Tuesday, 28 August 2007

Winning is the nuts

So I am enjoying poker at the moment, probably for two reasons. First, I haven't been playing all that much, and second, I'm winning what I do play. This is not a proud boast, because I've been playing very small games, just for fun.

In mid-July, I had the flu, and took a break from poker for a couple of weeks. Since then, I have been beating the $5 SNGs very nicely but have only been playing on average a couple a day. I'm confident that my stats are converging on my true win rate now. Opinions differ on how many games are enough. Some think you need to play thousands to be sure; but I read something in 2+2 magazine that suggested that, if your win rate is high enough, a few hundred games are enough. I have records for about 420 games, and I'm beating them pretty well. My plan remains to play a thousand and move up if I'm still beating them.

But at the moment, for fun I'm playing the turbo $1.50 HORSE SNGs on Stars. I've started crushing them, which is a sure sign my poker has improved, because, say six months ago, I was better than average but not running anything like as well as I am now. I'm probably running a bit hot, winning those close calls that so often crop up in turbo SNGs, but I feel I'm playing them well.

My opponents make lots of mistakes, the most painful being that they play far too many hands and then chase what are fundamentally bad draws. The way they play razz is simply hilarious. You are on fifth street, showing three babies, and they call your bet with paired kings and a baby. Now sometimes they are going to make their runner-runner low, but these guys will be drawing to an 8! Occasionally, they beat you because your much better draw doesn't come in and you can't beat an 8, but that's rare enough that they are not ever going to be winners at razz.

It's one of my better games at this level, simply because I'll play reasonably soundly and they won't. I realise, of course, that most players at the bottom do not know how to play razz, and don't care. If they mostly folded, that would probably be okay. Playing tight, in any form of poker, is usually going to be correct (at the earlier levels; some make the corresponding mistake of playing too tightly when very shorthanded).

I have an even bigger edge in holdem, and if we happen to be on holdem when fivehanded with high blinds, I like my chances. This is simply because I am good enough to beat microlimit holdem, and most of my opponents only play NL and have no idea how to adjust.

Omaha8 is tougher, because it is better for the fish, but playing for low is enough to see you through. It's difficult to play at this level because other players will have all sorts of hands, and you can't count too much out, so not having the nuts can kill you. For instance, I played a hand today in the BB, where I held 55xx. The flop came 995, giving me a full house. I'm almost certainly ahead on the flop, of course (because only 95xx and 99xx beat me, and they're pretty unlikely to be out), so I bet and get called in three places. Given that there's no low draw on the board, you just know that at least a couple of those guys have pairs and are drawing to their two outers. So, naturally, a guy turns his 7 and makes a bigger full house. Unfortunately, the 7 also made a flush, and some idiot bet that, so it cost me three bets to show down. I could and probably should have folded, but it was just about possible on that board that I'm against a low draw, a 9 and a flush, these players are so bad.

The stud games I'm improving at. Hi/lo is easier because players will so obviously be drawing for half the pot that you can often get half uncontested. I'm not very sound in stud, but I can hold my own. I've learned a few concepts recently that have helped (obvious things like this: before now, I might have folded mid pairs for a raise; now I will sometimes call if they are live because playing too tight is a mistake in stud -- same with draws: I'll call sometimes so long as my draw is very live and has other possibilities).

I've also had three goes at triple draw. And frankly, I rock. I've won two out of three. I read the Negreanu chapter in SuperSystem 2, and although his advice is for slower tournaments, what I remember of it works pretty well in an SNG. In tougher games, I'd need to pay more attention to pot odds and play more accurately, but at this level, there's no need at all. This is why. Threehanded, some guy limps and I raise with 732xx. I change two and he changes four. I am not kidding. I pick up a 4. I bet, he calls. I change one and miss. He changes three. I bet, he raises, I threebet the monster draw, he calls. I change one, and pick up the 5 to make the nuts. He stands pat. I bet, he calls and shows a 9-8-7. Well, maybe I'm bluffing on the end, and he has to call, but his play just sucks throughout. This is one of the better opponents. Others draw two to 9s, call raises and then show down hands that do not feature 2s or even 3s, refuse to call on the end when the pot is huge or call with pairs or very high lows in smallish pots. One gave me a lecture for folding for one more on the end. To be fair, the pot was reasonably big, but I had made a straight. The chances that the other guy had a hand I could beat were tiny. I said, I had a straight. He said, you are a idiot. I said, well, one of us is. Maybe he thought a straight was a winning hand.

