Lesson: about odds
Date: Fri, May 9, 2008 Internet
Okay, I've been thinking about it and this is probably the way conceptually to think about odds.
Say you are 3/1 to win a hand. What does that actually mean?
You are at point A, the action point. It's the point at which you must decide whether to bet, call or fold. Your odds at that point represent your chances of getting a certain outcome (the one favourable to you). All the figures we are bandying about express those chances.
So. You are at A, and after you decide, you will be at B. Say you take the odds.
It's as though there are four point Bs: B1, B2, B3, B4. Imagine this is a quantum universe (which it is), in which all possibilities happen (they probably do).
B1 is favourable for you.
B2, B3, B4 are not favourable for you.
3/1 says there are four outcomes, and one is good for you.
You can always think of odds in that way. Just sum the two sides and consider that you have that many outcomes. If your odds were 3/2, you have five outcomes, two favouring you.
Okay. So how does that fit in with a/ equity and b/ pot odds?
A. Equity
Your equity in this sense is the share your favourable outcomes have of all possible outcomes. When you are 3/1 to make your hand, you win it one out of four times.
You can figure out what your odds are as a percentage by simply doing this: divide 100 by the number of possible outcomes, then times that by the number of favourable outcomes.
I know that sounds complicated, but really it isn't. More importantly, you usually think of it the other way round.
We were talking about QQ vs AK. We say QQ has 56% equity versus AK.
So what are we saying? Well, equity always totals 100%. You can't win more than everything. And this is in any case how we describe probabilities: 56% just means 56 out of 100.
Out of 100 outcomes, if you hold QQ vs AK, there are 56 that are favourable. You can also write that as 0.56, which is handy when you're figuring out how much you stand to win or lose. (If you both have stacks of 1500, he shoves and turns over AK, and you are thinking about calling, you know that you stand to win 0.56 x 3000, and the amount you lose is always your bet. This just means that if you played the hand 100 times, you would expect to win 56 times and lose 44 times, which would average out to 0.56 x 3000.)
B. Pot odds
You can easily figure your pot odds. They are always (money in the pot) / (the bet you have to call).
If the pot is 100, some guy puts in 50, and you are asked whether you want to call, your pot odds are 100+50 / 50, which is 3/1. So when should you call?
You should call when your odds of winning are better than 3/1. How you can figure that out is for another day, but this is a key idea in poker.
3/1 means that out of four outcomes, one needs to be favourable to you. Remember our little formula? Sum the outcomes = 4. Divide that into 100 = 25. Times that by favourable outcomes - 25. You need to be a 25% chance against whatever he's betting with to win.
Luckily, there are tools to figure out whether you actually are that good a chance against his range, so long as you can make a reasonable estimate of what hands he can have. You can get by in STTs with a very sketchy and basic knowledge of pot odds. Basically, you need to know when you are good to push with a draw and when you are being offered such good odds that you should not fold. But you can learn both without having too good a grasp of the underlying concepts.
But this you do need to understand. Each set of outcomes makes a pie that totals 1. You are always going to end up with 1 or 0. But conceptually, before a play you can consider yourself to have a virtual slice of the pie. You will make a lot of decisions that depend on how big that slice is. And that pie is intimately connected with another (I know, way too many pies), which we will consider next. Just as you have equity in every hand (which is just the amount of outcomes that will favour you), you have equity in the tournament (which is the amount of the tournament's prizepool your chips are currently worth).
Conceptually, what matters is that you understand that even though you really end up with 1 or 0 -- or in prizes with 50/30/20 -- at any point, you have a virtual slice of the pie, which we can describe in percentages.
Meeeeowwwwwwwwwcunt
Date: Fri, May 9, 2008 Internet
I don't try to steal the blinds much at t50. No real point. But I've been worrying lately that I'm playing too passively. But actually, I'm probably better off just not bothering.
