[Closed] A Mathematical View on The SSS

Big Slick:
AK is often regarded as one of the "premium" hands in Texas Hold'em and it's certainly not a hand to be thrown into the muck lightly. However I am often worried about the Big Slick. It seems all too often to turn into a coinflip and leave a sour taste in the mouth as we fail to pair the board.

Strategy:
Basic strategy dictates that we raise AK against limpers, go all in against one raise and fold against a 3bet. It also says that we should call a raise behind us.

Sounds pretty simple, yuh?

Example 1: 3betting the Open-Raiser

Known players:
[tg]Position_Stack:hands/vp$ip/RaisePreflop/AF/WTS/ORL/BBvsSteal/W$SD;Hero$1.90:///////;MP1$10.35:48/29 /29 /-/20 /56 /0 /100 ;[/tg]
0.05/0.1 No-Limit Hold'em (8 handed)
Hand recorder used for this poker hand: PokerStrategy Elephant 0.67 by www.pokerstrategy.com.

Preflop: Hero is SB with A♠, K♠
UTG2 folds, MP1 raises to $0.40, 4 folds, Hero raises to $1.90 (All-In), BB folds, MP1 calls $1.50.

So here we have a fairly common situation. MP1 (fairly loose but aggressive) Open-Raises and it is folded to us. Now strategy dictates that we push our stack over the top of the raise. Is this profitable?

Equity:
If we assume that MP1 will call our push with TT+, AQ+ (4.7%) then we can calculate our equity as follows:

EV = P(fold)*Profit on fold + P(call)*Equity on call
= (25.3/30)*($0.40) + (4.7/30)*(0.51*$2.00 - 0.49*$2.00)
= +$0.34

So pushing over these open raises is profitable. We can see that even if the open raiser has stats like 5/5 (vp$ip/pfr) => No Fold Equity. We still have positive EV. Because our equity is often ahead of the calling range. If the open raiser calls us looser then our equity increases which only improves our EV. I am not sure what the optimal calling range is but the only situation this is unprofitable is against a really nitty 2/2 (vp$ip/pfr) style player that only open raises the very top end of hands.

Example 2: 3bet by Villain

Known players:
[tg]Position_Stack:hands/vp$ip/RaisePreflop/AF/WTS/ORL/BBvsSteal/W$SD;Hero$2:///////;CO$15.35:09/67 /56 /-/80 /50 /-/0 ;[/tg]
0.05/0.1 No-Limit Hold'em (8 handed)
Hand recorder used for this poker hand: PokerStrategy Elephant 0.67 by www.pokerstrategy.com.

Preflop: Hero is MP2 with K♣, A♦
2 folds, Hero raises to $0.40, MP3 folds, CO raises to $1.20, 3 folds, Hero raises to $2 (All-In), CO calls $0.65.

This time around we open raise from MP2. A villain in the cutoff 3bets us and everyone else folds. Now we are faced with the decision fold, call or shove?

A call is clearly not an option because we would cbet all in anyway on the flop . Our decision now is either to push or to fold.

Equity:
If we assume that the CO 3bets us fairly tight (JJ+, AK). Our equity is only 40% so our EV is as follows:

EV(fold) = -$0.40
EV(call) = (0.4*$2 - 0.6*$2) = -$0.40

Here we can see that our EV is the same in both situations. Our decision therefore must be based on the range we give the CO. If he is passive or tight we can probably make a fold in this spot. However against standard villains or looser fishies we can happily put our money in because our equity improves.

We can see from this example that a 3betting range is ahead of AK in equity so if we are faced with a 3bet before we get to act we can find an easy fold because of our poor equity.

Conclusion:
The rules for AK work as intended although one could argue it is possible to fold to a 3bet from a tight opponent. So next time your Big Slick is busted by pocket 3's feel confident that the money is going in well. ♦

Phil

Interesting post,good luck with ur SSS adventure.Post more stuff like these!!
I will only disagree in one thing,u may be quite right bout the 2nd example but i think that at NL10-25,its better to shove ur AK after the 3bet since more often u will be ahead since there are LOTS of fishes,but i can say aswell that after 15k hands at fulltilt(recently started)i have aswell met some regs who will 3bet me only with QQ+ so i fold here and there
i am aswell playing NL10 sss but at full tilt mostly,soon will be playing at stars too.

