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DanielNegreanu
Many Texas Hold 'em experts believe you shouldn't put all your money in on a drawing hand.


While that's true in many cases, it doesn't apply to monster draws. A monster draw is one in which you have 14 outs or more -- 14 or more cards that will improve your hand after the flop. Let's say, for example, that you put your opponent on pocket aces or pocket kings. You, on the other hand, hold 6h-7h, and the flop comes 3h-8h-9s. To improve to the best hand, you could hit one of the nine remaining hearts to make a flush, or six other cards -- 10s or 5s -- to fill the straight. Don't include the 10h or 5h because they've already been counted in the flush category. That would certainly be considered a monster draw! You'd have 15 outs with two cards still to come.

In fact, it would make your hand the best hand. Obviously, your seven-high doesn't beat A-A, but your hand will win more often than the aces will; your monster draw will improve to the best hand a little more than 56 percent of the time.

As a rule, 13 outs after the flop makes you very close to 50-50. Fourteen outs makes you a small favorite, and, as I mentioned before, 15 outs makes you a decent favorite over your opponent. So, in knowing this, let's now consider how to play these types of hands after the flop.

Betting on drawing hands after the flop is often called semi-bluffing, but it isn't exactly bluffing when your drawing hand is statistically the best hand, is it?

A semi-bluff gives you two ways of winning the pot: Your bet forces everyone to fold; or, your opponent calls your bet, and you fill your drawing hand. Therein lies the real power of the monster draw.

By playing these hands aggressively you either force your opponent into submission or get all of your money in as a slight favorite. Either outcome is good for you, but having your opponent fold to your aggressive bet produces a slightly better result in the long run. Playing monster draws in this manner will also help add deception to your game; opponents will have a much more difficult time putting you on a hand.

Let me illustrate. Suppose I've raised before the flop with A-A, and the flop comes 9h-3h-6s. Normally, this is an excellent flop for a big pair, as the only real threat, at this point, is someone holding a set (three 9s, three 6s, or three 3s). However, if someone is in fact holding a set, my chances of winning the pot would be slim to none. I'd have only a 9 percent chance of hitting one of the two remaining aces to win the hand. So what should I do if an extremely tight player goes all-in against me on a flop like that?

Well, I'd probably fold my aces. That would be the right play.

If, however, I were playing against a loose opponent who aggressively pushes on big draws, I'd be more likely to call his bet. While it's easy for me to put a tight player on a set and fold, it's trickier to face a loose player who raises my pocket bullets. That's an important lesson. You want that loose and deceptive image for yourself. That way, when you do flop a set, opponents will likely give you action, thinking that maybe you've raised with a drawing hand. Also, it's important that you make your aggressive bet on the flop -- don't wait for the turn.

Here's why: Your odds to win the hand with only one card to come decrease dramatically. A hand with 15 outs after the flop is a 56 percent favorite, but if you don't improve on the turn, that number drops all the way down to 34 percent.

That percentage is so low, that, if your opponent makes a large bet on the turn, he could shut you out of the hand -- something he couldn't do to you on the flop.

(If you liked this piece, send a letter or e-mail to your local newspaper and tell them you want Daniel Negreanu's poker column in your paper)
167-169
Are these writeups also of what to expect in the upcoming book this year?
silvap
Well i realy like these advices, thanks daniel. Helpfull stuff.
Actuary
uh...ty.

reading this makes me think there really isn't much difference betwen the top pros and the top strategy posters here.

that's encouraging
iggymcfly
Or it means that DN writes a lot of his articles for noobs. I think that's probably a more likely conclusion.
cjpaskert2
QUOTE (iggymcfly @ Monday, August 28th, 2006, 7:28 AM) *
Or it means that DN writes a lot of his articles for noobs. I think that's probably a more likely conclusion.


..which is exactly what us "noobs" need.
Actuary
QUOTE (iggymcfly @ Monday, August 28th, 2006, 3:28 AM) *
Or it means that DN writes a lot of his articles for noobs. I think that's probably a more likely conclusion.



Really?

Man, I was about to quit my job and go on the Tour!

sorry, i'll go away....
simo_8ball
Main thing is, in strat forum, you look at the hand, analyse it, apply ranges, work out equities, etc. and get to the correct move over time. The top pros can figure the best move a lot faster and can do it at the table. If we could all take 2 hours over every decision I'm sure many of the regulars in the strat forum would be extremely successful tournament pros.