PokerStars Game #17301504798: Tournament #87687371, $10+$1 Hold'em No Limit - Level III (25/50) - 2008/05/09 - 01:09:23 (ET)
Table '87687371 1' 9-max Seat #6 is the button
Seat 1: FR Vessant (3890 in chips)
Seat 5: forever_smex (2935 in chips)
Seat 6: gtdmo (2615 in chips)
Seat 7: jazzy22 (3070 in chips)
Seat 9: feelincrappy (990 in chips)
jazzy22: posts small blind 25
feelincrappy: posts big blind 50
*** HOLE CARDS ***
Dealt to FR Vessant [Ah Tc]
FR Vessant: raises 100 to 150
AT fivehanded is just too strong to fold.
forever_smex: folds
gtdmo: folds
jazzy22: calls 125
The guy's a total fish, so you have the double-edged sword. On one side, he's useless. On the other, his range for calling is pretty wide.
feelincrappy: folds
*** FLOP *** [9s 4c 9d]
jazzy22: bets 150
There's no way that hit him. He's got to be bluffing.
FR Vessant: calls 150
*** TURN *** [9s 4c 9d] [Kd]
jazzy22: bets 150
FR Vessant: calls 150
That may have hit him but he didn't bet enough for me to consider folding.
*** RIVER *** [9s 4c 9d Kd] [2h]
jazzy22: bets 150
FR Vessant: calls 150
I'm no worse off here than I was on the flop.
I realise that mostly he has a pair, but I can't fold the river at that price.
*** SHOW DOWN ***
jazzy22: shows [Js 4s] (two pair, Nines and Fours)
W. T. F.
No, really. He didn't just complete the blind with that shit. He called a raise.
And then hit the fucking flop with it. It's actually incredibly difficult to find a fold anywhere in that hand but there's nowhere I can put more money in and make him fold. Not that he would.
On the flop, his most likely hand is a bluff. He doesn't have a 9 often there, and there should be few or no 4s in even a fish's range. The turn may have improved him but he doesn't increase the bet, which many fishes do when they have been bluffing but now hit. On the river, the pot odds are too big to fold, although I'm rarely winning.
But Jeezus, could I please hit the flop? And when I do, could the other guy not have some weird fucking two pair hand? And when all that goes to plan, could my hand please hold up sometimes?
***
Poker Jeezus is not listening. Same guy. I have AT again.
PokerStars Game #17301661046: Tournament #87687371, $10+$1 Hold'em No Limit - Level IV (50/100) - 2008/05/09 - 01:21:13 (ET)
Table '87687371 1' 9-max Seat #5 is the button
Seat 1: FR Vessant (2315 in chips)
Seat 5: forever_smex (4310 in chips)
Seat 6: gtdmo (3390 in chips)
Seat 7: jazzy22 (3485 in chips)
gtdmo: posts small blind 50
jazzy22: posts big blind 100
*** HOLE CARDS ***
Dealt to FR Vessant [Th Ad]
FR Vessant: raises 150 to 250
I'm close to push/fold. smex already pushed over one raise, so I keep this small, because I'll have to fold again if anyone pushes.
forever_smex: folds
gtdmo: folds
jazzy22: calls 150
Of course. He can again have anything.
*** FLOP *** [Ah 9s Kc]
jazzy22: checks
FR Vessant: bets 300
Well, I hit the flop, so I have to bet.
jazzy22: calls 300
OMG. K9? Set of 9s?
*** TURN *** [Ah 9s Kc] [Qd]
jazzy22: bets 300
FR Vessant: calls 300
I have to call here. I have no reason to think he's beating me. He's retarded enough to bet QT here a lot. Mind you, he's also retarded enough to have Q9 or of course any ace. I have to just hope the river will be cheap.
*** RIVER *** [Ah 9s Kc Qd] [8s]
jazzy22: bets 400
FR Vessant: calls 400
I am all agog to see what shit he is going to show me.
*** SHOW DOWN ***
jazzy22: shows [As Jc] (a pair of Aces)
There are days when you just want to bury your own head in the garden.
***
And this is one of them:
PokerStars Game #17301766562: Tournament #87687472, $10+$1 Hold'em No Limit - Level V (75/150) - 2008/05/09 - 01:29:39 (ET)
Table '87687472 1' 9-max Seat #3 is the button
Seat 2: FR Vessant (1420 in chips)
Seat 3: Wolf_Pride (2595 in chips)
Seat 4: yumpoker! (2895 in chips)
Seat 5: ZLP1712 (3545 in chips)
Seat 8: brevenge (1155 in chips)
Seat 9: gumphry (1890 in chips)
yumpoker!: posts small blind 75
ZLP1712: posts big blind 150
*** HOLE CARDS ***
Dealt to FR Vessant [Ah Ac]
brevenge: folds
gumphry: raises 1740 to 1890 and is all-in
Hooray!
