Originally posted by Gerv
Oei Mathematical brawlfight over here.Popcorn is ready folks! ♠_cool:
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Have to start writing a new course today, so I'm eagerly looking for excuses not to. Of course! Blogging!
i) You'd think that one of the advantages of getting older would be not having spots. However this morning I find I'm growing a real monster right on the end of my nose! Bah! There's no escape kids! 
ii) Found out that mrs jb used my top quality, state of the art, chiropodist's nail pliers (don't get me started on my feet) to clip the guinea pigs' claws. WTF! Apparently it's OK because she washed them and their claws are 'much easier to clip than my toenails'. She knows me so well. 
iii) Had my first ever 'sweat session' (yes, those really are apostrophes) with goldchess and Paulius (thanks chaps). I live in the countryside, so my internet connection is a bit slow, which was a bit troublesome (btw, mikogo >> Teamviewer), but it was an interesting evening. A bit serious for my liking, but quite helpful. The annoying thing was that when the other two were watching, I had my first winning session for ages (BR $465). Maybe they should watch me more often. I was only playing five tables, so maybe 12 is too many for me. I'm going to try playing 8 successively instead of in sets next time and see whether this helps. I also think I'm pushing a bit too tight from late/mid position. Another thing that I found out is that my typical thought process is 'Hmmm, shall I push, looks close, don't know, oh, go on then!' . You'd think I'd be weighing up stack sizes and stats, but no. Something to work on there I think. Part of the problem is that that's how I do maths. Get it wrong a few times until I stumble across the right answer. Speaking of which, the solution to the AAKKQQ problem is coming up next.
iv) First hand of a $3.40 SnG. You pick up 88 UTG. What do you do? This is something we discussed last night. I folded. Goldchess would call. Paulius would raise. The PS approved method is limp/fold, which I hate. Anyone want to put a cogent argument for the right approach? I expect Dan Harrington would be looking at the second hand of his watch for inspiration. I'd like to see him trying to balance his play on the $3.40 turbos! 
The deck contains AKQ, in two suits. Players X and Y get a card each, $2 in the pot. X checks, Y can check or bet $1. If Y bets, X can call or fold.
Remember, the equilibrium solution to the AKQ game is that Y bets A, checks K and bluffs 1/3 of his Qs. X calls A and 1/3 of his Ks, and folds Q. This gives Y a profit of $1/18 per hand.
The equilibrium solution of the AAKKQQ game is that Y bets A, checks K and bluffs 1/3 of his Qs (as for the AKQ game). X calls A and 1/2 of his Ks, and folds Q. This gives Y a profit of $1/5 per hand.
The addition of an extra suit more than trebles Y's profit! This is because X has to call with more of his Ks, and loses half the pot when he folds Q to X's bluffs. X has less information in this game. If he has a Q he's not necessarily losing, as 1/5 of the time Y will have one too. It doesn't seem to me entirely obvious why the solution is the way that it is, but that's the reason we do the maths right?
Can this analysis be extended to a two suited deck with N cards? What happens as N -> infinity? (Presumably as N->infinity the fact the effect of having two suits instead of one tends to zero?)
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Solution of the AAKKQQ game
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We are looking for the optimal values of Y's betting frequency with Q and K (bQ, bK) and X's calling frequency with Q and K (cQ and cK). Y always bets A and X always calls with A.
With X's hand given first and Y's second, X's additional profit from the betting is (note the 1/5 and 2/5 weightings as different card combinations are twice as likely as QQ, KK, AA):
QQ, X loses $1 when Y bets and he folds, -bQ(1-cQ))/5
QK, X loses $1 if Y bets and he calls, -2 bK cQ/5
QA, X loses an extra $1 is he calls, -2 cQ/5
KQ, 2 bQ(cK-2(1-cK))/5
KK, -2bK(1-cK)/5
KA, -2cK/5
AQ, 2bQ/5
AK, 2bK/5
AA, 0
Adding this all together, X's profit is
P = (bQ(cQ+6cK-3)+2bK(cQ-cK)-2cQ-2cK)/5 = (cQ(bQ-2bK-2)+cK(6bQ+2bK-2)-3bQ)/5
Now, if you use Chen and Ankeman's indifference argument, you get that the equilibrium solution satisfies
cQ+6cK=3, cK-cQ = 0 => cQ = cK = 3/7
bQ-2bK=2, 6bQ+2bK=2, => bQ = 4/7, bK = -5/7.