It's far easier to make perfect decisions when you are out of the heat of the moment.
TheIceman71
I do not know if you read the comments that procede your posts, Daniel, but if you do, my question is this: is your advice on calling an all-in bet with a monster draw the same as the advice you give for pushing all-in with a monster draw?
Acid_Knight
QUOTE (TheIceman71 @ Saturday, September 30th, 2006, 10:11 PM) *
I do not know if you read the comments that procede your posts, Daniel, but if you do, my question is this: is your advice on calling an all-in bet with a monster draw the same as the advice you give for pushing all-in with a monster draw?


The lesson that is being taught is that monster draws are big hands and can be played accordingly. While it is almost certainly better to get your money in first so that you have fold equity, I would say that you should be mostly calling with those huge draws as well.

Think about it. Usually there are a couple of raises back and forth after the flop if you have a big draw and your opponent has an overpair. Let's say that you both started the hand with $1000 and each put in $50 preflop. You flop a huge draw and your opponent has a big overpair. You lead out for 75$, he raises you to $175 and you reraise to $400. He now goes all in. Do you call? Of course you do, the pot is now at about $1400 and you only have $600 left. you're getting 7-3 on your money when you're probably an even money favorite to win the pot, if not a small favorite.

Note that if the better orders were reversed, and it was you putting in the 4th bet, then a good player would probably lay down aces, giving you credit for a set or 2 pair. That's the strength of putting your chips in first. If you have to call a huge bet, the odds are probably with you and it's time to get in there, gamble a little bit, and hope your 7 high improves to beat his aces.
mrdannyg
YOU HEAR THAT PAUL WASICKA
Acid_Knight
QUOTE (mrdannyg @ Monday, October 2nd, 2006, 9:04 PM) *
YOU HEAR THAT PAUL WASICKA


I hope you're just poking fun there. There was almost no way that Wasicka should've called in that pot. Yes, he had a huge draw, but the thing is that he's not heads up. If Binger had a big pair and Gold had the flush draw, then Wasicka was screwed. Also, moving up 2 million dollars by folding one huge draw is not an opportunity that most people get. He also hadn't invested many chips in the pot to that point, so there was little reason for him to risk his tournament on a hand where he had invested so little.

Also, playing monster draws so aggressively is MUCH more effective in cash games. If you don't hit, no big deal. Rebuy.

Wasicka made the right fold in that hand.
Actuary
QUOTE (Acid_Knight @ Tuesday, October 3rd, 2006, 6:38 AM) *
I hope you're just poking fun there. There was almost no way that Wasicka should've called in that pot.


Then why get in the pot?
lol.
Big thread on this already.

Calling was his best chance to win the tourney vs the range of hands you can put the other guys on..not just the worst case scenarios

he already had 4MM, at that point 2MM more vs a chaqnce for 8 MM more and the bracelet. Once you have 4 MM, 2 MM more is less significant than the first 2MM

Certainly no guarantee Binger loses the hand. No gaurantee Paul gets 2nd

Paul way over estimated his Heads UP chances with Jamie. He really needed to gamble on the pot to have a decent chance to comeback and win
Acid_Knight
I'm sure there were lots of threads on the hand. I think that it's one of those things where it can really go either way.

If he called, there was a very real danger of being shown a flush draw larger than his, as well as a hand, like top pair, that he was drawing thin against.

Can you really criticize too much either way though?

If he calls and wins, he has a lot of chips and actually has a MUCH better shot at winning the tourney. However by folding, he's assuming that Binger will call and run the risk of being eliminated. If Binger is eliminated on the hand, he moves up just shy of $2,000,000 just by not entering the pot. That's a huge incentive to fold the massive draw. It's also a very rare opportunity.

If he called and made the draw, few people would've criticized the play. If he call, Binger folded, and he lost, I'm sure he'd never hear the end of it. The same thing would've happened if he called and missed the draw.

It was definitely an interesting hand. I really think that all things considered, there wasn't a definite right or wrong move there. You're 100% right that he would've had a much much more realistic shot to win the thing if he called and won.