FR Vessant: calls 1420 and is all-in
Have that bitch!
Wolf_Pride: folds
yumpoker!: folds
ZLP1712: folds
*** FLOP *** [3h 7d Jc]
Oh.
Bitches 2
Date: Thu, May 8, 2008 Internet
This is getting ridiculous.
PokerStars Game #17300429186: Tournament #87680989, $10+$1 Hold'em No Limit - Level IV (50/100) - 2008/05/08 - 23:58:08 (ET)
Table '87680989 1' 9-max Seat #3 is the button
Seat 1: chipleadercm (1640 in chips)
Seat 2: FR Vessant (1410 in chips)
Seat 3: srfdblovrhd (1235 in chips)
Seat 4: brevenge (1044 in chips)
Seat 6: georgiagolf (2635 in chips)
Seat 7: msEvsiNdreAd (4675 in chips)
Seat 8: zookwicket (861 in chips)
brevenge: posts small blind 50
georgiagolf: posts big blind 100
*** HOLE CARDS ***
Dealt to FR Vessant [Qh Qc]
msEvsiNdreAd: calls 100
zookwicket: folds
chipleadercm: folds
FR Vessant: raises 400 to 500
I have not played a hand in this tourney.
srfdblovrhd: folds
brevenge: folds
georgiagolf: raises 400 to 900
So he has to have AA/KK right?
msEvsiNdreAd: folds
FR Vessant: raises 510 to 1410 and is all-in
georgiagolf: calls 510
Nope. He has AJs. Well, I raised instead of shoving in the hope of getting shoved over, so I got what I asked for, and...
*** FLOP *** [9d As 4d]
Every. Fucking. Time. It's insane. I am not kidding. QQ is a premium hand and I am losing with it.
And again, the other guy's play is simply terrible. He must fold his hand. He is guaranteed to be behind me. Yes, he got lucky this time. Please do not comment that, because yes, I can see that he did. But his hand is a big dog against mine.
It is really sucking now. I don't feel I'm playing badly at all. Clearly, I didn't play this hand badly.
Next tourney, I shove over a minraise with AK. He has 88. I hit the A on the flop. River 8. I mean, wtf?
Sigh
Date: Thu, May 8, 2008 Internet
At this point, I decided to give up for the day.
PokerStars Game #17299350536: Tournament #87676215, $10+$1 Hold'em No Limit - Level III (25/50) - 2008/05/08 - 22:58:01 (ET)
Table '87676215 1' 9-max Seat #6 is the button
Seat 1: VILAGEIDIOT1 (2200 in chips)
Seat 2: gapoker#9 (1160 in chips)
Seat 4: TheKamikaze (1625 in chips)
Seat 5: Geissler1987 (725 in chips)
Seat 6: FR Vessant (1210 in chips)
Seat 8: hunterblue (4885 in chips)
Seat 9: bullwild (1695 in chips)
hunterblue: posts small blind 25
bullwild: posts big blind 50
*** HOLE CARDS ***
Dealt to FR Vessant [As Kh]
VILAGEIDIOT1: folds
gapoker#9: folds
TheKamikaze: calls 50
Geissler1987: calls 50
FR Vessant: raises 1160 to 1210 and is all-in
This is pretty standard. It's not a huge pot, but it's about 15% of my stack and I can take it with low risk.
hunterblue: folds
bullwild: folds
TheKamikaze: calls 1160
He has QQ. His play is beyond retarded. If I limp and the blinds also limp, he is playing QQ fivehanded. Any K or A comes, he's going to have to fold to a bet.
Gotta raise your big pairs. It's stupid to limp and hope someone else raises for you, because you so rarely get a decent hand that wasting it is fucking criminal.
Geissler1987: folds
*** FLOP *** [Kd 9h Ks]
Hooray. At last the poker gods have given me a break.
*** TURN *** [Kd 9h Ks] [5h]
*** RIVER *** [Kd 9h Ks 5h] [Qc]
Oh no, I see they haven't.
