Proper play for flush draw

[grv575]

Ok I'm dealt a 3-flush in 7-card stud with 8 players. There is a bet and a raise and everyone calls the double bet. So I figure I'm getting 5 to 1 odds on the draw vs. 8 to 1 pot odds. Therefore I should stay in, correct?

On 4th street, a single bet is called by everyone, yet I did not get my 4th suit. I figure I have 10 to 1 odds against making the flush now but pot odds for this round are 1 bet to win 24 bets or 24 to 1 making a call the correct play. Is this flawed thinking? Somehow those 10 to 1 odds don't sound profitable.

Or should I now (on 4th) still be thinking effective odds and evaluating the pot as 3 bets total for 24, giving 8 to 1 pot odds making a fold the correct play. Can someone analyze the math here and let me know what is the proper play in this case (missing the 4th suit on 4th street - fold or call...is calling considered chasing or what?)

[Louie Landale]

Pure pot-odds calculations presume you know the cost and the pay-off and your exact chances and that you will win if you make it and lose if you don't. A flush draw with one card to go against a known straight is a pure pot-odds situation.

Little of that applies to your situation [1] You don't know the cost since you are going to have to draw a 2nd time if you DO snag your 4-flush. What if you make the 4-flush on 5th and the two opponents cap it? [2] You don't know the pay off since you don't know how much money the opponents are going to put in while you are still drawing. [3] You don't know if you'll win if you make it (someone fills up) or if you'll lose if you don't make it (you accidentally win with a pair of Ks). [4] You don't know how much money you'll win or lose when you DO make it.

Anyway, your big problem here is you need to downgrade your pot-odds calculation to reflect [1] the chances you draw on 4th if you do NOT snag a 4-flush, and [2] the cost of drawing on 5th and 6th when you DO snag the 4-flush. I'm guessing but I'd downgrade your pot-odds by 20% for 4th street betting and 40% for 5th street betting, just to account for your back-door draw.

I don't think 5:1 against on 3rd and 10:1 against on 4th is correct for a 3-flush, but I don't know what is correct. Someone will no doubt inform us.

Realistically in that situation, play if your suit is live and you've got a big over-card. The other realistic issue is this: if you are unsure that a call is correct then throw it away. That will save some money most of the time and cost only a little some of the time.

- Louie

[grv575]

OK thanks for the pointers but I'm still real confused. Let's simplify the situation. All I really want to know is mathematically (in an average situation, 8 players to the table, average amount of dead cards fall, etc.) is there a positive or negative expectation for the following two situations. Let's also assume that on both streets you are last to act.

3rd street: you have 3-suited, see 2 dead cards, and it is only 1 small bet to call. The correct way to evaluate this is just to consider your current pot odds as 8:1 and your drawing odds as (sorry it is I believe) 4:1. If you have to absorb too many raises in later round to justify THOSE pot odds then you will fold then...correct? (Note it is even OK to absorb 2 small bets on 3rd if noone folds and there is only 1 dead card...correct?)

4-th street: Now still 7 players call, your turn to act, the bet is 1 small bet to call and you should be getting 9:1 drawing odds to fill. Here it would be proper to fold using pot odds alone (8:1 vs 9:1) yet using implied odds of the future betting rounds should swing the effective odds in your favor if enough people stay in...no? Just want to make sure I'm understanding how to use this all correctly (and simply).

[grv575]

OK this is interesting stuff to play with. Breaking it down into a purely theoretical and very favorable situation for a flush draw, lets calculate a strategy over 150 average hands.

The strategy being this: Using pure pot odds alone, it seems unprofitable to call on 4-th street with only 3 to a flush. You are getting something like 9:1 odds against so a fold looks like the correct play. However lets say you call on small bet on each street till 5-th street to try for a 4-flush draw by 5th. If you don't have 4 to a flush on 5th you always fold.