"he already had 4MM, at that point 2MM more vs a chaqnce for 8 MM more and the bracelet. Once you have 4 MM, 2 MM more is less significant than the first 2MM"

That is a basic thing from economics called Marginal Benefit. I think that in this case though, that extra 2 million means A LOT to you. It's not like he already had like 40 milllion locked up. He can increase his winnings be 50% by simply not getting involved. While your point is valid, I disagree that the next 2 million is less significant than the first 2.
Actuary
to me 4 MM is huge.
And 2 MM more is less of a factor at that point than going for the Bracelet.

I could live 80 yrs on 4 MM even after taxes

At 5% 2.4MM yields: 120k / yr.

And, to clarify, Paul's best chance to win was by Calling.
Without even saying he won or not.
Obviously, it's true if he wins.
But even given the risk of busting, calling gives him the best chance to win.

Yes, Jamie could have a higer FD.
We're against a range of hands, not the worst case scenario
And Binger could also win and we're still in jeopardy of 3rd
mrdannyg
QUOTE (Acid_Knight @ Tuesday, October 3rd, 2006, 4:48 PM) *
That is a basic thing from economics called Marginal Benefit. I think that in this case though, that extra 2 million means A LOT to you. It's not like he already had like 40 milllion locked up. He can increase his winnings be 50% by simply not getting involved. While your point is valid, I disagree that the next 2 million is less significant than the first 2.


we've discussed this at length, so i won't hijack it here.

i can only suggest that his marginal benefit in this spot is relatively small. the reason being another basic economics turn, diminishing marginal returns.

he already had several million locked up. another two million is not THAT important when you consider he could win several more and the bracelet. if we were discussing a fold that guaranteed him two million instead of nothing, then i could easily understand folding pretty much anything.
Acid_Knight
That's the thing about diminishing marginal returns and marginal benefits - they differ from one person to another.

I agree that 2 million more on top of 4 already won isn't as big as 2 million vs nothing, but it's also not like he had tens of millions locked up or anything.


Also, I know the comment I made about Wasicka looking good or bad based on results doesn't matter, becuase he can't know what the cards are. I'm just saying that against the range of hands that TWO opponents might hold, even an OESFD can find itself with many fewer outs than it would like. Against one opponent, you're never in trouble. Against two, things change a little.
ThaKid
That's a decent piece of advice there daniel, cheers mayne
NEtwowilldo
Wasicka has written more than one article on that hand explaining his thought process. Basically he put Gold on a higher flush draw.

ESPN.com and bluffmagazine.com
pokerguy33
So Daniel, I always hear that "Tight is right" Which in your opinion is better. Having a tight table image, or a loose table image. I think in the AA hand with all low cards on the table with a loose image your getting action here, but with a tight image I doubt you get any action at all. Just your thoughts?
CrazyJoe
QUOTE (pokerguy33 @ Saturday, March 3rd, 2007, 8:05 PM) *
So Daniel, I always hear that "Tight is right" Which in your opinion is better. Having a tight table image, or a loose table image. I think in the AA hand with all low cards on the table with a loose image your getting action here, but with a tight image I doubt you get any action at all. Just your thoughts?



the most favourable is playing tight/aggressive when you have a loose image, and playing loose/aggressive when you have a tight image and changing gears when your image changes, notice there's always aggression.
nicapoker
..
conor_mw
good to see danielle is keeping up with the once a day thing icon_biggrin.gif
PokerChest
Yes, there are very few hard and fast rules. It's good that you explained the exception. bubble_cool.gif Thanks!
thefossil
Hi I'd like to ask Daniel a specific question. Can I start my own topic here or is this forum reserved for daniel's topics only?
Zach6668
There is no place to ask Daniel specific questions.

I believe he has a forum email address, or you can try PM'ing him, but I'm sure he gets a lot of both, so I Can't guarantee any replies, etc.
DonkeySchool
*EDIT: I'm a bit retarded, feel free to rid this post for giggles, but I am so wrong it's not funny*

Daniel, I have to commend you on this post, if you ever read this *Unlikely* because this post was the reason I registered.

There is so many things wrong here, I don't know where to start. *Ooooh I can see the flame war already*

Daniel, as a professional poker player, I am sure you are aware of this, in fact this is an advanced strategy rarely if EVER discussed in poker books, is it because the Poker pro's don't want you to know it? Maybe, I doubt that somehow. I just think it's one of the cardinal things in poker you just don't talk about.