Bitches
Date: Thu, May 8, 2008 Internet
This is just routine but QQ is becoming my least-favourite hand by a street.
PokerStars Game #17297980657: Tournament #87669967, $10+$1 Hold'em No Limit - Level II (15/30) - 2008/05/08 - 21:49:34 (ET)
Table '87669967 1' 9-max Seat #9 is the button
Seat 1: alksolo (1050 in chips)
Seat 2: FR Vessant (1425 in chips)
Seat 3: Timberland31 (1135 in chips)
Seat 4: loosh23 (2355 in chips)
Seat 6: xgocubsx (4435 in chips)
Seat 8: omandon (1595 in chips)
Seat 9: TGAVALLEY (1505 in chips)
alksolo: posts small blind 15
FR Vessant: posts big blind 30
*** HOLE CARDS ***
Dealt to FR Vessant [Qd Qh]
Timberland31: folds
loosh23: calls 30
xgocubsx: calls 30
omandon: folds
TGAVALLEY: folds
alksolo: calls 15
FR Vessant: raises 120 to 150
That raise is slightly light, but it's still in the bounds of okay.
loosh23: folds
xgocubsx: calls 120
alksolo: calls 120
They can have anything, but it really doesn't matter. If they have kings, a king will come on the flop. If they have aces, an ace will come. Guaranteed.
*** FLOP *** [Jc Ks 8d]
My heart sinks. I'll probably have to continuation bet at it, and obviously will lose.
alksolo: bets 900 and is all-in
"I have a king."
FR Vessant: folds
xgocubsx: calls 900
FR Vessant said, "that hand just never fcking holds up"
Too true, FR.
*** TURN *** [Jc Ks 8d] [Ad]
*** RIVER *** [Jc Ks 8d Ad] [Jh]
*** SHOW DOWN ***
alksolo: shows [9s Kd] (two pair, Kings and Jacks)
WTF? Limping that shit is bad. Calling a raise is inexcusable.
xgocubsx: shows [7c Kc] (two pair, Kings and Jacks)
Even worse. You can excuse his limp in the first place: it's sooooooted and if you squint he's just about in late position.
Okay, no. You can't excuse limping that shit either. These boys are just going to lose a ton of money.
LOL at shoving the flop, as well. That's terrible. What can I have? If I'm anything like the standard player I have a big ace or a decent pair. I might have KQ.
Well, if I have AK or KQ, you just busted yourself. If I don't, you make no more chips because I simply fold. The guy can only hope to make money from worse kings, and mate, there should not be any worse kings out there.
This is what novice players do. If you can avoid that mistake, you have learned a lesson in poker. In his spot, check to the raiser, who often bets. Then you can shove over with your top pair and win his bet. The downside is the same, but you have the benefit of winning more when you're ahead.
FR Vessant said, "wtf at both calls though"
No coaching FR. We don't actually want them to get better.
alksolo collected 1140 from pot
xgocubsx collected 1140 from pot
*** SUMMARY ***
Total pot 2280 | Rake 0
Board [Jc Ks 8d Ad Jh]
Seat 1: alksolo (small blind) showed [9s Kd] and won (1140) with two pair, Kings and Jacks
Seat 2: FR Vessant (big blind) folded on the Flop
Seat 3: Timberland31 folded before Flop (didn't bet)
Seat 4: loosh23 folded before Flop
Seat 6: xgocubsx showed [7c Kc] and won (1140) with two pair, Kings and Jacks
Seat 8: omandon folded before Flop (didn't bet)
Seat 9: TGAVALLEY (button) folded before Flop (didn't bet)
Luckily, xgocubsx gave my chips back a bit later when he called a raise and a cbet with K8 and then checked it down with me. I had AK.
TGAVALLEY also excelled himself by limping QQ at t50. On a T74 flop, he betted 100. I called with A7s, which was loose, but I felt he might actually not have me beat. He betted the same turn and river, and I didn't improve. I think on balance it was worth 300 chips to find out that he's a complete moron, although truth to tell, had he bet more, I would have lost less.
***
Sadly, xgocubsx's retarded play ended up hurting him less than me. He limped on the bubble and I pushed over with AT. I am taking the risk doing that that he will call me wide--he had 6K chips and I had 900, and he'd limped for 100--but the upside is that if he does, I crush him. Well, I crushed him preflop, sure enough, because he called with J8s, but not so much postflop, because he sucked out to an 8.