Sunday, 19 August 2007

Small woot

Sometimes my progress in poker has seemed agonisingly slow, and the milestones far apart. So little things mean a lot. I've been playing $10 sngs on Party, because I was clearing a bonus and the rake is the same for a 10 as a 5, ridiculously. I've been going okay, not having much luck, and was breakeven before today (in only a handful of games). The games are ridiculously soft, so that's no big thing.

So I have been playing a few games at Party, and a couple of 5s at PokerRoom. First up, I came third in a 10, which made me just better than breakeven, which made me happy. In a five, I limped and called a raise from the BB with 99. The flop came Jxx, rainbow and raggy. The BB checked and I bet. He called. Now, only a clueless player would raise AJ at low blinds in an sng, and you'd need to be double clueless to flatcall a bet with it here. So I'm putting him on AK/AQ, maybe a pair, and when the turn is a rag, I'm willing to get the money in. Sigh. Most times, I shut it down on the turn, because even if I'm good, I don't want a big pot, but I thought I might get paid by a big ace.

Well, if I didn't make mistakes, I'd be a robot. He turned over AJ and IGH.

Next up, I was delighted to get my chips in preflop with KK. My opponent, loose and retarded throughout, had TT, which made me even more delighted. I was a lot less delighted to see a T on the flop. At the same time I was playing a turbo, and with a bit of luck, which you need in turbos I think, particularly if the other players are tightish, which they were, I got to heads up. No luck though. The blinds were huge, so it was pretty much a crapshoot. I do a lot better when there's some play, and I can use fold equity to win a lot of pots.

I had already started another five and the ten had filled, so I was playing both while finishing the turbo. So I got a nice stack in the ten, and a not so nice one in the five, but the players in the latter seemed to want to throw chips at me, so by the time we got to the money, I was in good shape, with three of us on about the same size stack. My two opponents obliged me by going all in, and I had the luxury of throwing away a decent hand -- AT, I think -- knowing that I would be guaranteed second. The guy who won that clash had played quite LAGgy throughout, having pulled a big stack early. I had let him steal a couple of pots with minraises, and now he tried that again, and I punished him several times with resteals. I soon overhauled him, and I think that demoralises bad players, so that they lose discipline. I easily won it from there, with the other guy calling a push from my top pair with nothing at all. Meanwhile, in the ten I'd played a nice game, patient early, aggressive later, and had the luxury again of watching players with decent stacks knock each other out. A huge suckout in the money, with 55 catching its set against QQ, finally paid me back some of the bad luck I'd been suffering. I then caught the same guy stealing, calling his push with K5s with 99, which held up.

So I'm heads up at both tables, and going well. I pick up KQ in the ten and get it in. The other guy calls with K9s and of course he flushes. Now 1740 chips at t600 blinds is what we call being in very bad shape. At Party, there are 20,000 chips in play, so the guy has me more than 10 to 1 in chips.

So I pick up 84 and push. I'm pushing any two every time until I am no longer blinded out. There's no option. Of course, I'd like better cards, because he has to call here.

Or not. Unbelievable! I sometimes just cannot believe how bad the players I'm against are. I'm no Phil Ivey, fair enough, but how bad do you have to be to fold in the big blind against a guy with less than three BBs! I started cursing that I was so far behind, because this guy totally deserved to lose. Next hand, he folded. What teh fuck?

Next hand I picked up Ac9c and pushed. He folded again. Next he called in the SB and I pushed with J5. He folded again. Unreal.

Now I'm in better shape, although still on the ventilator. I fold my next hand, J4, because I am sure he will have to spite-call the next push. I figure that I can wait till the next hand to go for it again. So I pick up 54s in the BB and he minraises. There is no way I'm folding, and he might, so I stick it in. He has K8s, so my cards are live, and I river a 5 to double up.

Now I know I will win. I am still way behind, nearly 2 to 1 in chips, but I know that I will win this game. He just isn't good enough to beat me.

