Have I been wrong in calculating my outs.....

[Abu Turab]

I've been working through Petriv's book and also read Matros' article on odds in Card Player. Until now I have been doing the following for a flush draw: after the flop 47/9 and after the turn 46/9. But after doing the calcualtion based on Petriv's book, my turn is calc is 1.86/1 vs 4.2/1(47/9) thus I have been pricing myself out of draws. Which is the the correct way to use the calculation?

[Siegmund]

Depends what you are counting.

You have a 38:9 chance to complete your flush on the turn, and another 37:9 chance to complete it on the river (a privilege for which you'll usually be paying an extra big bet.) In other words, no, you aren't miscounting your outs.

However the combined effect of the last two cards is that a four-flush on the flop has 1.86:1 odds of making the flush before the showdown. This means, for instance, you can raise for value on the flop if you are getting 2 or more callers, instead of just calling all the way.

[Mike Haven]

This means, for instance, you can raise for value on the flop if you are getting 2 or more callers, instead of just calling all the way.

Why does it mean that?

[Mike Haven]

You should have been calculating 38/9 and 37/9, or 4.2 to 1 and 4.1 to 1.

[Siegmund]

[ QUOTE ]

Why does it mean that?


[/ QUOTE ]

Pot odds tell you when calling is better than folding. They don't tell you anything about whether raising is right, or whether betting is better than checking.

When you have a 4-flush on the flop and have odds to stay in, you expect to be taking down the pot 35% of the time (when your flush comes in.) If you raise and get say 3 callers, you are paying $1 now in exchange for a 35% chance a pot that is $4 larger, a long-run gain of 40 cents.

[Mike Haven]

so let's say it's a 10-20 game and three of us are in for the flop = 30 pot

one bets 10, the other raises to 20 - if i get it right you say we should raise to 30 for value as we are getting 3 to 1 on 20, much better than 1.8 to 1, = 120 pot

but then isn't it the case that when we miss 81 times out of 100 and face a bet of 20 or 40 we are in effect now getting only 110 to our 50, or 150 to our 70, for a 4.1 to 1 shot?

or are you hoping the 19 times out of 100 that we turn a flush, with three flush cards showing on the board, and we don't get beaten by bigger flushes or by boats, we will win enough to make up for those 81 misses and loss of effective odds to catch on the river?

[Siegmund]

In your situation, folding is probably a little bit better than calling (you're getting 6:2 or 7:2 to call now and will be getting 4:1 or 5:1 on the turn), and if you raise the first bettor might fold rather than call two more. The decision is clearer when the flop hasn't already been raised ahead of you.


Let's suppose 3 of you see the flop, it's bet and *called* to you. There is 50 on the table, you can call or raise.

If you call:

3BB on the turn. 19% of the time you'll hit; let's say you are +4BB when that happens. the other 81% of the time, let's say it is bet and folded to you, so you're offered 4:1 to draw again and essentially break even. Your net: you are paying 1SB on the flop to win an average of 0.76 BB = 1.52 SB later. Calling is better than folding, as we know.

If you raise, and everyone calls:

4.5BB on the turn. 19% of the time you will hit, call those +5.5BB profits. 81% of the time let's say it is bet and folded to you and you have 5.5:1 to take another card off, about a +0.3BB position for you. Now you are paying 2SB on the flop to get 1.29BB=2.58SB later. A tiny improvement.

Now let's suppose FOUR people see the flop, and it's bet-call-call to you. 7:1 pot odds.

If you call: 4BB on the turn, 19% chance you hit and win +5BB on average; 81% chance you draw with 5:1 odds, +0.14BB onaverage; net +1.06BB=+2.12SB return on a 1SB investment.

If you raise and it's called around: 6BB on the turn. 19% chance you hit and win +7BB on average; 81% chance you draw with 7:1 odds, +0.52BB on average; net 1.75BB=3.50SB return on 2SB investment.

---

Basically there are two decisions going on at each turn: comparing odds against improving on the next card vs. pot odds to decide if calling makes sense, and compaing odds of winning the final pot vs. number of expected callers if you raise to decide if raising makes sense.

[Mike Haven]

i am really trying to follow your calculations, but i keep getting lost, i'm afraid

however, i think that you are including your own money in the winnings you make when you hit on the river as profit

if that's the case, although the money put into the pot on the flop isn't yours any more, neither is it profit to you if you end up winning the pot

i am still not convinced you should raise a draw for value

[Siegmund]

[ QUOTE ]

however, i think that you are including your own money in the winnings you make when you hit on the river as profit


[/ QUOTE ]

Yes. I find it simpler to speak of it this way. "I lose $1 65% of the time and win $3 35% of the time" is exactly the same thing as "I pay $1 now for a 35% chance to win $4."