Lets look at a nice 9 person table situation *which lets face it, if you play MTT's is where you are going to spend most of your time*. Lets say early position doubles, plays really tight, and everyone folds except for you, in the bb, you call with your 6 7h

The flop comes down with the 'Monster Draw' 3h 8h 9s

You have 15 outs. wow, percentage wise, you have the best hand.

But do you really believe no one else held a single heart?
how about a 10?
how about a 5?

in 9 handed, assuming you get headsup flop action. 17 cards are out that you don't know what are. 22 cards are already out, 5 of which you know. just under HALF THE DECK is already in play, including folded cards and the first burn.

Now let me ask you this

Do you really have 15 outs? On a good day you would have 13-15, an average day 11, and a bad day, 8 or less.
Should you put all your money into the pot when you are behind?

----

Next problem I have with this post. So many problems with this one.

QUOTE
Your odds to win the hand with only one card to come decrease dramatically. A hand with 15 outs after the flop is a 56 percent favorite, but if you don't improve on the turn, that number drops all the way down to 34 percent.


See this is why I hate, loathe, disgust poker calculators. They are completely unrealistic, firstly: I have a problem with 56 changing to 34. I'm not saying which one is wrong here, because I frankly don't care, but your percentage chance should be more or less halved with only one card to come *so 56 goes to 28ish or 34 should be 68 to improve on the turn* But listen guys, rather than use a 'odds calculator' why don't you just use some simple maths in your head.

After the flop 22 cards out of a 52 card deck have been used, that means that if you have exactly 15 outs still in that deck *good luck kiddo* since there are 30 cards left in the deck, what do you imagine your odds are that you will hit your card on the turn? 30 cards, divide by 15, hmmm...I don't know if I can work that out.

You have a 50% chance to make your hand on the turn, assuming you have all your outs still in the deck. what's amusing is that, if the turn card doesn't help you, and you still believe you have 15 outs by some godly fate, there is now 28 cards left in the deck, 15 of which can help you. Your chance to hit on the river increased even more.

I'm not trying to say my odds and math are correct *Though basic year 9 math we learn in school says it is* But I am trying to say that Daniels here *I'm not blaming daniel, I'm blaming whatever odds calculator he used* are.

---

In closing. When thinking about decisions like these, PLEASE figure out how many cards are already out, and adjust your outs to go with that. There is a good chance you really only have about 10, sometimes more, sometimes less on a full 9 handed table, 10 outs....hmm, decent favorite indeed.

*The poster admits that she is probably going to get flamed massively for this post, and as such has allowed users to send her e-mails. The poster also admits she might get banned for this post, but she hopes it isn't the case*
David_Nicoson
I don't think anyone gets banned for trolling, DonkeySchool.
DonkeySchool
Actually I'm not trying to bait anyone into an argumentative response, I seriously feel that there are massive massive problems with what daniel posted *shrugs*
DonkeySchool
I do apologise about being so very very agressive in my initial post. I feel very strongly about this
adamjoz
Sorry DS, but you got your maths wrong. Obviously sometimes your odds of making your hand are a bit smaller or a bit greater than those calculated by the general method (odds of hitting N cards out of 47 unseen cards in 2 tries), but it shouldn't matter for your calculations because there is virtually no way you know other players' cards at any point and you can't take them into account. The general method works fine, as the above odds and EV even out in long term. For more reading and research I'd reccomend the appendix in Barry Greenstein's "Ace on the river" - his calculations are a bit hard to follow at some points, so if you fail, he has a degree in maths and I hope he'll be enough of an authority to you to just accept the numbers.
DonkeySchool
Okay, I made this post elsewhere, since poker is a game of making educated guesses on what people hold *it's how you put your opponent 'on a hand'* why can't you go one further.

