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Old 09-17-2007, 01:33 PM
fishyak fishyak is offline
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Default Getting into the math of slowplay

Slowplaying is one of the subjects here that tends to get strong negative emotional reactions, but not much analysis. I admit that my opinion has been that there is a limited place for slowplay, particularly live. But I want to look more closely at the math and ask the question, is slowplay which gives people the chance to try to catch up worth it?

Here is yesterday's hand from 4/8 @ Commerce. Table has quieted down and is fairly LAP at the moment.

3 limpers to me. I have KQo in HJ. My raise buys me the Button. I get 4 callers. (9 SB). Flop is QQ6r. Assume for this discussion that if I bet, they fold around. There were visual clues that was the case. Check around.

Turn is an A [img]/images/graemlins/heart.gif[/img], putting two hearts on the board. 3 checks and the player next to me bets into me. With two hearts on the board, slowplay time is over. I raise. All fold back to the original bettor who calls. (6 1/2 BB)

River A [img]/images/graemlins/diamond.gif[/img]! I get checked to. The guy is worried I have AK. He has A5s. I know he has an Ace. I check. He has always made the call on the river before.

I risked 4.5 BB to try and get just 1 BB more as it turns out. Still, my Villian had to hit a 2 outter, a 20 to one shot, to best me. So the math of the slowplay still looks OK, but the impact on my stack, and I am steaming over it, etc., bring other factors into play. Should I give up a small math edge by betting the flop? (Again, just go with my assumption that everyone would have folded. It does happen. See Mr. Weak Tight's post. I would suggest reading that post in conjuction with one before you respond. In his post, he bet and took down the pot. In this pot, I didn't and got caught.)

Thoughts on the math? Thoughts on the non-math elements?
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  #2  
Old 09-17-2007, 01:49 PM
KitCloudkicker KitCloudkicker is offline
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Default Re: Getting into the math of slowplay

this question honestly is very vague because it isnt clear how "steaming" precisely affects your EV in future hands. theres too many variables. you cant solve for x and y in your equation if you dont know x or y.

fwiw I always bet a flop that I hit if I raise preflop. I dont care if i flop quads.
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Old 09-17-2007, 03:03 PM
fishyak fishyak is offline
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Default Re: Getting into the math of slowplay

I thought I'd made it clear to separate the math - risking a sure 4.5 BB win to win just 1 BB more, kind of a worst case scenario for slowplaying, from the emotional factors. Make them separate analyses and discussions.
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Old 09-17-2007, 03:04 PM
dedenburn dedenburn is offline
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Default Re: Getting into the math of slowplay

Without getting into the math of slowplaying (because I have no idea how to figure it) I'd say that this hand doesn't meet the general guidelines.

Although checking can give another player a good, but still second best hand (it happened) and won't likely give up a card that beats you, it still provides opportunities to set up a strong redraw.

Second, the pot is not small. No, 9sb on the flop isn't huge, but 4 players for 2 bets is big enough to play a little more straightforward.

I think that the basic point is that our flop play allowed villian to play his hand exactly as he should, which is -EV here.
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  #5  
Old 09-17-2007, 06:01 PM
BigAlChicago BigAlChicago is offline
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Default Re: Getting into the math of slowplay

I like betting this flop, too. If we raise preflop and whiff -- say the same flop but we raised preflop with AJo -- aren't we c-betting to try and take it down right on the flop? If we are betting there, shouldn't we be betting when we hit?

As to the math, I will try to do an oversimplified calculation. Let's assume as the baseline that you will take down 4.5 BB's every time you bet that flop.

If you slowplay, you will take it down with just your turn bet X% of the time, winning the same 4.5 BBs. 1-X% of the time, someone will hit something that they will want to draw to so that they will pay 1 (or 2 BBs if you get in a raise, as here). More often than not, it will be to the backdoor flush than the runner runner overcards. To oversimplify things, I will again assume that if someone hits his draw, it will cost you 2 BBs (that is, 1 bet on the turn and a crying call on the river), but when villain misses, he will not pay you off on the river. Assume villain hits his draw Z% of the time.