Cheers

Nice work, but I think it should be noted that the ranges you give villains for their moves are way too tight on average. Only a Basic SSS player or complete rock/nit will play this tight.

The Hands you actually posted have some Stats on them and we can see that the villains will raise/call with a far wider range than you have stated In future maybe modify the stats a bit to fall in line with the ranges you post!

Good Luck in your SSS endevour, You sound like someone who should be able to go a long way using this strategy! Oh, and have fun too ♦

Feedback:
Thanks for the feedback guys. I agree that in order to fold AK to a 3bet I think you need a real strong read that the player is 3betting very tightly. In most situations you can shove your money in and have good equity.

If I have estimated the villains ranges too tight then putting in a looser range should yield even better results. I am not entirely sure on the exact ranges that a standard player 3bets. Can I retrieve this information in Elephant somehow?

Progress Report #1 - First 5,000 Hands of NL10:
So I have now played my first 5k hands. This is just using basic strategy without any steals or resteals. I have been trying to follow the preflop rules exactly and have been playing very conservatively when I get a freeplay. I am currently running at a winrate of 3.8BB/100. It was a little higher but I caught a minor downswing at the end.

I'm always looking for leaks in my game and I think the next areas I need to assess are how to play accurately double stacked (at the moment I am just leaving as soon as I double) and the conditions that I should not cbet (at the moment I cbet most of the time against 1 player).

I am still very optimistic about the strategy, I believe it to have some great potential especially when I refine my postflop play. However I am worried about the money/hour potential it may have. Can anyone reassure me that it is worth the time?

Phil

Phil look,on NL10 u will never make decent money,maybe NL50+ and up..
Imo c-bets dont work for 2 reasons only,A)villain is a calling station
and B)ur sitting too much time at the table so people know that u are c-betting a flop no matter what.
I wanted to ask u,how many tables do u play and what kind of sessions?
When i was playing SH bss i used to play 150-500 hands sessions,now i on average play 1k hands.
Also i dont seem to understand the double stacked issue,since i dont know if its in the silver articles but i thought that u must leave with 25bbs,i tbh leave at 27-28+ if tables is tight,if juicy i hang around till doubling up.

A Hidden Leak:
The nature of the SSS is that we double up often. We are often putting our money in preflop and playing a double or nothing style. The strategy of course is to leave the table after we double. However the more critical players out there will want to play the extra "free" hands before we have to pay another blind.

How do we adjust our play during these extra free hands?
The articles on the SSS say that it is unprofitable with a stack of over 25BB. This is why we in principle buy out. We cannot therefore play double stacked the same way as a Shortie. However we also cannot play in the same manner as a Big Stack because we don't have 100BB.

We face a problem because we to invest a 40BB stack with TPTK is often overplayed but we also lack the implied odds to play Suited Connectors and Low Pairs. What I therefore suggest is an extremely tight range. Essentially we are hoping that we catch a premium hand that we can happily go broke with in most situations.

Cowboys and Rockets:
AA/KK is obviously going to be played from every position with any stack size. We can make very few mistakes investing a 40BB (or bigger) stack with either of these hands. If we are experienced postflop I think we could also add QQ/AK to our range but this depends on whether we can handle the increase in variance from losing our initial stake and profit in one go.

Is it worth the bother?
The less pedantic readers will by now be screaming "Why bother?" but consider that KK+ is almost 1% of the cards. If we get between 0 and 8 free hands each time we double up then we can see that after roughly 25 doubles we are going to catch a premium hand and get a nice extra bonus. ♦ It might make the difference between profitable SSS and breakeven. The best bit of course is that it is completely free!

Putting it into Practice:
A little trick I thought of to tell when we are playing double stacked is to simply put a "X" in the chat box. This means that while heavily multitabling we can see which tables we are playing double stacked and which we are playing SSS very quickly. You saw it here first

Final Note:
The best bit about the extra bonus is that it occurs infrequently so it is a good moral boost. When the session is beginning to drag and you are feeling down catching Aces twice in a row is a brilliant feeling!