Over 150 hands:
a) 1/5 you get a 4th suit on 4th street * ~1/2 drawing odds to make the flush * 150 hands = 15 made flushes.
b) 4/5 you don't get that 4th suit but try again * 1/5 you get a 4th suit on 5th street * ~1/3 drawing odds to fill * 150 hands = 8 flushes.

Assuming no raises, no folds, you will win 8 small bets per player = 8 * 8 = 32bb for each flush. So 32 * 23 = 736sb

You will invest 6 extra sb 23times = 138sb plus 254sb (to get to 5th) = 392sb.

Clearly in a large-way showdown where you can limp in till 5th it has positive expectation to see the 5th card to your suit even though straight pots odds would dictate otherwise (note that of the 736 won, 480 was won case a) and 256 was won from case b). the cost was 4/5 * 1/2 * 254 = 102 extra (using the only fold on 5th strategy vs. folding a miss on 4th) to see 5th for case b) + 48 to continue with case b) making it profitable only if enough people stay in, the bets are small to complete your draw, and hopefully you can extract more bets on the end once you complete). So case b) costs 150 and wins 256 small blinds in this overly optimistic example. Therefore it is usually correct to fold a 3-flush that did not improve on 4-th if there are not enough people in the pot, there is a raise in front of you, or there are no other outs for your hand (such as overcards or pairs)

Is the reasoning sound? Is this the generally accepted strategy or are there other good reasons to continue drawing a 3-flush on 4th? Any criticism (besides being overly optimistic about the showdown)?

[Louie Landale]

[1] Your presumption that everyone pays you off for one bet when you make the flush is rediculous. You'll need more realistic "implied" odds than that.

[2] Pot-odds calculations compare the SizeOfBet/SizeOfPot ratio to your ChanceOfWinning/ChanceOfLosing ratio; where "wining" means "actually win the pot". Specifically, its NOT compared to your ChanceOfNotImproving/ChanceOfImproving ratio. And pure Pot-Odds don't work at all if you must catch 2 good cards.

[3] You need effective odds calculations: TotalCostToDraw/TotalPayOffWhenWin compared to ChanceOfWinning/ChanceOfLosing. And your Total numbers must take into account the Cost when you don't improve and the cost when you do; and simiarly for the PayOff. This option lets you use your implied odds.

[4] The initial bet on 3rd street is typically the bring in which is usually around 30% of a small bet. The bet on 4th street is usually bigger, one small bet.

[5] I couldn't follow everything that you calculated. You seem to have correctly calculated the cost of making your 4-flush, but haven't calculated the cost to make the 5-flush once you do make the 4-flush.

[6] You may lose when you make the flush and might even win if you don't.

Yes, rarely if ever chase a busted 3-flush on 4th street for a bet unless you have some significant other way to win the pot.

- Louie

[grv575]

[1] Your presumption that everyone pays you off for one bet when you make the flush is rediculous. You'll need more realistic "implied" odds than that.

Yes but then bluffing comes into play. If someone is frequently unwilling to see your cards when you have either nothing showing (suits in the hole) or an obvious flush showing (remember whether you really have a flush with 4 suits showing is a coin toss) then you can make up for those lost bets on the end with bluffing later rounds.

[2] Pot-odds calculations compare the SizeOfBet/SizeOfPot ratio to your ChanceOfWinning/ChanceOfLosing ratio; where "wining" means "actually win the pot". Specifically, its NOT compared to your ChanceOfNotImproving/ChanceOfImproving ratio. And pure Pot-Odds don't work at all if you must catch 2 good cards.

Sure you have to scale your odds by the chance that you will hold the best hand if you hit.

[3] You need effective odds calculations: TotalCostToDraw/TotalPayOffWhenWin compared to ChanceOfWinning/ChanceOfLosing. And your Total numbers must take into account the Cost when you don't improve and the cost when you do; and simiarly for the PayOff. This option lets you use your implied odds.

Sure, you have to be careful of higher flushes but that's where reading cards comes into play.

[4] The initial bet on 3rd street is typically the bring in which is usually around 30% of a small bet. The bet on 4th street is usually bigger, one small bet.