Hmmmm. Negative bluffing frequencies are to be avoided! Looks like we need to be more careful.
The four conditions to be satisfied are:
1) cQ+6cK=3, or cQ+6cK>3 and bQ = 0, or cQ+6cK<3 and bQ=1,
2) cK = cQ, or cK>cQ and bK = 0, or cK<cQ and bK = 1,
3) bQ-2bK = 2, or bQ-2bK>2 and cQ=1, or bQ-2bK<2 and cQ = 0,
4) 6bQ+2bK = 2, or 6bQ+2bK>2 and cK=1, or 6bQ+2bK<2 and cK=0
Interpretations
1) if X calls too much/too little, Y never/always bluffs
2) if X calls with K more/less than with Q, Y never/always bets with K
3) if Y bets with Q much more/much less than with K, X always/never calls with Q
4) if Y bets too often/too infrequently with Q and K, X always/never calls with K
we start by looking at the three cases that arise from 1)
i) cQ+6cK = 3
Three subcases from 2)
a) cK = cQ => cQ = cK = 3/7, and then the other two conditions give bQ = 4/7, bK = -5/7. No good!
b) cK>cQ, bK = 0. Then 3) => cQ = 0, cK = 1/2, 4) => bQ = 1/3. This is the equilibrium solution.
c) cK<cQ, bK = 1. Then 3) => cQ = 0 < cK, a contradiction.
ii) cQ+6cK>3, bQ = 0. Then 3) => cQ = 0, and 4) => either bK = 1, when 2) gives cK<cQ = 0, no good, or bK<1 and cK = 0, so that cQ+6cK = 0 < 3, again, a contradiction.
iii) cQ+6cK<3, bQ = 1. Then 3) => cQ = 0 and 4) => cK=1, so that cQ+6cK = 6 > 3, a contradiction.
QED
Actually, since 0<=bQ<=1 and 0<=bK<=1, it's clear that bQ-2bK<2, so that 3) gives cQ = 0 immediately, and we could make the proof somewhat easier, but CBA! (I learnt CBA from my son. It's his guiding philosophy.)
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Tried playing successive instead of sets last night. 8 tabling. Managed to get 20 in. Started well then went down the pan (BR $445). Did a hand review this morning, and found QQ pushed into KK, AK sucked out by AQ, AA cracked by QJ. Standard stuff. I will suck it up, and assume I still have an edge, as I can't find anything obviously wrong. Posted a couple of troublesome hands on the HR forum. Must get SnGWiz though. All the other boys and girls seem to have it and I want it too! 
Mrs jb has gone to Hampton Court flower show today (alright for some!), so I have the beasts for the day. School fun day this afternoon, so will spend 2+ hours in bouncy castle/burnt burgers hell. And it's too f**king hot! Am melting.
Off to trot up and down the road making sure my daughter doesn't fall of her bike. Happy days. I want to play poker!
Am tempted by the 100FPP silverstar MTT on Pokerstars tonight. Haven't played an MTT for a while now. I miss that 'wow, sucked out on the bubble' feeling! 7.30 may be too early though.
