decision by how others bet it. See how this matrix uses hand strength and position to dictate the play? I’m sure it’s not perfect, but I will say it works pretty well if you follow it.
Okay, now let’s discuss the hand of A-Qo in the Blinds. You’ll notice that I didn’t make a distinction between the Small Blind and the Big Blind in the matrix. I did that primarily to keep it simple, but also because in most no-limit cash games the Blinds are a relatively unimportant part of the pot. Admittedly, they can be a factor in tournaments, but we’ll discuss that in a later lesson. For now, treat the SB and the BB the same. With A-Q in either Blind, re-raise a Late Position raise, but just call a raise made by a player in any other position. So, if the UTG raises, for example and you have A-Qo in one of the Blinds, just call, assuming it’s a 3x to 4x BB raise. If you re-raise a Late Position (“button”) raise and that player re-raises again, just call. How do you know to do that? You know because there’s not a “RR2″ designation on the hand. Looking at the notes on the bottom, you’ll see this: RR2 = Raise a Reraise. You’ll also see that RR2 applies only to A-A, K-K and A-Ks. So, a re-raise of your raise by a LP player warrants only a call.
Let’s say you’re in the BB with A-Qo and everyone has limped in. Regardless of their position – early, middle, late or SB – you should raise about the size of the pot, but certainly not less than 3 times the Big Blind bet. If someone subsequently re-raises you, it’s just a call because there’s no “RR2″ next to the hand, remember? If everyone folds to the SB and s/he limps by only completing the bet, then you should raise. If the SB raises, that’s a Late Position raise, so you should re-raise. Of course, if you have A-Qo in the SB, it’s the same as if you had it in the BB: re-raise a Late Position raise. But if the BB or anyone else re-raises you, then just call, because A-Qo doesn’t rate a “RR2″ designation.
You can see that there’s a (1) next to Q-Js in the Blinds column. That relates to the comment at the bottom. If everyone has limped into the pot, then raise from the SB or BB with Q-Js or higher. “Higher” refers to every hand above it in the left-hand column, which essentially means you’ll raise in that situation with any of the playable hands I show on the matrix. This situation will actually occur quite often in cash games because people like to see cheap flops, but you’re not going to let that happen, are you? If you get re-raised, just call because Q-Js does not have the RR2 designation.
And that’s basically it for now. Just play your hand as shown for the position you’re in and you’ll soon be holding your own in No-Limit Hold ‘Em. (Poor pun, I know.) When in doubt, fold; there’ll be another hand coming along soon enough. I’m not trying to turn you into a wimpy player, but folding is the best tactic if you’re confused about a hand. In time, you’ll begin to feel real comfortable with this matrix and as the $$$ come rolling in, you’ll know it’s working.
Oops! I almost forgot the ** designation that you’ll find next to the LP column up top. In the notes at the bottom, you’ll see this: **LP = 2-3 players left. This is a reminder that you must “open up” your game when you get down to 2 or 3 players left. As time goes on, you’ll find yourself as one of the last few players in SnGs and, because the Blind bets will be coming around a lot quicker, you cannot sit and wait for premium hands. When that happens, start making all of your plays according to the LP column regardless of the position you’re in. In the case of A-Qo, for example, you’d raise and call a re-raise even if you were UTG at the short-handed table. A-Qo isn’t a great hand at a full table, but it’s not bad when there are only three of you left.
In a game played with a fixed limit betting structure, a player chooses only whether to bet or not – the amount is fixed by rule. To enable the possibility of bluffing, the fixed amount generally doubles at some point in the game. This double wager amount is referred to as a big bet.
For example, a four-round game called “20 and 40 limit” (usually written as $20/$40) may specify that each bet in the first two rounds is $20, and that each big bet used in the third and fourth rounds is $40. This amount applies to each raise, not the total amount bet in a round, so a player may bet $20, be raised $20, and then re-raise another $20, for a total bet of $60, in such a game.
Four bet maximum
Most fixed limit games are played with a four bet maximum. This means that in a given betting round, there can be no more than three raises, meaning that on the betting round, only four bets of the given limit have been made.
Consider this example in a $20/$40 game, during a $20 round with three players that proceeds as follows:
Player A bets $20.
Player B puts in another bet, raises another $20, making it $40 to play.
Player C puts in a third bet, raising another $20 on that, thus making it $60 to play.
Player A puts in the fourth bet (she is usually said to cap the betting).
Once Player A has made her final bet, Players B and C may only call another three and two bets (respectively); they may not raise again because the betting is capped.
A common exception in this rule practiced in some card rooms is to allow unlimited raising when a pot is played heads up (when only two players remain). Usually, this has occurred because all other players have folded, and only two remain. Many card rooms will permit these two players to re-raise each other until one player is all in.
Some variations do exist for this exception. For example, some card rooms require that the pot became heads up before the third bet has entered the pot on that betting round. It is widely believed that this variation exists to prevent two colluding players from raising a third player out of the pot.
This exception to the four bet maximum has been observed in nearly all card rooms in the USA. It has never been observed in Internet card rooms.
In some card rooms, there is a five bet maximum instead of four.
Kill game
Sometimes a fixed limit game is played as a kill game. Such a game is played with an additional blind, called the kill blind. The kill blind can be posted from any position at the table. The amount posted is typically twice the typical blind for that game. For example, in a $20/$40 game, the large blind is typically $20. If this game were played with a full kill, the kill blind would be $40.