Unless the opener makes a full small bet to open which is frequently done. And even when he brings it in, it is usually raised to a full bet in my experience.

[5] I couldn't follow everything that you calculated. You seem to have correctly calculated the cost of making your 4-flush, but haven't calculated the cost to make the 5-flush once you do make the 4-flush.

That's the ~1/2 figure. It's actually about 47% but 1 in 2 is close enough.
The ~1/3 figure is to fill with a 4-flush on 5th.

[6] You may lose when you make the flush and might even win if you don't.

Exactly. You definately have to adjust when you have other outs as well.

Yes, rarely if ever chase a busted 3-flush on 4th street for a bet unless you have some significant other way to win the pot.

Well if you have an overcard and enough people in then it seems like the numbers favor limping till 5th

[Louie Landale]

[1] Yes, if nobody is going to pay you off then you have significant hard-to-calculate bluffing equity. But that doesn't mean its OK to presume 8 folks pay your off; its means you should presume 1 or 2.

[2] Yup scale your odds, but that means your pure pot-odds calculations are inaccurate.

[4] Bring in is usually a complete bet? I've NEVER played in such a game.

[5] Yes, calculating 1/2 on 4th and 1/3 on 5th is accurate enough for your chances to make the hand. But no, it does NOT calculate the COST of trying to make it. For example on 4th with the 4-flush you can reasonably presume its going to cost you 1sb(4th)+1bb(5th)+1bb(6th) when you DON'T make the flush.

[6] Unless you are drawing to the nuts it is USUALLY the case that you lose more money when you make the hand (lose to a full) than you win when you don't (snagging a winning pair of Ks). So usually pot-odds ..err.. effective-odds calculations need to be downgraded.

Yup, go ahead and limp until 5th in these hopelessly loose-passive games.

- Louie

[flopmeister_1]

[ QUOTE ]
Ok I'm dealt a 3-flush in 7-card stud with 8 players. There is a bet and a raise and everyone calls the double bet. So I figure I'm getting 5 to 1 odds on the draw vs. 8 to 1 pot odds. Therefore I should stay in, correct?

[img]/images/graemlins/diamond.gif[/img] [img]/images/graemlins/diamond.gif[/img]Well we'll assume ( you don't say otherwise ) that there are no flush cards of yours on the doors. You are more like 4.2:1 as there are 10 remaining flush cards and 42 unseen cards. I WOULD STAY

On 4th street, a single bet is called by everyone, yet I did not get my 4th suit. I figure I have 10 to 1 odds against making the flush now but pot odds for this round are 1 bet to win 24 bets or 24 to 1 making a call the correct play. Is this flawed thinking? Somehow those 10 to 1 odds don't sound profitable.

[img]/images/graemlins/diamond.gif[/img] [img]/images/graemlins/diamond.gif[/img]NOt profitable odds? Again, we will assume that you saw none of your cards showed on the board. YOu are still 4.2:1. YOu can do the math and figure it out though.pot pays 24:1 and you are still wondering if it's profitable to stay. STAY! I don't think you are even marginal yet at 10:1 like you state. [img]/images/graemlins/smile.gif[/img]

Or should I now (on 4th) still be thinking effective odds and evaluating the pot as 3 bets total for 24, giving 8 to 1 pot odds making a fold the correct play. Can someone analyze the math here and let me know what is the proper play in this case (missing the 4th suit on 4th street - fold or call...is calling considered chasing or what?)

[img]/images/graemlins/diamond.gif[/img] [img]/images/graemlins/diamond.gif[/img] What does the other players up cards looklike? any paired door cards yet? two same suit higher than you r best?

It's always about improving to a WINNING hand not just improving that matters. BESIDES you still have 3 cards to come andall the info is out there on the board unlike hold 'em.

Now let's just suppose that that guy w/ K,4s on 4th is just calling. 5th is another friendly suit card and he raises, you better believe you are in trouble if all you have is 4 parts w/ a Q!

Stud is all about seeing what is out there and doing the math on your hand and whom you think you need to beat to win!


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