And, frankly, I found the idea of raising draws for value very hard to accept for a long time. The concept of pot equity is very poorly covered in ToP and HPFAP, but discussed in some detail in SSHE. I'd rate it as fully as important as pot odds from a theory standpoint but it seems to figure much less prominently in most books and websites.

[Moonsugar]

you are in the big blind with Ah 2h in a 10 handed game

everyone calls and you check

flop comes Qh 7h 3s

you check

utg bets and all call

you raise for value

i know the example is extreme and there are better ones in the literature just trying to help

[Mike Haven]

thanks for the example, Moonsugar

please explain why that it a raise for value rather than a semi-bluff raise?

[MarkGrandy]

You have to also take account the case that both turn and river are flush cards, that increases probability to 36,2 %.
-----------------
Part of the possible flush cards pairs the table and makes full house possible to someone other player.

[Mike Haven]

by the way, it's not the raise i'm questioning - it's calling it a "raise for value" - so i am being somewhat pedantic here - i would happily raise a flush draw against the right two opponents as a semi-bluff raise

but the "right two opponents" is the operative phrase - a value bet implies that it should be the default, and i don't think that is the case

it is sometimes difficult to see all the mathematics involved when you need to include implied odds, as in this case, and therefore it can be easier to follow if you consider all in situations

looking at our 10-20 game, 30 pot on the flop, if we raise the 10 bet to us, all in, although we raised when we were getting 40 to 20 odds, we ended up with, at best, 70 to 20, or, at worst, 50 to 20 - this situation is fine, and we will win in the long run, assuming the flush wins when it hits - yes, it would be a value bet in those unique circumstances

however, it's when we raise and we're not all in until the turn bet which defines the move as a semi-bluff raise rather than a value bet

let's say we've raised and been called by our two opponents - there is now 90 in the pot

if we have missed our draw, a bet is made, and we have to call all in with our last 20 - our best odds are 130 to 20 - which sounds great - until we remember our flop raise and realise we have received pot odds at best of only 110 to 40 or 2.75 to 1 for our now 4.1 to 1 shot

expanding on what has happened here: if we hit our flush and get paid maximum we have won 110 35% of the time = 38.50 profit, but we have lost 40 65% of the time = 26.00 loss = 12.50 net profit

if we had called the flop and raised the turn or called a river bet with our last 20 only if we hit we would have lost 30 65% of the time = 19.50 loss but won 110 35% of the time = 38.50 profit = 19.00 net profit

at this time i believe that the above proves conclusively that if you call instead of raise on the flop with a flush draw you are considerably better off in the long run, without bringing implied odds and winning by opponents folding into the equation, (which you probably could do, profitably, in certain situations against certain opponents)

this makes the flop flush-draw-raise a semi-bluff, not a value bet, and one to use only if you think it is reasonably likely that both of your opponents will fold because of your raise (like at ub /images/graemlins/tongue.gif )

incidentally, if this wasn't the case, in some situations there could be arguments that a raise with K2o on a Q72r flop was a value bet even though you knew someone held Qx - i doubt if many people could be confused into thinking that would be correct, yet in effect it is the same situation

[kiddj]

Check out this site/thread: http://slicer.fekali.com:3455/16/26, or search for pot equity on micro-limit.

It may help you understand this concept.

My simplification: with 2 other players, you are putting in 33% of the money on the flop, expecting to win 35% of the time. If you have 3 other players, you are putting in 25% of the money on the flop, expecting to win 35% of the time.

-It's better if you are drawing to the nuts.

-It helps to have better position. If you miss on the turn, you can fall back on pot odds or take a free card if it's checked to you.

[Siegmund]

*Against a large enough field*, a draw to the best hand can be raised for value. "Large enough", specifically that your chance of the draw coming in is better than #ofcallers-to-one.

If you bet a flush draw heads up on the turn, that's pure semibluff, and an expensive mistake against a calling station.

Betting a draw into two or three people is dangerous unless they are, as you say, the right two or three people. You need them to either ALL fold sometimes, making it a good semibluff, or ALL call almost all the time which makes it basically a break-even bet.

Betting a draw to the nuts into a large field with many expected to call, as in moon's example, is a straight value bet. You aren't gaining any fold equity. You simply expect to win 35% of the money in the middle of the table, so if six people are putting chips in, you expect to be getting double your money back.

In the case of a flush draw on the flop with all 9 outs clean, you are 1.86:1 to win and need only two callers to make it a value bet (by only a few cents), and are making lots of money if you are getting three or more callers.