Thought I'd have a go at SSS since Gerv said it's all maths. I tried it once before but got bored as I was only playing four tables. Managed to stick the kids in front of the TV after the school fun day (Donked off £20 there!), and watched Gerv's first three videos. It all seemed fairly straightforward, so I gave it a try on 10 tables and managed to put in 1.5K hands on NL10 with the results below. I got sucked out on a fair few times, so I was pretty happy with how I played. I loosened up my blind stealing ranges a bit, and also my restealing ranges, as the basic PS strategy seemed a bit tight. I also tended to shove profitable hands SB v BB, and BB v SB complete. I think I'll stick with this for a while. There's a strangely mechanical, hypnotic quality to playing like this, but I love the fact that you don't have to worry about chip EV v equity EV, and all that ICM stuff, which is the main problem with SnGs. Guess I'm lazy. My reading of SSS is that steal and resteals are where the main problems arise. Looking forward to parts 4 and 5 of Gerv's video series.
SSS - the ultimate intro to the preflop game. Great compliment to SnGs, methinks. Family day for me too, today. Luckily she's too small for bikes 
Hmmmm. Not a bad song, but they don't look old enough to have much idea about midlife crises. And why is he carrying a spade?
And poop, I just lost my gold status. Never mind!
Shortstacked another 1.5K NL10 hands, which I enjoyed, even though I had a losing session. I felt I got my money in good (should be 'got my money in well', but I'm going to have to concede that certain adverbs are dying!), but got sucked out on a lot (runner-runner flush twice). What I'd like to know is, is that what this graph shows? Is the fact that the 'net expected BB won' is so much higher than my actual winnings an indication that I got my money in good but was unlucky? After all, SSS doesn't involve much in the way of hero laydowns! How do they calculate this graph? (Mathematical details please if possible.)
BTW, you'll be glad to hear that 'sadertic' is now, thanks to this blog, officially a word according to google. How sadertic is that?!
Have also now won three games of scrabble in a row against number one son, even though last game he managed to get the 10 point rude word bonus three time with 'wank', 'wanked' and 'nob'. How appropriate. And he gave up after I put down the seven letter word 'lectern'. ♠_cool:
I've answered my own question posed above, (Expected BB won is based on all in EV, which is pretty much what you're winning with SSS I think) and I do think I had an unlucky session last night. I like SSS because it's pretty obvious when you're getting it in good and getting sucked out on, and vice versa. Going to stick with it for a while I think. It all seems a bit like my view of life ( 
). I've been following the 'have you read the Holy Bible' thread, and it does seem that, like me, a lot of poker players are athiests. If you're the sort of person who sees patterns in everything, and that some things are predestined, and that we have no power over fate, you're also going to be the sort of poker player who thinks that FT is rigged and they 'never hit' and that they're unlucky. Life is a huge sea of random events, and successful people, like successful poker players, ride this out as best they can. When I was playing SnGs I never had the chat box at the top, but now I'm trying SSS I can see the sort of nonsense that people type in. The number of people who think that Pokerstars gives good cards to players who are 'employees' is astonishing.
Having said that, the hand below was obviously won by a mofo Pokerstars employee, because clearly the whole f***ing thing is rigged! ♦
PokerStars No-Limit Hold'em, $0.10 BB (8 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com
UTG ($1.92)
UTG+1 ($5.49)
MP1 ($2.49)
MP2 ($2)
CO ($5.49)
Button ($6.62)
SB ($1.26)
Hero (BB) ($1.85)
Preflop: Hero is BB with 7
, 8
1 fold, UTG+1 calls $0.10, 5 folds, Hero checks
Flop: ($0.25) 2, 8
, 7
(2 players)
Hero bets $0.20, UTG+1 calls $0.20
Turn: ($0.65) K (2 players)
Hero bets $0.60, UTG+1 raises to $1.20, Hero raises to $1.55 (All-In), UTG+1 calls $0.35
River: ($3.75) K (2 players, 1 all-in)
Total pot: $3.75 | Rake: $0.18
Results:
Hero had 7, 8 (two pair, Kings and eights).
UTG+1 had K, A (three of a kind, Kings).
Outcome: UTG+1 won $3.57
And the icing on the cake was that he followed up his sophisticated EP limp of AK by typing 'nh donk' into the chat box. Pfffffffff!