Which of these two statements is more likely to be true in regards to those that folded

1 - One of my opponents folded a heart, 10, or 5
2 - None of my opponents folded a heart, 10 or 5

No you cannot 'know' what your opponents folded, just like you can't 'know' your opponent has AA or KK, but you can make educated guesses to the point,
DonkeySchool
From a site where I wanted to find out wether or not I made a retarded post or not tongue.gif

QUOTE
To explain further so you might understand, because you dont know what the unseen cards are, you have no idea how many are outs and how many are bricks. In calculating outs, it makes no difference that other players may be holding some of them, there are 47 unknown cards (on the flop) and you can no more discount the unknown cards in players hands or the muck than you can the remaining cards in the deck. On TV you may see the calculations take into account which outs are no good based on what others have (and true, this is a more accurate calculation), but since you dont know what those are when youre playing, you cant take them into account in doing a mathematical estimation of your chances to hit your needed cards. Your post in the DN forum made reference to your chances "going down" more with each additional person at the table, because they may hold the outs. What youre not seeing is that taking those hidden cards into account could improve your chances as well. Each one that isnt an out gives you a slightly better chance to hit your draw, and each one that is an out lessens your chances. But again, that doesnt matter unless youre watching on tv and know what the other cards are. Sorry, but your theory that discounting outs based on other players unknown holdings is not a well kept secret of top professionals that you stumbled upon - you just werent thinking about it the right way. Hope this clears it up instead of confusing you more.

Also, your point on DNs forum that the odds for you to hit your outs should be precisely halved for hitting on the turn, as opposed to the river is incorrect. Without going into heavy math, hitting on the turn is X in 47 (unknown cards), where X is your number of outs. From turn to river, one more card is exposed, and if it isnt your out, then one more card is known, and since it wasnt one that you wanted, your outs are now X in 46, which makes a bit of a difference. Your odds of hitting it on the river if you didnt get there on the turn will be a bit more than half of your chances of getting there, flop to river. Or in other words, your chances of hitting your out on the river are slightly better than your chances of hitting on the turn (assuming you missed on the turn).


I guess I should apologize to daniel, but I figure in the long run I sent more traffic to his forum wink.gif

Please forgive my moronic post,
DonkeySchool
adamjoz
QUOTE (DonkeySchool @ Thursday, December 20th, 2007, 12:28 AM) *
Okay, I made this post elsewhere, since poker is a game of making educated guesses on what people hold *it's how you put your opponent 'on a hand'* why can't you go one further.

Which of these two statements is more likely to be true in regards to those that folded

1 - One of my opponents folded a heart, 10, or 5
2 - None of my opponents folded a heart, 10 or 5

No you cannot 'know' what your opponents folded, just like you can't 'know' your opponent has AA or KK, but you can make educated guesses to the point,


If noone folded a heart, 10 or 5, you're a bigger favourite than what the calculator tells you (not the same as you seem to rekckon), if a lot of (vague, but easy to calculate depending on the situation) people folded hearts, 5s or 10s, you're a smaller favourite. It evens out and doesn't affect your EV in long term.

Please read Ace on the River bit first, analyse it and let us know which bit of maths Barry got wrong.

edit: I see you got there before I posted this, gg
pt special
QUOTE (DonkeySchool @ Wednesday, December 19th, 2007, 4:13 PM) *
*EDIT: I'm a bit retarded, feel free to rid this post for giggles, but I am so wrong it's not funny*

Daniel, I have to commend you on this post, if you ever read this *Unlikely* because this post was the reason I registered.

There is so many things wrong here, I don't know where to start. *Ooooh I can see the flame war already*

Daniel, as a professional poker player, I am sure you are aware of this, in fact this is an advanced strategy rarely if EVER discussed in poker books, is it because the Poker pro's don't want you to know it? Maybe, I doubt that somehow. I just think it's one of the cardinal things in poker you just don't talk about.

Lets look at a nice 9 person table situation *which lets face it, if you play MTT's is where you are going to spend most of your time*. Lets say early position doubles, plays really tight, and everyone folds except for you, in the bb, you call with your 6 7h

The flop comes down with the 'Monster Draw' 3h 8h 9s

You have 15 outs. wow, percentage wise, you have the best hand.

But do you really believe no one else held a single heart?
how about a 10?
how about a 5?

in 9 handed, assuming you get headsup flop action. 17 cards are out that you don't know what are. 22 cards are already out, 5 of which you know. just under HALF THE DECK is already in play, including folded cards and the first burn.

Now let me ask you this

Do you really have 15 outs? On a good day you would have 13-15, an average day 11, and a bad day, 8 or less.
Should you put all your money into the pot when you are behind?