So a small woot for me. I won a $10 sng for the first time. It doesn't sound like much, I know, in a game that sees millions bet, won and lost every day, but in my small corner of it, it's a big thing.

Wednesday, 15 August 2007

Think about the future

So I'm playing a HORSE tourney, and I pick up 9d8d. Here is the hand:

PokerStars Limit Hold'em Tourney, Big Blind t500 (7 handed) Hand History converter Courtesy of PokerZion.com

MP2 (t666)

Hero (t6444)

Button (t6758)

SB (t16859)

BB (t3545)

UTG (t6537)

MP1 (t9133)

Preflop: Hero is CO with 9d, 8d.

2 folds, MP2 raises, Hero calls, 1 fold, SB calls, BB calls.

I should note that the raise was to 660 or so.

Flop: (5.32 SB, t2664) 4c, 7d, Jd (4 players)

SB checks, BB checks, Hero bets, SB folds, BB folds.

Turn: (3.16 BB, t3164) Qc (2 players)

River: (3.16 BB, t3164) 4h (2 players)

Final Pot: 3.164 BB (t3164)

So the other players start whining in chat. A guy posts "?" and I know he means "why did you bet into the sidepot?" So I tell him it was for value. "You didn't get any," he said. (The allin guy had A7 and I didn't draw out on him.)

I realise I am having a conversation with someone who knows nothing and I should stop. I say I'm too busy to give them a lesson in poker.

And the other guy says "dude, there is no value in betting at an empty side pot with someone all in".

But there is! How clueless can you be? A bet for value hopes for a call. I wanted both guys to call me, paying me 2 to 1 on my gutshot straight flush draw. I have 12 outs to beat top pair! If one calls, with precisely top pair, I don't make the value I hoped for, but if both fold, and the allin guy has less than top pair, which is very likely, I have 18 outs (and if I'd folded out a bigger 8 or 9, and an 8 comes, my bet was a coup!). By putting money into the sidepot, I also increase my chances of getting paid another bet when I make my hand. With the dry sidepot, it's easy for these guys to fold when the flush card comes. With money in it, they might think their pair is still good and call what they take to be a bluff.

Eighteen outs make me a huge favourite. Poker is about betting when you have the best of it, not about taking results as a guide to how well you played. You don't always get value when you bet for value. Sometimes you are actually behind; sometimes you fold to a bluff. But you calculate spots where you should have some value and make the right play. The only bad outcome for me in this hand is just one caller with a pair better than 9s or better (or who has several of my outs, or both: say he holds TcTd). As it happens, I had the 18 outs, and I was unlucky. They don't grasp that.

Players don't. They see what they take to be terrible plays and cannot grasp why they weren't. That's why it's possible to win. Take the following two plays.

In an sng, I raised with some shit like A6s, A7s. The BB pushed. I called. I was being offered more than 2 to 1 by the pot, and had him covered. He had a bigger ace, but I sucked out. Cue the whining. "Only idiots get lucky like that..." he whined. He thinks I'm an idiot for calling with A6s? Dude, only an idiot would fold. The blinds were high and he can be pushing pretty wide. Against the top 20% I'm 45/55! Against the top 10%, hands that nearly everyone would push from the BB in this spot, I'm 39/61. I think the guy's looser than he is tight, but even at the tight end, I have a thin call. The guy has just looked at his cards, and looked at my cards and thought, he's called with trash. He hasn't given any thought to the pot odds on offer, or to the fact that I don't know his hand until he turns it over, and must guess what he might have.

In another game, it's the bubble. I'm UTG with KJs. I have the BB covered, but not by very much. Neither of us is very very short, but we both have about 6BB. The bigger stacks have been playing tightly, and are not enormous. I shove and he calls.

He should show me AA/KK. Anything less is an autofold.