Thus, slowplaying comes down to this:

+4.5 BB X%
+5.5 BB (1-X%)*(1-Z%)
-2.0 BB (1-X%)*Z%

For sake of looking at numbers, I assumed that 50% of the time your turn bet just takes down the pot. The other 50% of the time represents an opponent hitting a draw. If villain is roughly 20% to make his draw on the river (i.e., a flush draw) when he picks up the draw on the turn, then you will win 5.5 BB 40% of the time you slowplay and lose 2 BB 10% of the time. The overall expectation for this play is +4.25 BB (50% of 4.5 plus 40% of 5.5 minus 10% of 2.) If these assumptions are accurate, then slowplaying cost you .25 BB.

Of course, this oversimplifies the math. There will be times when the flush hits, but you make your boat. There will be other times when someone makes a pair, but calls you down to the river putting you on AK. Also, my assumptions of getting called versus taking the pot down on the river might be all wrong.

Based on this analysis (winning 1 BB when called and you win and losing 2 BB's when your opponent hits a draw on the river), if your opponent is drawing to six outs or less, then you will make money in this scenario.

Of course, what this calculation does not take into account is the number of times someone will bet into you and call your raise. In that case, if you assume you will win 2 more BB, instead of just 1 more BB, when you win, then this will be a money making proposition. (Of course, this assumes you fold to the river bet when you get beat on the river!) Based on the previous number, you would win an additional .4 BB. That makes this play worth 4.65 BBs compared to taking down the 4.5 BB pot with a flop bet.

Someone, please critique this analysis from a mathematical standpoint.
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  #6  
Old 09-17-2007, 09:10 PM
fishyak fishyak is offline
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Default Re: Getting into the math of slowplay

While your math is oversimplified, it offers a good starting point on putting a price tag on slowplay. And my example was chosen as a favorable position to try and slowplay. The math is worse than I thought. Your basic game plan shows slowplay as -EV on these assumptions.

People can argue about the assumptions, but the point is clear. Slowplay risks a bird in hand for possibly too small a reward.

Can someone take us "deeper" on the math?
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Old 09-18-2007, 02:48 AM
SNOWBALL SNOWBALL is offline
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Default Re: Getting into the math of slowplay

if you know everyone would fold on the flop then this is a pretty ez spot to check. The exception is if a guy with 9T will still CF on you when a 9 or a T comes off. Then you just need to bet because they only action you are buying yourself is when sets hit on you or someone picks up a flush draw (hint: you do not want them to pick up a flush draw) or when someone hits a K or an A on the turn (you hold a K, and they need to also hold a K, so that's 2 kings + 3 aces remember they have to have one)
which only adds up to 5 cards. pretty meh. You give yourself a ten percent shot of getting extra action AND THAT'S ASSUMING THAT THEY DON'T CALL ON THE FLOP AND THAT SOMEONE ACTUALLY HOLDS A DAMN K OR A

Sorry if my sentence structure sucks, but I think my points are worth considering even if maybe you have to read my post a bit closely.

For more on this general concept, check out the hand example in Greenstein's book where hero openchecks top trips on the flop (I think w/ AK)

to summarize: if someone catching a low pair on the turn will cause them to pay you off I like checking. If all you are hoping for is an A or a K to roll off, then it's pretty meh. You're more likely to give the field a shot at picking up a set (full house) to kill you on the turn or a flush draw which you do not want them to have.

Also, I KNOW your example said "assume they all fold" but that sucks. Someone could have a Q with you or pay you off with a really silly hand. We see it all the damn time in small stakes games.
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  #8  
Old 09-18-2007, 08:42 AM
James. James. is offline
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Default Re: Getting into the math of slowplay

you don't want opponents to correctly draw unless you beat what they are drawing to.

also, it's not just strong hands that should be slowplayed. you want to consider a "slowplay" when, relative to your opponent's holdings, the value of your holding is going to stay the same. like KK on an Ahigh flop, for example.