When the kill blind is posted, it changes the stakes of the game. For that hand, the game is played as if the game were a higher limit. In a $20/$40 game with a full kill blind posted, the hand is played as if the limit were $40/$80. The kill is said to be active when the kill blind is posted and the game is played at the higher limit.
Rules on how the kill is activated vary. On the east coast of the USA, the kill is typically activated by the previous pot being over a particular value. The most typical value is ten times the value of the large bet (in a $20/$40 game, the kill would be active if the previous pot won was greater than $400). The winner of that pot is required to post the kill blind for the next hand.
In the Pacific Northwest of the USA, a kill is typically activated when a particular player wins two pots in a row. After that player wins her second pot, she is required to post a kill blind and the kill is active for the next hand.
Note that a kill need not always be a full kill. For example, it is common to find a game with a half kill. For example, when the kill is active in $4/$8 game with a half kill, the game is played at a $6/$12 limit.
The term kill, when used in this context, should not be confused with killing a hand, which is a term used for a hand that was made a dead hand by action of a game official.
Okay, as promised, here’s a chart of probabilities for various hands you might hold at the flop, which means the first three community cards have been dealt. This chart assumes you’ll get to see two more cards – the turn and the river – and further assumes you won’t have to make any futher bets. That’s not likely to happen, of course, but remember that you might make your hand on the turn in which case the numbers become unimportant, because you’ll likely call (if not raise) any bet from that point forward.
Hand at the Flop
Becomes
At this rate of probability
Bet Multiplier
Two-pair
Full House
6.5%
-card Flush
Flush
5.0%
-card open-ended Straight
Straight
1.5%
.3
-card inside Straight
Straight
6.5%
Any Pair
Three-of-a-kind
.5%
2
Any Three-of-a-kind
Four-of-a-kind
.4%
2
If you miss making your hand on the turn, here’s a chart to help you decide if you should call a bet before the river card is dealt:
Hand at the Turn
Becomes
At this rate of probability
Bet Multiplier
Two-pair
Full House
.7%
2
-card Flush
Flush
9.5%
-card open-ended Straight
Straight
7.4%
-card inside Straight
Straight
.7%
2
Any Pair
Three-of-a-kind
.3%
2
Any Three-of-a-kind
Four-of-a-kind
.1%
8
The numbers to use to multiply your proposed bet in order to compare it with the pot to see if you’ll be betting with a positive expectation are a little on the conservative side, so adjust them if you can live with more risk, especially where you already have a “made” hand, such as Trips, etc. As I explained above, sometimes the hand you’re hoping to improve will be good enough to win the pot, so over-betting a little probably won’t hurt you in the long run, but remember that 4-card Straights and Flushes are basically worthless if they don’t convert, so I’d advise against “pushing the envelope” when it comes to betting those hands.
As I said in Lesson 1, Internet poker rooms are different than their brick-and-mortar counterparts and the instant tabulation of the pot’s value is one of those distinctions. Rather than spending your time trying to figure what’s in the pot, you can spend it by seeing if your bet will have a positive EV and, in the long run, that’ll be worth a lot of $$$ to you.
In poker, a made hand is one that does not need improvement to win, in contrast to a drawing hand. For example in Draw poker, if you have two pair, and your opponent is drawing for a straight or flush, you are said to have a made hand because even though you will be drawing a card just as he will, you can win even if you don’t draw a card that improves your hand, while he cannot win unless he improves.
* = fold if a player before you raises preflop and you’re not in the Blinds
R = Raise – Should typically be 3-4x Big Blind
RR = Reraise – Should be at least double the raise
RR2 = Raise a Reraise – Usually want to get all-in
EPR = Early Position Raise
MPR = Middle Position Raise
LPR = Late positon Raise; includes SB if you’re BB
**LP = 2-3 players left
(1) If all players limp in, then raise w/Q-Js or higher from the BB
Copyright 2005 GameMaster OnLine, Inc. Permission to copy for personal use is granted.
Revised 2-05
Got it? Good. The first thing you’ll notice is that it’s not very big and certainly not nearly as complicated as the matrix for Limit Hold ‘em. The reason is simple: All of the hands you should play are listed in the first column. If it’s not on here, you shouldn’t play it, period. No A-5 suited, no K-10 offsuit, no 6-7 of any type; you just don’t play hands like that in no-limit Hold ‘em, at least as a beginner. Okay, I know I opened a door here by saying “at least as a beginner” and I know you see Fossilman and Gus Hansen and Clonie Gowan playing hands like that, but remember, they’re not beginners. This isn’t limit Hold ‘em where a dumb mistake can cost you a bet or two – this is no-limit Hold ‘em where a dumb mistake can cost you your entire stack, be it tournament chips or real $$$. Plus, this matrix is designed to have you open the betting with a raise as often as possible, but seldom just call a raise ahead of you.
A game of skill is a game where the outcome is determined mainly by mental and/or physical skill, rather than by pure chance.
One benefit of games of skill is that they are a means of exploring one’s own capabilities. Games encourage people to look at, understand, and experience things. They teach people lessons about themselves and possibly the world, and allow such insights to be passed on to others.
Morton’s theorem is a poker principle articulated by Andy Morton. It states that in multiway pots, a player’s expectation may be maximised by an opponent making a correct decision.