But he has AQ. If I push as loosely as the top 20% (and I don't), he is less than 60/40 to double up. But, as I discussed, doubling your chips is not doubling your equity, and this is a bad bet to take. This player will probably never understand that. Which is why, over the long term, he will lose money at sngs, and I will win it. (In case anyone reads this who doesn't get why his call is bad, imagine you have ten occasions to make it. You win six times, and lose four. The six you win, your equity increases from, say, $20 to $30, the four you lose, your equity is of course $0. So when you win, your equity gain is 6 x 10 = $60, and when you lose, you lose 4 x 20 = 80. These aren't the correct figures, but the general idea is correct. The fall in equity when you lose is so much bigger than the rise when you win that you lose money in the long term by taking even those gambles that favour you strongly.)

AQ is a good hand. It's hard to fold it. But being able to fold is a key skill in poker.

But was my push good? Surely I have more risk? Well yes, if I know he has AQ, and furthermore, know he will call. But I don't. (Well, I could be pretty sure he would call with that because he hadn't shown any sign of having a clue.) Mostly, all fold. There are a lot more bad hands than good ones! I probably wouldn't push this hand at a table that was calling loosely, but this one had been playing tightly, as I noted. My hand will play well if I'm called. My combined chances are good enough to make a push worthwhile here.

Thursday, 2 August 2007

Dan don't do donkaments

You see this advice all the time.

Play tight early, steal blinds as you get shorter, become insanely aggressive when you have a very short stack.

It's the received wisdom. It's how Dan Harrington plays. But Dan Harrington doesn't play donkaments.

I play like this too. Ultratight early, gradually loosening up. Most tourneys I go fairly deep but I'm fairly short. I cash quite often but not usually for much money. I'm kind of at the mercy of my cards. If I get decent cards, I might double up early and then I'm well fixed. If I double up twice, I can usually go quite deep.

Hang on. There's a theme in there, isn't there? I do well when I double up. I don't do well when I just survive. So why am I playing just to survive? I'm all too aware that converting AA/KK into a doubleup requires a bit of luck: someone willing to gamble with you with a worse hand.

Now, doubtless in a 10K entry tourney, with two-hour blinds, playing ultratight is best. You are going to get plenty of hands and you do not have too much pressure on you. You might only get 60 hands at those blinds, or even fewer, but that's a lot more than the 10 min, 20 max that I get in a donkament. You will also be at the same table for some time. In donkaments, I am usually moved in the first hour. What's the point of having an ultratight image if you're moved before you can use it to advantage?

So I've started playing like a fish on the button. But only on the button. I'll play just about any hand for a single bet, and I'll play anything promising for a raise. The donkeys never fold, so I can't win by bluffing. I have to hit my hand. It's still possible to smallball a few pots when things go your way -- I'm not saying I have to nutpeddle. I'm just saying that with weaker starting hands, you cannot be so sure that your pair is good. But playing tight just does not give you sufficient chances to hit anything in a donkament and playing more pots gives me more chance to take the money from the useless players who are spraying chips around early.

I suppose what it boils down to is this: say I play in a 300-player tourney. I play virtually no cards and watch all the dead money rearrange itself. I get down to 1000 chips and have to pick a hand to commit to. So I'm pushing my AQ. And get called by a pair of 3s and IGH. That's half my tourneys. The other half, I chip up but get stuck behind a bigstack who is LAGging it up, never pick up anything I can challenge him with, and find myself at t200 with 2500 chips, finding myself unable to raise anything that I don't want to commit myself to going all the way with. That's the problem with the play tight, then loosen up plan. My opponents already play looser than I do, even if I loosen up. And they are not as scared of the bubble as theorists think. They'll call you with that pair of 3s if they have you covered.

Wednesday, 1 August 2007

Information is power is money

Information is power. More commonly, people say that knowledge is power, but information is more readily quanitifiable. Often, if I know how much information advantage I have over you, I know how much power I have over you. I think this is a key concept for a realist such as me. Another, related, concept is that no information is hidden. This is a different thing from saying no information is obscured or even no information is unknown. It says no information is privileged. Basically, information is in principle discoverable by anybody and is never esoteric. This doesn't mean you will be able to uncover all information, because you may not have the tools to understand or use it, but it means that you could in principle acquire it without having to know magic words, do rituals or sacrifice goats.

There aren't too many discussions of ICM online, so maybe people will stumble on this and it will help. Maybe not.

Two things boots said in comments lead me to make this post:

I'm not sure what "ICM" is but I think it might be a mistake to equate any specific school of thought with capability.