one of my big issues with slowplaying is the big hand over big hand confrontations. those are the ones that constitute most of your EV in these situations, even though they are rare. if you don't jam early, you don't get as much money in because someone else might be slowplaying, also. factor in the numerous scare cards that can come and how strange it looks for an aggro player to suddenly start check/calling and playing fast is often going to have more merit. now there is a time and place for everything, but slowplaying is one of those things that gets too much emphasis.
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  #9  
Old 09-18-2007, 11:56 AM
fishyak fishyak is offline
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Default Re: Getting into the math of slowplay

James,

Big hand vs. big hand should be a far different scenario than what I presented. We'll all seen big flops turn an aggressive table into pussycats. Because it is infrequent, players understandably struggle for the right line. I wouldn't even calling it slowplaying when you KNOW there is another big hand or hands or draw(s) out there. I am talking about the situations where you are clearly way ahead.

Oh, and Snowball - I wanted to move this discussion away from the issue - you know they'll call - for two reasons. 1) It would interfere with the math others were trying to help with, and 2) You weren't there. This table was ready to fold this hand. That happens, too.

The real important point may be that there appears to be limited and potentially negative financial value to slowplaying. When in doubt, bet.
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  #10  
Old 09-18-2007, 02:15 PM
Xhad Xhad is offline
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Default Re: Getting into the math of slowplay

[ QUOTE ]
Slowplaying is one of the subjects here that tends to get strong negative emotional reactions, but not much analysis.

[/ QUOTE ]

I agree. Slowplaying is almost always wrong in small stakes, but many people either:

-Don't know this
-Do know this, but don't know why, and therefore miss the spots where it is correct

[ QUOTE ]
also, it's not just strong hands that should be slowplayed. you want to consider a "slowplay" when, relative to your opponent's holdings, the value of your holding is going to stay the same. like KK on an Ahigh flop, for example.

[/ QUOTE ]

This is key.

A lot of slowplay posts are "OMG, I flopped the nuts, can I slowplay?" When it's not the absolute strength of your hand or even the relative strength of your hand, but the relative strength of your hand compared to the hands that give you action. Slowplaying 5 [img]/images/graemlins/spade.gif[/img] 9 [img]/images/graemlins/spade.gif[/img] on a 678 [img]/images/graemlins/spade.gif[/img] board is nearly always going to be wrong, while slowplaying T5 on a Q55 board can make sense. [img]/images/graemlins/wink.gif[/img]

For the initial post, if we're assuming your hand is good and your opponents will all fold if you bet, here's about as mathy as I know how to get:

-(your opponents' combined equity) * potsize: This is what betting and taking down the pot nets you and therefore what you immediately risk with a slowplay. This is also why the decision of whether or not to slowplay usually revolves around potsize and how likely you are to get outdrawn. If you can't make at least this much EV on future streets by checking, you're better off just betting even if you know you will immediately win the pot.
-(likelihood you get outdrawn) * (amount you lose when this happens) - A reason not to slowplay; this is how much your slowplay costs you on future streets.
-(likelihood that your opponents improve, decide their hand is good, or decide to bluff) * (amount they bet over future streets) - This is, in a nutshell, how much slowplaying nets you. If this is less than the last two terms combined, you should not slowplay (even if you are always good and they will always fold).

If we remove the assumption that our hand is good, then we have to consider how much money we make or save against better hands, and how much action we gain or lose from worse hands. Usually if we slowplay due to these considerations we call it "WA/WB". [img]/images/graemlins/wink.gif[/img]

If we remove the assumption that our opponents will fold, this obviously argues against slowplaying period (why not bet your hand if they're going to give action?). If there is already a bet or two, and the hands that play if you call are pretty much the same ones that play if you raise, then slowplaying misses bets. Here the only consideration is the possibility that you will only get to raise once, and that you might rather wait for the turn than raise on the flop (conversely, sometimes raising on the flop looks like protection, pumping a draw, or buying a free card while a turn raise looks like a big hand, so you only get to raise once because you waited for the turn). Another consideration as james pointed out is scare cards, which can either slow your opponent down, or slow you down because some draw that was a large part of his range got there and now you can't win if that's what he has.
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