Phil

Hi Phil, nice to see you taken a professional approach to the game, using math for making the right decisions. This is how Grev started...

Two comments regading one of your posts.
-Big slick- AK suited if the 4th best hand in Holdem (after QQ,KK,AA) , AKo is only 10th.
-EV(fold) is always zero.

Good Luck,
see you in the hand evaluation section.

Hey Phil,

Very interesting blog you've got here. I like your theory discussions and this approach to the game will take you very far.I shall try to participate as mucha s possible =D

Regarding playing double stacked, I believe it is very important that a player can feel comfortable with an increased stack before he should venture into it. If he isn't, then it's probably best to restrict his range to QQ+ or even a more tight KK+, which, as you said, leave nearly no room for mistakes or -EV moves. But as you get a better notion of equity and develop confidence in your post flop game you'll pretty much be able to play any of the hands in the SHC and more. A few notions of BSS will surely help as well, as you can make minor changes such as limping with mid PPs for set-mining.

I wish you the best in your endeavour! Regards.

Thanks for all the wonderful feedback. Its great to have a place to really argue over the minor details. I'm trying to be professional because I believe minor leaks can make or break the SSS. And of course every little bit of profit that can be made is extra profit waiting to be had! ♦

Regarding AKo:
Very interesting to note that AKs is the 4th best and AKo is the 10th. I assume that is based on some sort of equity? If so should we play these two hands differently in any situations?

My rough guess would be that we would have significantly better equity in multiway pots with AKs compared to AKo. However Equilator takes a while to run even a 3way simulation so it is hard to analyse effectively (quickly).

EV(fold):
The act of folding has 0 EV but I've never come up with a very satisfactory way of saying that by folding we are giving up a stake that we have placed in the middle. What would be the correct terminology?

Big Stack:
I have quite a large range of experience with 100BB stacks but very little with middle (40BB) stacks. I personally agree that QQ and AK should be playable with a double stack but it really depends on your personal experience of a bigger stack. I think set-mining is likely unprofitable because to get correct odds you would need to limp which then the implied odds go way down.

Poker Brothers:
Dandycal your blog really inspired me to give SSS another try. Its great to see you've gone professional. I'm an Englander so I would have to make a lot more than $400 to go professional Oh why can't I live in a poor country.

All the best everyone,
Phil

AKs = 4th best AKos = 10th Best

Is this subjective or objective? AKs = 4th = common position. AKos' position in hand ranking seems to differ depending on the source of info i.e no consistant agreement.

Looking Foolish:
Picture the situation. We're dealt AKo on the button. We put in a legitimate raise and the BB calls. The flop comes Q 7 3 :diamond:. Its checked to us and we put in a standard cbet hoping to take down the pot. Now the worst possible thing happens and the BB wakes up and pushes all in.

We're stranded with half our chips in the middle and being forced to make a decision for the rest. Worse - we don't even have a hand! We make the fold and look like another over aggressive player who fell into the trap.

Can I get lucky this one time?
A thought that often runs through my head at a time like this is "Do I have the odds to call this?". My heart yearns to gamble and hope to hit my lucky cards. Of course we cannot give in to this speculation and often not being entirely sure of myself I fold. Preferring to make a bad fold than a potentially stupid call.

Do we ever get the odds to call?
I am now going to look at a few situations where I folded and with a bit more time and diligence than I have ingame assess whether I could've actually made a correct call. I will focus purely on overcards on dry boards. Calling with non-overpairs is more an assessment of whether the opponent is bluffing than pot odds and wet boards are more troublesome because of the possibility of strong draws.

Example 1: AQo

Known players:
[tg]Position_Stack:hands/vp$ip/RaisePreflop/AF/WTS/ORL/BBvsSteal/W$SD;Hero$2.00:///////;MP3$12.05:15/53 /20 /3.0/25 /50 /-/100 ;[/tg]
0.05/0.1 No-Limit Hold'em (6 handed)
Hand recorder used for this poker hand: PokerStrategy Elephant 0.67 by www.pokerstrategy.com.