----

Next problem I have with this post. So many problems with this one.
See this is why I hate, loathe, disgust poker calculators. They are completely unrealistic, firstly: I have a problem with 56 changing to 34. I'm not saying which one is wrong here, because I frankly don't care, but your percentage chance should be more or less halved with only one card to come *so 56 goes to 28ish or 34 should be 68 to improve on the turn* But listen guys, rather than use a 'odds calculator' why don't you just use some simple maths in your head.

After the flop 22 cards out of a 52 card deck have been used, that means that if you have exactly 15 outs still in that deck *good luck kiddo* since there are 30 cards left in the deck, what do you imagine your odds are that you will hit your card on the turn? 30 cards, divide by 15, hmmm...I don't know if I can work that out.

You have a 50% chance to make your hand on the turn, assuming you have all your outs still in the deck. what's amusing is that, if the turn card doesn't help you, and you still believe you have 15 outs by some godly fate, there is now 28 cards left in the deck, 15 of which can help you. Your chance to hit on the river increased even more.

I'm not trying to say my odds and math are correct *Though basic year 9 math we learn in school says it is* But I am trying to say that Daniels here *I'm not blaming daniel, I'm blaming whatever odds calculator he used* are.

---

In closing. When thinking about decisions like these, PLEASE figure out how many cards are already out, and adjust your outs to go with that. There is a good chance you really only have about 10, sometimes more, sometimes less on a full 9 handed table, 10 outs....hmm, decent favorite indeed.

*The poster admits that she is probably going to get flamed massively for this post, and as such has allowed users to send her e-mails. The poster also admits she might get banned for this post, but she hopes it isn't the case*


this has to be one gigantic level....or the worst post ever
ROBBBIGG
awesome
TheMathProf
QUOTE
Also, your point on DNs forum that the odds for you to hit your outs should be precisely halved for hitting on the turn, as opposed to the river is incorrect. Without going into heavy math, hitting on the turn is X in 47 (unknown cards), where X is your number of outs. From turn to river, one more card is exposed, and if it isnt your out, then one more card is known, and since it wasnt one that you wanted, your outs are now X in 46, which makes a bit of a difference. Your odds of hitting it on the river if you didnt get there on the turn will be a bit more than half of your chances of getting there, flop to river. Or in other words, your chances of hitting your out on the river are slightly better than your chances of hitting on the turn (assuming you missed on the turn).


It's not even just that, because the difference between X in 46 and X in 47 is negligible (usually within 1%, for smallish values of X). Other factors can come into play between the turn and the river, some of which positively impact the probability and some of which negatively impact the probability.

One such instance is the possibility of going runner-runner that is included in the turn probability, but not included in the river probability where you did not improve. For instance, suppose that you hold 6h-7h, and the flop comes 3h-8h-9s. (This is essentially the scenario that Daniel brings up to start this thread.) In addition to the fifteen outs of any 5, any 10, and any heart (remembering not to double-count the 5h and the 10h), you can also win the pot by hitting running cards of 6-6, 7-7, or 6-7. The probability of these events occurring is (5/46) * (4/45), which contributes approximately 1% to the turn probability.

But the biggest factor in contributing to the percentages in this case has to do with the fact that your turn percentage is discounted because improving twice is irrelevant. Unimproved on the turn, you have a roughly 33% chance of winning on the river (15/46). But let's think about what this is really saying about the turn probability:

The turn probability incorporates two factors: you improve on the turn, in which case the river is irrelevant (except for the case of drawing the 9h, where the opponent may have redraws to a full house) OR you don't improve on the turn and improve on the river. Notice that the second possibility requires that two distinct events happen: you have to not improve on the turn AND you have to improve on the river.

The first possibility is relatively easy to calculate: you improve on the turn with probability 15/47 (approximately 32%).

The second possibility is more difficult: the first event has probability 32/47 (it's the remaining probability from the first possibility above) and the second event has probability 15/46. So the probability of both happening is 32/47 * 15/46 (approximately 22%).

So the probability of winning on the turn is approximately 54% (it's the sum of the previous two probabilities), while the probability of winning on the river is approximately 33% (the 15/46 we calculated earlier).

In other words, since improving on the river really only matters in cases where we didn't improve on the turn, and this only happens about 2/3rds of the time, the win percentage for the turn is only approximately 5/3 (1 + 2/3) times the win percentage of the win percentage for the river. Indeed, the approximation 5/3 * 33 = 55 is pretty darn close to the 54% that we got calculating the probability more authentically.