It puzzles me how you can expect to grind out $50/hour playing poker when you seem to think it is a matter of maths and mindreading.

Knowing the answers to the two questions implicit in these comments is the key to winning SNGs, and I know both answers. If you bear with me, you will too.

I will begin with the second. In a hand of holdem, the players are given two cards that they can see and others cannot. The hands are dealt quasirandomly.

It's not important that random number generators are not truly random, so long as the distribution of outcomes from them resembles the distribution of random outcomes sufficiently closely. For the purposes of poker, it does. You might think that a computer could create more random outcomes than a human dealer, but you would be wrong. A well-shuffled deck (which is rather less shuffled than you might think) will give a truly random outcome.

Here is a key understanding that boots lacks. The distribution of outcomes in a poker game is normal and the outcomes will converge on expected values over enough trials. These are important things to know, because they underpin the mathematical understanding of poker. If you're not clear what I mean, I'll explain. Say you flip a coin with me. You probably know that your chances are 50/50. But you could flip a coin a hundred times and get 60 heads, 40 tails. This does not mean your coin is not fair. Chance converges on expected values over many trials. Flip the coin a million times and you'll be close to 50/50. I won't explain why (mostly because I have an intuitive grasp of why and can't explain the statistics adequately, but much of statistics depends on its being true).

Now it's true that in a normal distribution, not every outcome sits neatly around the mean. You do get outliers, and it's perfectly possible to see a long run of outlying values. So you can be "lucky" in this sense. But working on the assumption that values are close to their expected values will generally be correct. What does this mean? Two things. First, the distribution of cards dealt will tend to be "sane". You won't see many hands in which two guys have aces, and two guys have kings. You might see that hand. It's possible, and every possible deal has equal likelihood (an important thing to remember in considering random outcomes: in a lottery 1 2 3 4 5 6 truly is equally likely as 1 23 32 37 42 45; however, a mistake people make is to think that you are as likely to have the consecutive numbers as spread ones -- you aren't: there are far more outcomes with spread numbers, so they are much more likely). Second, outcomes on the flop, turn and river will tend to their expected values. Say you have four to the flush on the flop. Your chances of hitting by the river are a bit less than 2 to 1, on some (slightly dodgy but necessary) assumptions (we always assume that all unseen cards are equally likely, but of course ones held by your opponents are not). So you would expect to hit one in three times. But you can hit three, four, a dozen flushes in a row.

What can a player do about that? Try his luck and hope he gets the flush when he doesn't have the odds? No. He plays to maximise his value over the long run. What he tries to do is lay his distribution of actions over the distribution of outcomes, so that his profit over the long run, when outcomes converge on expected values, is at the maximum.

This is the correct way to play poker. Whatever you think, boots, however much you sneer at playing by maths, this is the best method to increase profit over a lifetime. Those three words are important. Remember, you can flip 60 heads from 100. Over 100 trials, you might or might not be maximising your profit by playing the odds. Over ten million, you can count on it.

I'll come back to the mindreading.

I'm not sure what "ICM" is but I think it might be a mistake to equate any specific school of thought with capability.

I'll explain ICM. It's a reasonably simple concept, but essential to SNGs, and yes, it does equate with capability.

Two concepts need to be understood. First, at each point in a tournament, all remaining players have a "share" in the pool of winnings. (Even if someone has been paid out, there is still a remaining pool that you share in.) This is called your equity. It's somewhat like equity in a company. It has a value that is not realisable on the spot but is quite real. If you have a stock, you have a share in a company that can go up and down. And your equity in a poker tourney goes up and down. Second, SNGs are not generally winner take all. In this discussion, they have a distribution of prizes of 50/30/20. In a $5 tourney, the winner takes $25, second place $15, third place $10.

When I begin an SNG, I have 1500 chips. So does everyone else. The prize pool is $50. My equity is $5. This is because I have 1500/15000 = 1/10 of the chips, so I have 1/10 of the prize pool. But this is because I have 1/10 of first ($2.50), 1/10 of second ($1.50) and 1/10 of third ($1).