Preflop: Hero is MP2 with A♣, Q♠
Hero raises to $0.40, MP3 calls $0.40, 4 folds.

Flop: ($0.95) 3♦, J♠, 7♣ (2 players)
Hero bets $0.50, MP3 raises to $1.60, Hero folds, MP3 gets uncalled bet back.

Final Pot: $1.95

In this hand we can see an open raise by the hero, a dry board with an OOP cbet followed by a push from the villain. The villain is pretty aggressive over the 15 hands we've seen but I'm going to assume that he is holding some sort of sensible hand. I think we can also assume (provisionally) that he does not hold QQ+ because almost all players 3bet these hands preflop.

For the sake of arguement we will assume he holds Jx which means the hands that are inside his calling range (20%) that he pushes over our cbet are: AJ, KJ, QJ, JJ, JT and J9s.

Against this range we have 18% equity. However it costs us $1.10 to call to win a pot of $4. So our pot odds are 27.5%. Since our pot odds are worse than our equity we should always find a fold with our overcards.

Example 2: AKo with dead money

Known players:
[tg]Position_Stack:hands/vp$ip/RaisePreflop/AF/WTS/ORL/BBvsSteal/W$SD;SB$1.90:29/24 /10 /-/25 /0 /-/0 ;Hero$2.00:///////;BU$5.50:49/76 /15 /2.5/27 /0 /0 /20 ;[/tg]
0.05/0.1 No-Limit Hold'em (8 handed)
Hand recorder used for this poker hand: PokerStrategy Elephant 0.67 by www.pokerstrategy.com.

Preflop: Hero is BB with A♥, K♠
5 folds, BU calls $0.10, SB calls $0.05, Hero raises to $0.60, BU calls $0.50, SB folds.

Flop: ($1.30) Q♣, 8♦, 2♥ (2 players)
Hero bets $0.60, BU raises to $2, Hero folds, BU gets uncalled bet back.

Final Pot: $2.50

This example is very similar but we have more dead money in the pot and a shorter remaining stack. Will our odds have increased enough for us to call our overcards this time?

If we assume the villain again to have Qx then our equity is 16%. Our pot odds are 20%. Again our equity is lower than the odds offered and we have to fold.

Poor equity needs excellent odds:
Since our equity against a made hand tends to lie below 20% we need excellent pot odds to play cbet/call. Infact I would suggest (without any proof because I am lazy) that our odds will never be good enough to play cbet/call because we would instead have cbet all in.

Conclusion:
Overcards are not good enough hands to play cbet/call against a sensible opponent. We may feel like an aggressive fool because of our failed cbet but at least we are not a stupid calling station hoping for a suckout. ♠_cool:

Originally posted by Smileyphil

Final Note:
The best bit about the extra bonus is that it occurs infrequently so it is a good moral boost. When the session is beginning to drag and you are feeling down catching Aces twice in a row is a brilliant feeling!

Phil

It's a great morale boost when you win. What about the classic preflop all in with KK against some aggressive guy with AK, and the ace comes on the river - you lose all 40 of your big blinds.. Now that does exactly the opposite.

Although a couple of times I've doubled up, then in my final rotation waiting for the blinds to leave, I got AA twice and doubled up twice to have 4 stacks at the table before I left! That's a morale boost.

An Immoral Boost:
Too true that when our KK+ gets busted its going to hurt. But at the end of the day I am comfortable with getting any amount of money in with both these hands even if they don't hold up. I think one of the first anti-tilt lessons we must learn is to be happy with the strategy even if our results don't show immediately.

Still if you are the sort of player who is going to tilt when you lose 40BB it may be better not to bother waiting because it will only cause you problems.

Coaching:
Today I attended the SSS basic coaching. I have to say it was brilliant. For any beginners out there who are just starting with the SSS I cannot stress how useful this will be to your progress. I got rather more involved than I intended and asked lots of questions until I realised I hadn't eaten since breakfast and had to rush off before I starved to death. Keep up the good work Gerv.