It's possible that just checking would have been best there, but I was outstacked by all three fish, so what can I do? I'm going to have to take a stand somewhere with a decent hand, and I suppose it's better with 900 chips than it ever will be with 500.
blah
Date: Thu, May 8, 2008 Internet
I fucking hate PokerRoom. I definitely have the doomswitch there. In the space of five minutes, I get it all in with KK on a Q high flop, am called by AJ, which turns an A, then get it in with 88 when I hit a set on a twoflush flop, get called by AA that has one of the flush suit and then he hits runner diamonds to make the flush. Totally unreal. What can you do? I am absolutely miles ahead both times, and I end up busted twice. This is like the bad run I had last month, just quite amazing bad beats one after another.
I mean, look. In the first hand, the guy doesn't even have a pair. Not even a draw. Nothing. He is just shoving wildly. In the second, the guy completely forgot to raise preflop, then got it in when I'm crushing him, and sucked out in a truly bizarre way. Ah well. You can complain to the poker gods, you can wail and moan and bitch, but what you can't do is scrub out the results in your ledger. Sometimes the horrible retards take your money and that's just poker.
Lesson: EV
Date: Wed, May 7, 2008 Internet
Poker involves wagering. Yes, you know it is a form of gambling, in which you put up x dollars as your stake, and the prize is to win y dollars. But every action you take in poker is also a wager.
It's easy to understand what your expectation is for a series of tourneys. Say you play the $10 games with no "rake" (the vig you must pay the poker room for running the table). You have an ROI of 10%. So if you play 100 games, you expect to net (10 x 1.1) x 100 = $1100. Divide that by 100 and you get $11. So your "expected value" for each game is $11. Hang on, you're thinking, you cannot win $11 in an STT with a standard payout scheme. Right. EV does not correspond with immediate reward. It is your average return over the series you're considering. You are going to win some and lose some, but over the whole 100 games, you'll average out to taking $11 a game. In poker, we talk about the long term. This is basically the series of games we will play in our lives, and it doesn't have a term. It's not infinite, but it's not bounded (because we have no idea how many games it will be). So we think about decisions playing out over that long term.
Say you have a flush draw on the turn. Your chances of catching a flush card on the river are a bit more than 4/1. Now, I'm sure boots will tell you that they are in fact either 100% or 0%, and that's true. The next card either is, or is not, a flush card. And even if it is not yet selected, so will be random, some of the flush cards can be in other guys' hands, so your odds are not actually 4/1. None of that matters. You don't know what the next card is and must make a decision. (And actually, there being fewer or more outs actually in existence is balanced out by other factors, and your expectation is not affected by that.)
So your expectation is that you will get your flush one in five times. But you don't know which of the five times you are going to have! What you can do is consider your expectation as 0.2 (which is just another way of writing 20%, because 20% of the time you expect to win the pot), and make your decision accordingly. Note again that in fact you either will or won't make your flush. You will or won't win the pot. But think about that series of tourneys. In them, you either make $40, $20, $10 or $0, but your expectation for each tourney is not one of those figures, but the figure that describes the proportion of each that you expect: $11.
So when you are considering whether to call with a flush draw, you can look at the pot, and look at the bet you face, and if it pays enough, you call the bet. Why? Let's say we are playing limit, where the bets are fixed. The pot has five bets in it and you face paying one bet to see the river. Let's say that if your flush comes, you will not make any more money because your opponent will just fold. So the pot is paying five to one.
Okay. This time, you may win five for your one or you may just lose your bet. But you don't know which it will be. Over the long term, you will win one out of five though, and you will face this bet many times over the long term. What you can do is take the bet when it favours you every time you are offered it. Then, over the long term, you are bound to profit (so long as the laws of probability don't get overturned by the poker gods). A bet that offers better odds than its probability of coming in is said to have "positive expectation" or is "+EV". In this case, you will win 0.2 x 6 = 1.2 bets, and you have to wager one bet. So long as the return is bigger than the amount you're betting, you're +EV.