Say I double up. I now have 3000 chips and one guy has gone. So I have $10 equity, right? Wrong. The guy has surrendered his entire chance at the prize pool, and you can only win half of it at most! You take most of his chances of winning but you cannot take all. Why? Because you cannot finish first, second and third. You can only fill one spot and it is not winner takes all. Everyone else has also improved their chance of a share in the prize pool. They retain the same chance of coming first (yours has doubled), but they improve their chance of coming second (because the extra time you win, you cannot also come second! Someone else must fill that spot, and now there are only nine players to share it, and each has an equal chance). There it is, the key to ICM. When we all had the same amount of chips, I had one chance of winning the tourney. When I double up, I have two chances. But I do not have two chances of coming second and third, because when I come first the extra time, I cannot also come second. My chances of coming second and third do improve dramatically, but they do not double, because of that one extra time I win.

Well, why does that matter? Remember what I said. A poker player tries to lay the distribution of his outcomes over the normal distribution of outcomes to make the most profit. We call this "expected value". Say I have four to the nut flush and I am facing an allin. The pot holds $300 and I must pay $100 to call. This is an easy call. Over a lifetime, I can expect to win the pot one in 2.86 times (I am 1.8 to 1). The pot pays three for my one. My expected value, or EV, is huge: 3/1.8. Whichever action has the highest EV is the one you should take. (If this isn't obvious, comment, and I will explain, but it should be.) This doesn't mean I will make money on this particular flush, or on any particular flush. It means that over my poker lifetime, given this spot, I will make that money. (This is a simplification, because of course my opponent can pair the board sometimes and beat me with his set, but let's say that our flush will always win to make it easy to understand.)

In a cash game, your equity in chips exactly equals your equity in dollars. In the example I give, $100 in chips is worth $100 in cash. So if I make the call, I make my EV in dollars.

In an SNG, my equity in chips corresponds to a dollar value, but not in the same way. At the start of the tourney, 1500=$5, but as my stack grows, the relationship between the two changes. As we discussed, if I improve my chances of winning, I cannot improve my chances of coming second by the same degree, because it is not winner takes all, and I cannot be second at the same time I am first. Every time you win, someone else comes second; every time you improve your chance of coming first, whether you double it, increased it by a third, or whatever proportion, you are not in the race for second that same proportion.

This is the ICM -- the independent chip model. It is the understanding that because if you have all the chips, you will win 60% of the prize, not all of it, there is a scale of value between 1500=$5 and 15000=$25. 10x the chips does not equal 10x the money! But we are playing to win money, not chips. I can't go to the bank with my virtual chips. My bank insists on hard cash.

So here's the thing. Let's say I'm playing a cash game and I have QQ. My opponent shows me that he has AK and goes all in. I am last to act and no one else has called. I should call. Not calling in this spot is horrible because you are 57/43 to win. You may not win this time (43% is quite high!) but over a lifetime you will win 57% of the time. You should also call this early in a tournament, when the value of chips and the value of money are closely correlated. This is often called a "coinflip" in poker, but it should be clear that this is not a coinflip at all. QQ is heavily favoured. The numbers look close but think about this. If I offer you a series of a million coinflips at $1 a pop, you will win 500,000 and lose 500,000 and net nothing. If I offered you 57/43 odds on heads, you can pick heads every time and win 570,000 and lose 430,000. $140,000 is a lot of money! Make the right choice on a "coinflip" in poker a million times and you will make a ton of money.

But let's say I'm playing in an SNG and we're at the bubble. The bubble is the point at which you get paid. So it's when four players remain. Whoever comes fourth gets nothing. So let's say the guy has you covered, shows you he has AJ and goes all in. You have 66. You are 55/45. So you call, right? Wrong. In a cash game, you call. In an SNG, you fold. Call the value of my hand $10. If I call and lose, the value of my hand becomes $0. You get nothing for coming fourth. If I call and win, I double up in chips, but my equity does not double, as we discussed. Nothing like it. How much it increases depends on how many chips everyone else has. But because one guy loses a ton of his equity (all of mine if I lose, most of his if he does), everyone else gains some (because their chances of coming first remain the same, but their chance of coming third has just shot through the roof! If I am knocked out, they are certain of at least third).