Phil

GO GO DR. PHIL!!! ♠_evil:

10k hands now!
So I have now played 10k hands. It is going very well. I've got a steady vp$ip of 6. May seem a bit low to some SSS but I am not playing any steals at all at the moment. I think the fish at NL10 call a little too often for me to steal with a wide range. I will need to run some simulations. For most of the hands my winrate was hovering around 5BB/100 but towards the end it edged up towards 6BB/100. Whether this is because my play is improving or my luck is improving I am unsure at the moment.

Regarding Variance:
Many people have said that the SSS is swingy and have graphs that zoom up and down. So far mine is an almost straight line gradually sloping upwards. I am almost expecting some sort of swing so I am ready mentally but I have to ask whether the majority of these "swings" are actually leaks/tilt?

Update Frequency:
I have considered how often to post "progress" reports and have decided about every 5k hands will be suitable. I don't want to report every minor swing because no-one wants to see a hundred posts where AA lost to KK and then AK beat AQ. At the same time I like a good brag when I'm winning and a good whine when I'm losing. It keeps me motivated. ♦ Every 5k hands should be roughly every 3/5 days depending on my other commitments so that should be perfect.

Phil

Originally posted by Smileyphil
10k hands now!
So I have now played 10k hands. It is going very well. I've got a steady vp$ip of 6. May seem a bit low to some SSS but I am not playing any steals at all at the moment. I think the fish at NL10 call a little too often for me to steal with a wide range. I will need to run some simulations. For most of the hands my winrate was hovering around 5BB/100 but towards the end it edged up towards 6BB/100. Whether this is because my play is improving or my luck is improving I am unsure at the moment.

You can steal easily even on NL10 (against regulars, PS SSS'ers). But winrate is very good, so may be it is not worth...

Cast out the Fishing Lines:
Every SSS player loves to be sat, in position of course, on the crazy bet/bet/bet player who hasn't found the fold button. But how do we find these players? A player with a large database could potentially search the tables by hand and look for open seats next to said players. This however seems like hard work. Especially when we are multitabling and don't have time for tedious searching.

Fishing Rod vs Whole Net:
The approach above illustrates a method of searching for one particular known fish and focusing on taking his money. I propose instead using the table statistics in the poker software to increase the likelyhood that we are sat with weak players.

Player/Flop Statistic:
If we consider a table where twice as many players see the flop from another table. We can provisionally assume then that they will also call bets twice as loose. (Big assumption I know). If they call our raises twice as often then it means that time between all in's is halved. So in theory our profit is doubled.

Average Pot Statistic:
This statistic comes in handy as well because the larger the average pot the more money is being put into the middle on a regular basis. Since you can only sort by one stat I tend to use Player/Flop but a higher Average Pot is a another strong indicator of a loose table.

Equity:
The other big advantage comes from our equity. If the players call twice as often then they are calling with far worse hands. This means that when we are called we are more likely to win and further increases our profit. If we are feeling particularly observant we can further adjust to our opponents wider ranges to increase our profits further - however this is a more advanced play.

Conclusion:
It is worth checking often on the "fishiness" of the tables we are sat at because of the extra boost to our winrate it provides.

Phil

NL10 - 15k hands:
So I've now played 15k hands. In the last 5k I had a few spells of breakeven that have reduced my winrate below 5BB/100. I think some of this is partly due to some increased variance. I am now playing draws slightly more. In the first hands I played check/fold and if they let me see it free I would bet after I caught. This leaks a little bit but is better than bad calls. I'm now calling when I have odds which is better but has higher variance. I'm more than half way to my bonus which is going to be a nice boost. Hopefully by 20k hands I will have the bankroll for NL25 but if it takes 25k hands that is fine by me.

Originally posted by Smileyphil
Cast out the Fishing Lines:
Every SSS player loves to be sat, in position of course, on the crazy bet/bet/bet player who hasn't found the fold button. But how do we find these players? Phil

On Titan you can mark found fishy players as 'buddies' and use the search function to what tables they are playing