Have turned into sicko SSS grindbot (Thanks Gerv!). Have clicked 'fold' so often am getting repetitive strain injury (or, wanker's wrist as it used to be known). Have lost the use of pronouns like sad Bridget Jones clone.
But seriously, I'm really enjoying this. What does that say about me? Boring bastard I reckon (No offence Gerv. BTW, don't you just hate people who start sentences 'No offence', as if it means that they're then allowed to say any appalling thing they like and somehow it doesn't matter? Almost as bad as people who say 'Well I like to speak my mind. What you see is what you get with me.', when what they mean is 'I have no social skills whatsoever.')
Keep getting sucked out on, losing 99 v 77, AA v QQ, donks chasing inside straights, AQ v AJ, etc. The graph below confirms this. But I don't really mind. I know I'm getting my money in good, so it'll come right. Plus I'm clearing my bonus and generating strategy points at about the same rate as when I was 12 tabling $3.40 turbos. And I'm playing NL10 when I'm bankrolled (BR $460) for NL50! Happy days!
Had to stop early tonight. Feel my game is OK and should be pofitable, but still keep getting those suckouts. Thought I ought to stop. I was above all in EV for a while, but then the hand below happened (see if you can spot it on the graph kids!). Didn't think I was tilting afterwards, but better safe than sorry!
Speaking of trauma, my parents are visiting tomorrow and staying for the weekend. For any under 25s reading this, if you're hoping that one day your parents will treat you like an adult, forget it, it isn't going to happen! Just suck it up and humour them.
Over and out until Sunday night. Will no doubt have amusing parent-related stories to report. Actually, mrs jb suggested teaching them how to play poker. 
PokerStars No-Limit Hold'em, $0.10 BB (7 handed) - Poker-Stars Converter Tool from FlopTurnRiver.com
Button ($2.63)
SB ($8.46)
BB ($4.88)
Hero (UTG) ($2.10)
MP1 ($4.90)
MP2 ($1.94)
CO ($3.83)
Preflop: Hero is UTG with A, A
Hero bets $0.40, MP1 calls $0.40, 4 folds, BB raises to $2.50, Hero calls $1.70 (All-In), MP1 calls $2.10
Flop: ($7.15) 4, 2, 5 (3 players, 1 all-in)
BB bets $0.50, MP1 raises to $2.40 (All-In), BB calls $1.88 (All-In)
Turn: ($11.91) 4 (3 players, 3 all-in)
River: ($11.91) 5 (3 players, 3 all-in)
Total pot: $11.91 | Rake: $0.57
Results:
BB had K, K (two pair, Kings and fives).
Hero had A, A (two pair, Aces and fives).
MP1 had Q, K (flush, King high).
Outcome: MP1 won $11.34
I just got a reply to an email I sent to pzhon (what a nice chap!) about maths and poker. He pointed me to the home page of Thomas Ferguson (Chris Ferguson's father!) where there are copies of three mathematical, father and son, papers on poker. Haven't read them yet, but thought I'd record this here in case anyone else is interested.
Thanks pzhon!
hi jbpatzer! Good job with SSS! but dont worry about the EV diference with only 6000 hands, neither when it still continue with 60.000 hands, it will happen...xD
Originally posted by taavi1337
Good luck! (you won't need it, but it's a nice wish)
I would have thought that if there's one thing my results demonstrate it's that I doooooooo need some luck!
Originally posted by oskrgy
hi jbpatzer! Good job with SSS! but dont worry about the EV diference with only 6000 hands, neither when it still continue with 60.000 hands, it will happen...xD
When you say 'it will happen' do you mean, 'sometimes it happens', or 'it always happens'? Serious question. I'm really not sure what I should be expecting from SSS.
I am sorry...but I meant...It will happen...:evil:
If you are a SSS player, you dont have to learn to overcome varianze, you have to learn to love varianze.