But I should caution you: that 2/3rds approximation really only worked for that specific case (outs on the turn = 15). When the number of outs is relatively small (say 4), then the probability that we make it to the river unimproved is significantly larger. Note that the probability of winning with 4 outs on the river is 9%, where as the probability of winning with 4 outs on the turn is closer to 17%, almost exactly the double that you originally expected. That's because our multiplier in this case is 1.91 (1 + the .91 probability that we didn't improve on the turn), and 1.91 itself is really close to 2.

Anyway, hopefully, that clarifies a little more of what's going on between those percentages.
Nimue1995
Dam I knew I should have paid more attention to math in school. Maybe I'll send a copy of this to my son so he will.
az.poker.mind
QUOTE (TheMathProf @ Sunday, December 30th, 2007, 2:02 AM) *
It's not even just that, because the difference between X in 46 and X in 47 is negligible (usually within 1%, for smallish values of X). Other factors can come into play between the turn and the river, some of which positively impact the probability and some of which negatively impact the probability.

One such instance is the possibility of going runner-runner that is included in the turn probability, but not included in the river probability where you did not improve. For instance, suppose that you hold 6h-7h, and the flop comes 3h-8h-9s. (This is essentially the scenario that Daniel brings up to start this thread.) In addition to the fifteen outs of any 5, any 10, and any heart (remembering not to double-count the 5h and the 10h), you can also win the pot by hitting running cards of 6-6, 7-7, or 6-7. The probability of these events occurring is (5/46) * (4/45), which contributes approximately 1% to the turn probability.

But the biggest factor in contributing to the percentages in this case has to do with the fact that your turn percentage is discounted because improving twice is irrelevant. Unimproved on the turn, you have a roughly 33% chance of winning on the river (15/46). But let's think about what this is really saying about the turn probability:

The turn probability incorporates two factors: you improve on the turn, in which case the river is irrelevant (except for the case of drawing the 9h, where the opponent may have redraws to a full house) OR you don't improve on the turn and improve on the river. Notice that the second possibility requires that two distinct events happen: you have to not improve on the turn AND you have to improve on the river.

The first possibility is relatively easy to calculate: you improve on the turn with probability 15/47 (approximately 32%).

The second possibility is more difficult: the first event has probability 32/47 (it's the remaining probability from the first possibility above) and the second event has probability 15/46. So the probability of both happening is 32/47 * 15/46 (approximately 22%).

So the probability of winning on the turn is approximately 54% (it's the sum of the previous two probabilities), while the probability of winning on the river is approximately 33% (the 15/46 we calculated earlier).

In other words, since improving on the river really only matters in cases where we didn't improve on the turn, and this only happens about 2/3rds of the time, the win percentage for the turn is only approximately 5/3 (1 + 2/3) times the win percentage of the win percentage for the river. Indeed, the approximation 5/3 * 33 = 55 is pretty darn close to the 54% that we got calculating the probability more authentically.

But I should caution you: that 2/3rds approximation really only worked for that specific case (outs on the turn = 15). When the number of outs is relatively small (say 4), then the probability that we make it to the river unimproved is significantly larger. Note that the probability of winning with 4 outs on the river is 9%, where as the probability of winning with 4 outs on the turn is closer to 17%, almost exactly the double that you originally expected. That's because our multiplier in this case is 1.91 (1 + the .91 probability that we didn't improve on the turn), and 1.91 itself is really close to 2.

Anyway, hopefully, that clarifies a little more of what's going on between those percentages.



Great post TheMathProf... thanks for being so detailed.
copernicus
QUOTE (David_Nicoson @ Wednesday, December 19th, 2007, 3:46 PM) *
I don't think anyone gets banned for trolling, DonkeySchool.


Cant believe I missed DonkeySchool's post. Id just add that nobody gets banned for not having a clue about probability, but if they did, DonkeySchool would be up for a lifetime ban.
frisellan
I love when people comment on the plays of someone making decisions for millions of dollars.
Paul did quite well for himself.
tongue.gif

The power of a monster draw is in acting first. Making the other player make a tough decision for his/her chips.
If they call - ok you are a favorite but you still have to hit. If they fold - you made a profit without a made hand.
Win Win

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