I ended up folding the KK. I figured there was going to be more raising on the turn and/or river (b/c the drunk guy was raising and check-raising a lot), so I let it go.

I haven't been back yet. Had some relatives in town, was sick for a few days, and I wanted to finish re-reading SSHE before I go back. I'm sure I'll have more hands to ask about once I do go back.

Yes. Here is the math.

http://people.math.sfu.ca/~alspach/comp47.pdf

I take it you got your numbers from the table on page 5. Those don't apply to a post-flop setting, where you get to see three more cards. I'm pretty sure my calculation is correct. But we can double-check it by using the same combinatorics-based approach as the authors of the paper:

Look at the top of page 5, where it says, "The remaining hands are being chosen from 50 cards of which 3 are aces and 47 are not aces. This sets the parameters for the calculations that follow." That's preflop, right? Well post-flop, the remaining hands are being chosen from 47 cards, and 44 are not aces.

So substitute "44" for "47", and substitute "47" for "50" in the calculations put forth in the first full paragraph on page 5. Thus the chance that the nine remaining players have no aces is:

(44 choose 18)/(47 choose 18) = 0.2253469

QED.

Corrected. Thanks for the explanation.

What we care about is the likelihood of someone having an ace when a ace flops and we don't have an ace.

Just in case, I ran a simple Monte Carlo simulation in R:

> Deck <- c(1,1,1,rep(0,44)) # 1's are Aces; 0's are non-Aces
> NRuns <- 1000
> NoAces <- 0
> for (i in 1:NRuns) {
+ NineHands <- sample(Deck,18) # Deal nine hands, or 18 cards
+ if (sum(NineHands)<1) NoAces <- NoAces + 1 # If no Aces, bump up counter
+ }
> NoAces/NRuns
[1] 0.225

EDITED TO ADD: It was a total fluke that the simulation came out with exactly 225/1000 hands with no Aces on the first run! What is the chance of that happening??

Answer: About 3%. Using the binomial distribution probability function:
> choose(1000,225)*(0.2253469^225)*((1-0.2253469)^775)
[1] 0.03018887

You are actually correct, if your concern is what level to play based on the swings you care about the $ amount.

That's already a well known number though, for live play you should have between 400-600BB for a low risk (under 3-5% going by memory) of losing it all. 100 to 150 BB downswings aren't that rare in 1k hours of play. If you play with a full kill, make that more like -200BB.

The more passive the game, the closer to 400 BB, the more agressive closer to 600.

What numbers are you using for WR and SD?

Given that it's a high rake environment, I ballparked it using .5BB/hr, with stdev of 13, but it's probably "similar"up to .75 BB/hr (in the sense that 5% "feels" the same a priory as 2%) .

Thruth be told, I'd recommend that amount to a 1BB/hr winner just so that (even if they don't have the money available) they don't completely freak out after the first 100BB loss. If this loss happens early, their RoR is probably close to 1% anyway.

Edit: I'm throwing around the term "1BB/hr winner" like we can estimate that accurately, but we can't for live play (as you know), but we have to live with that limitation. That's why (as you know) it's always good to run the calcs with a range of winrates.

I think your SD is pretty high, but I could be wrong.

So I've put in several hundred more hands, and I have to admit, I'm having a hard time getting my game up to the next level. I think my preflop play is pretty good, but post-flop is a lot tougher.

I've read and I understand the concepts in SSHE. I can count the bets in the pot. I know how to count my outs, and to compare the pot-odds with my chances of drawing out. I can narrow (some) players' ranges, and I'm getting a little better at reading them.

But doing all of this at the same time, in the middle of a hand, is pretty tough to do. These hands move fast. It's a lot of information to juggle and analyze that quickly. I can do one or two of these things in the same hand, but not all of them. And it gets tedious counting everything all the time... It's so much easier just to fall back on my instincts...

So far I'm down about 10 BB after 15 hours of play at 6/12, so the lessons aren't getting too expensive yet, but I also don't feel like I'm progressing very much.

On the plus side, my variance has been quite low so far (albeit over a pretty small number of hands.) At no point have I been down more than one rack. (And again, I realize this number of hands is barely a drop in the bucket.)

So question for you guys: How many hands did you have to put in at live play before you felt like you had a strong command over the various post-flop tactics set out in SSHE?

Measure your progress by seeing how often you make good decisions and if they are becoming easier to make. Another metric is how much easier it is for you to spot errors by others.

Don't use results or variance to gauge your play. Make sure you aren't playing with scared money and passing +ev raises for fear of losing bets. These extra bets will provide the cushion needed during periods of runbad. Make sure you review your play on winning sessions too.

I'd say try to play 300-400hrs at this new level to get comfortable with the game to the point where most decisions are easy. It'll also allow you to get a good understanding of how the regulars play and adjust to each of them.

Make sure you know how much is in the pot befor the next card comes out.

Pre-calc and memorize the minimum odds you need to continue for some common situations - flush draw, flush draw with 1 overcard, flush draw with 2 overs, flush draw with a pair, etc. You can decide pretty quick once you've done that. It also keeps you from forgetting outs as you tend to forget about the overcards, etc.

This I can do. For example I know when I'm getting good pot odds on a flush or straight draw that will be good enough win the hand. But this happens fairly rarely.

What I find much harder is counting outs in less obvious (and more common) situations. E.g. I have a made hand, but a couple players are betting aggressively back at me, and I think I might need to improve, but I'm not sure, and I'm not sure by how much. Or when I think it's possible I'm drawing dead, and I'm not sure how much value to assign to an out (e.g. with a small flush or the low end of a straight draw.)

I don't always do this stuff, but probably the proper sequence to think about the hands is this:

Preflop, you have this down, so good. If people limp, it's hard to assign them a range because it's so wide, so don't worry about this. It's more the raisers that you can use to narrow their range.

If you break down the sequence of a hand, you can concentrate on only certain aspects of the game at each part. Trying to do everything at once is hard, so prep yourself for each stage before it happens, else trying to add up the pot while you're trying to make a decision is too many things happening simultaneously.

[Preflop: Dealer brings in bets and burns a card] -- count the number of bets. Simple multiplication, # of players x # of bets each. I usually double-check my cards at this point to memorize the suits so I don't have to recheck them in the middle of the hand.

[Dealer starts dealing the flop] -- if there are like 6 people in the hand, don't worry about it. If there are like 2-3, watch the players instead of the cards to try to read a reaction.

[Flop: Everyone checks to you or you're first to act] -- you don't really care about people's ranges, you just evaluate your hand vs. board and figure out if you have a good enough hand to bet.

[Flop: Bets or raises to you] -- now you should be thinking about the players in the hand and their ranges/tendencies.

[Dealer burns a card and starts dealing the turn] -- add up the pot again.

[Dealer deals turn] -- watch the players reactions again.

Same on river.

I think it took me about 600 hours before I really was playing SSHE strategies at a reasonable level.

grunch

online (merge) would be a great place to start. Grab HEM/PT, play whatever stakes you want or can afford, and after a couple thousand hands you can see/fix whatever holes you may have in your game after not having played for so long.