OESDs are often outdrawable/not to the nuts so only worth about 6 outs, and need at least three and preferably four callers to make money.

Value betting of draws on the turn is rare - a flush needs five callers. Basically only happens if you have one of those monster 15-out draws in a family pot.

So, to sum up, semibluffs work in small fields, value bets in large fields, and in between you are stuck with fold-or-call according to the pot odds.

[Moonsugar]

who would semibluff 9 people?

1/3 (or so) of every dollar that goes into this pot on the flop is yours. as long as you get 2 callers this raise is profitable, almost everyone will call here. .33 x 9 sb = 3sb value for the raise of 1 sb

but you already know all this, why are you busting my (our) chops?

[Nottom]

1.86:1 is the odds of a flopped 4-flush hitting by the river. 4.x:1 is the odds of it hitting on the turn. In most cases you shouldn't worry abou tthe odds with 2 cards to come since you will usually have to put in more money on the turn, so the math doesn't really work that way.

I'm sure other people will talk about pumping a flush draw for value on the flop, but from a pure pot-odds perspective you were doing it it right all along.

[Nottom]

[ QUOTE ]
thanks for the example, Moonsugar

please explain why that it a raise for value rather than a semi-bluff raise?

[/ QUOTE ]

I'm quite shocked to see a poster like you questioning what I thought was a 2+2 mantra practically mike.

Assume you have the nut flush draw (thus you cannot lose to a bigger flush, although in most cases you can play smaller flushes strong as well). Odds say if you flop a flush draw, you will make it by the river just over 1 time in 3.

So lets say you are on the button with Axs for the nut flush draw, UTG bets and gets 2 callers. You should raise even if you expect to be called 100% of the time. If UTG 3-bets and both players call, you should cap.

Basically, you are getting 3-1 on a 2-1 shot.

It doesn't matter what happens on the turn, you put in your money with an edge on the flop and have made money. Even if you NEVER win the pot with the raise, NEVER win without making your flush, and NEVER get a free card on the turn, you made a +EV play. Since you will also sometimes get some of these other benefits the play becomes even better.


Lemme take a more extreme example to drive home the point.

You have KQ /images/graemlins/club.gif and the flop comes J /images/graemlins/club.gif T/images/graemlins/club.gif 7/images/graemlins/heart.gif. For some reason you KNOW your opponent has red 55 and is a fish and will go to the river with his hand regardless of the action. You have basically 21 outs twice. Now you will make your hand on the turn about 45% of the time, but it should be obviousl that you want as much money in the pot as you can get on the flop since you will win the hand by the river almost 75% of the time.

[Mike Haven]

really, i am mainly questioning the jargon

i think of it as a semi-bluff raise when i don't have the good hand at the time of raising, and, in this particular instance, the "two players" comment caught my eye

if i raise on the flop against two players and don't catch, and if i then face a bet and a raise on the turn, and i can't call, i think of it as a failed semi-bluff raise

if i should think of the flop raise as a compulsory raise for value, then i've missed the definition somewhere along the line - my apologies for wasting everyone's time

[BaronVonCP]

Its pretty much all about equity as others have said. Even if you hold the worst hand, if you are a 35% favorite to have the best hand by the end against 4 players you want to get as much in as possible. There is 'value' in getting money in against the field.

We are disregarding fold equity which is an important factor in the semibluff.

[Mike Haven]

ok - i take the point - thank you

however, i am still reluctant to accede that it is a raise for value with only two opponents, (mathematically: because of the change in size of bets from small bets to big bets), which is what started me off in the first place

cheers

[SNOWBALL138]

if you win a bet more than 1/3 of the time versus two players who are putting in even money, you are making a profit.

[SNOWBALL138]

you aren't getting 3 to 1 on a bet or a raise in a 3 way pot. You are getting 2 to 1.

In the hand you described, raising might be a bad play b/c you could lose the first bettor.

[Mike Haven]

you aren't getting 3 to 1 on a bet or a raise in a 3 way pot. You are getting 2 to 1.

I wrote:

"so let's say it's a 10-20 game and three of us are in for the flop = 30 pot

one bets 10, the other raises to 20 - if i get it right you say we should raise to 30 for value as we are getting 3 to 1 on 20, much better than 1.8 to 1, = 120 pot"

At the time of our bet there is 30+10+20 = 60 in the pot, which is 3 to 1 for our required 20.

In the hand you described, raising might be a bad play b/c you could lose the first bettor.

If we reraise and are called only by the raiser we are still getting 30+10+20+10 = 70 to 30 or 2.3 to 1 for our money, better than the less than 1.8 to 1 we need to complete a flush with two cards to come.