If I folded this hand, my equity will not change. I will have the same number of chips and the same chances of winning, placing second and placing third. If I win, my chances will improve to the value that double my chips has. But the risk I should be willing to take should not exceed new cash value of chips/old cash value of chips. In a cash game, it's simple: the cash value of my chips is their face value. But in an SNG, I need to know the ICM to know what the cash value of my chips is.

Knowing ICM is crucial to making money in SNGs. If I make calls that decrease my cash equity in the prize pool, I am losing money. It's on paper, if you like, because no one has been paid yet, but it's like having a share: 100 shares at $5 are worth $500, and if they fall to $3, you really have lost $200. Imagine that you held those shares but had to cash them out on 31 December. Whatever they're worth then, that's what you get. That fall of $200 is money that you've really lost. You are going to need to gain it back before the cashout, or your wallet takes a hit. An SNG's cashout date is the point at which you bust out! Whenever I gamble in an SNG, I'm gambling my equity. Sometimes, of course, I will bust out and my investment will be worth nothing. On a 55/45, that will happen 45% of the time. So I must ensure that the 55% of the times I get paid compensate for all those times I win nothing. In a cash game, they will (keep thinking of the coinflips if you struggle to understand why: this flip you lose your dollar, next you win: 45% of the time you lose the dollar, so out of a million, you lose 450,000 times and $450,000 dollars, but you win the dollar 550,000 times to make up for it). In an SNG, they won't.

Where does the mindreading come into it? Well, players do not show you their hands. It's tragic that they don't, but that's the cross you've got to bear. Remember what I said. Information is power. In poker, knowing what someone has is very powerful information.

Say I'm playing cash. I have 66. Some guy pushes all in. If I knew he had AJ, I have an easy call, as we've seen. But I can't know that. And as I also noted, information is not hidden. It's not unknowable that he has AJ. He knows! There's no secret to it either. If he turned his cards face up, they would be revealed as AJ. They don't magically become AJ in the act of being turned over. The information was always there. It was not created de novo.

But I do not know that the guy has AJ. What I know is that I've seen him play a few hands and he's pushed a few times. Because the cards are received at random, they have, over the long term, a predictable distribution. So you can assume that he has had that distribution. He may have had a heater, and have been dealt aces five or six times. But you cannot assume that your sample diverges from the true population of hands, even though it's perfectly possible that it does. (If they never did diverge, poker would be a lot easier!) You have to deal in models because the actual distribution of his hands is, and will remain, unknown to you. The model is an approximation and can be wrong, but it's your best guess.

So the guy has pushed a few times and you think he's doing it a bit light. He can't have been doing it that many times. So you give him a range. These are the cards you think he might have. It is not an exact science! You just do your best. The ranges you put people on get closer to what they actually have depending on how many hands they've shown down, how tricky you think they are and how much you think they balance their play (by mixing in hands that do not fit so obviously into their range -- a player might raise AA/KK/QQ UTG but also raise 76s so that he gains some value from your uncertainty over whether he does have the big pair).

You compare your 66's chances against that range. You do not know which hand he has, but you do know your chances against his range of possible hands, so far as you know them. You consider your equity vs the range your opponent has. This is how you calculate ICM. A guy pushes, you have to decide whether to call. You cannot know his cards, but you can have an idea what percentage of cards he will play here. So you calculate your chances against that percentage. He might be pushing the top end of it, and your chances are worse than you think. He might be pushing the bottom end, and they're better. But your aim, remember, is to lay all your outcomes over the distribution of outcomes, not just this one outcome. So you choose the correct action in the long run. You are not having just this one flip of the coin. There will be many many flips.

Experience helps you pick ranges that fit players. And knowledge of ICM helps you make the correct choices given those ranges. At first, you have to work it out (or use software that helps) but with training, you have a good feel for it (you might already have a good feel for it, and the training just hones your intuition).

Information is power is money in poker. If I have information about your hand (or the range of hands you might hold when you do an action), my actions will be better. I will be empowered to make the correct choices. And if I have learned ICM, I will make the choices that make me money, while you, lacking the information I have, will make the choices that lose you money. Yes, you will stumble on the right choice a lot of the time, but you will make the wrong ones sometimes, and each wrong choice will cost you just as not choosing to sell a share the day before it falls in value costs you.