What if there were only three bets in the pot? Now your expectation is 0.2 x 4 = 0.8 bets. You expect to lose. (If you're wondering why four bets and not three in that equation; it's because when the flush card comes, you win back your bet if you win.) This sort of bet is -EV. Note again, you may win this time. You may win this one and the next one and the next. But if you keep taking -EV bets, you will lose money.
The odds that the pot offers you by virtue of its size are called "pot odds". In most forms of poker, you are willing to take bets where pot odds are greater than the odds of the outcome being favourable. There are three further considerations though that we can mention briefly. (We'll talk about them in more detail later.) First, your opponent does not always fold on the river. Sometimes you will be paid another bet or bets. You can sometimes factor this into your decision whether to call. In our example the pot odds may be 4/1, indicating a fold, but you figure the other guy, fish that he is, will always call on the river. So you can count on another bet, making your "implied odds" 5/1, giving you a call. This is a subtle concept, because the pot odds are certain, but the implied odds vary depending on many factors. Second, you make wagers in tournaments with tournament chips, not with money, but you must consider your bets in terms of dollars. That's not easy but it's essential, because you cannot replace your chips and must weigh their use correctly. Sometimes, chasing that flush, which you would do in a cash game, will be wrong because although it shows a profit in chips, it doesn't show one in dollars. Third, it's straightforward to draw to a flush and win if you make it, lose if you don't. But you are rarely working out your EV so simply. You don't always know what your opponent has, or what he's drawing to. The best you can do is figure out the "range" he has: the hands he is likely to have, and work out your EV against the range.
What do I mean? Well, let's say you have KK. You raise preflop. Some guy calls. He's quite tight, and (I won't go into how) you figure that 55% of the time he has a smaller pair, 40% of the time he has a big ace and 5% of the time AA. The flop comes A73. You are to act. You want to know whether you should bet. You don't know what he actually has though. But you can do what would be right against his whole range. Let's assume you are pushing or folding and he is calling with everything. Let's say the pot has 500 chips in it and you have 1000 more to bet.
He has 77 or 33 10% of the time (a little less because of course there are a 7 and a 3 on the flop, but we aren't looking for precision here). They have a set, which crushes you, and you will "draw out" on them roughly 9% of the time. Let's say you lose 9% of the time to those pairs.
He has AA 5% of the time, and effectively you're "drawing dead" against AA. (You need to turn and river Ks to beat him. Good luck with that.) So you lose 5% of the time to that.
He has a big ace 40% of the time, and that is beating you. About 9% of the time, you'll draw out on those too, so let's say you lose 35% of the time to them.
He has a smaller pair that is not 77/33 45% of the time. They will draw out on you about 9% of the time, so let's say you lose 5% of the time to them.
You're losing 54% of the time. You expect to win less often than you lose, so you fold right?
Wrong. There is money already in the pot. Don't forget the money already in the pot! Your expectation is .46 x 2500 = 1150. So for your 1000 bet, you expect to win 1150. Of course, you will lose 1000 when he has the hands that beat you and you don't draw out, and win his 1000 plus the 500 in the pot when he has something that you beat. But over the long term, presented with this bet over and over and over, he will have different hands each time. Sometimes, you're crushed; this time, maybe, you're crushed. But you can't know that. So you push, he calls, and...
***
I just need to add a sentence. When we say that 46% of the time you will win the pot, we can also say that your "equity" in the outcome is 46%. Your equity in a hand will shift from street to street, but you always have equity unless you're drawing dead. We say that you have equity vs a particular hand or equity vs a range. Think of equity as your share of outcomes and you have mastered it. Here's a quick example that should make it clear. You have 1000 chips. Villain has 1000 chips. You are going to get it in and he will call. So there are 2000 chips at stake. Now, you figure you will win 60% of the time. So your expectation is .6 x 2000 = 1200 chips, or +200. So we say your EV is 200. It's worth 200 to you to get it in with this guy. Remember, you will not win 200 ever. Only 1000 sometimes. Your equity can be described as 60%, because your "share" of the outcome is 60%, or 1200. But note that equity and EV are not the same thing. Say you and villain were heads up before this hand and it's a winner takes all tourney. Your equity in the tournament was, of course, 50% before you pushed, and will be 100% or 0% after.
So to be clear, equity is your share in the outcome of the tourney or hand, EV is the change in your equity that an action will bring.