Time to calculate my spewyness (Math Day)
I don’t know what was with me today, but I found myself making moves on Stars against regs when I should maybe avoid doing so at 100 NL. You don’t have to make aggressive moves there to be able to beat the games for a decent rate (as long as you use table selection), so frankly I don’t have an excuse. Maybe I’m trying to develop my reads? Go on what I think will work? For so long I avoided making spewy plays just to make the easy profit. But maybe making spewy plays improves me as a player and will make me a lot more money in the long run. There, that’s why I made the play today.
Okay, so lets get to the hand. My reads on my opponent was that he was fairly aggressive. This is the 2nd time he’s 3bet me but I’ve yet to see him show anything down. I was unaware of the fact that this table was pot limit; I might have changed the way I played it had I realized that. The raw hand history is here:
PokerStars Game #21787346347: Hold’em Pot Limit ($0.50/$1.00) - 2008/11/05 16:37:06 ET
Table ‘Moguntia’ 9-max Seat #5 is the button
Seat 2: Ferch18 ($60.50 in chips)
Seat 3: beginnerluck ($97.40 in chips)
Seat 4: sm0kelm ($97.50 in chips)
Seat 5: CodeRedRulez ($102 in chips)
Seat 6: PeterQuint ($66.45 in chips)
Seat 7: my zak44 ($131 in chips)
Seat 8: TBCrepNY ($104.10 in chips)
Seat 9: MikeMcD ($101.45 in chips)
PeterQuint: posts small blind $0.50
my zak44: posts big blind $1
*** HOLE CARDS ***
Dealt to CodeRedRulez [6d 7d]
TBCrepNY: folds
MikeMcD: folds
Ferch18: folds
beginnerluck: folds
sm0kelm: folds
CodeRedRulez: raises $2 to $3
PeterQuint: folds
my zak44: raises $6.50 to $9.50
CodeRedRulez: calls $6.50
*** FLOP *** [4h 8h 8d]
my zak44: bets $14
CodeRedRulez: raises $46.55 to $60.55
This is about as close to an ‘all in’ as I could have made it given it was a pot limit game. So for sake of calculation I’ll go ahead and treat my raise like it was all in, because I’d have to call it off anyway. We’ve got our EV calculation formula if you remember here:
EV = %Fold * Amount we Win + % Call * (Amount we lose)
We’ll make %Fold = X, %Call = (1-X), Amount we win when he folds= (9.5+9.5+.5+14 = $33.5).
That make’s the last one, Amount we lose, the hardest to figure out. The formula for that is:
(%Win*Amount we win + %Lose*Amount we lose)
So lets do some calculating:
The Amount we win in this case would be the amount in the pot plus the remaining money in our stack: $102+9.5+.5+14 = $126 (I find the easiest way to do this is put your effective stack first then add in the amount of money your opponent has already put in the pot).
The Amount we lose is our remaining stack, so in this case it would be $102-9.5, or $92.50.
The %Win and %Lose are off the same equity analysis, for which we will use Poker Stove with. The thing is, we have to find out what our opponent is going to stack off with on this flop after the action given. QQ-AA are the best things that come to mind, as well as any flush draw. The most obvious flush draws are AhKh, AhQh. Given that he was 20/15 through my very small sample I’ll throw in 1 suited connector there (even though it could be much more), say JhTh. Against that range my equity is 20.87%, not exactly something to brag about. Even if you throw in JJ our equity stays above 20% and for every flush draw you add in it increase our equity by about .5%. So, I think 20.87% equity is a good amount. Thus, we will win 20.87% and conversely we will lose 79.13% of the time. Now we have all the components of our formula:
EV = %Fold * Amount we Win + % Call * (Amount we lose)
EV = X * 33.5 + (1-X) *(.2087*$126 + .7913* (-92.50))
EV = 33.5x + (1-X)*(26.30 - 73.20)
EV = 33.5x + 46.9X - 46.9
EV = 80.4X - 46.9
Alright, so using this equation lets find out our break even fold equity. To find this out we must set our EV to 0:
0 = 80.4x - 46.9
46.9 = 80.4x
X = 46.9/80.4
X = 58.6 %
So, that means our opponent must fold nearly 59% of the time in order for our shove to be profitable. If he folds more than that then it is a +EV play, less than that and its spewy. How do we know how much fold equity we actually have? Well, lets put our opponent on a range, then find out his stacking off combinations.
Given our read, our opponent is always reraising AK here, as well as AQ. He’ll probably reraise QQ+ for value (while only cold call pairs less than that). He’s probably also got a couple suited connectors in his bluff range, but we dont really know which ones or how many, so lets just use our previous example of JTs. The number of combinations for each of these hands:
AK: 16
AQ: 16
QQ-AA = 18 (6 each)
JTs = 4
Total = 16+16+18+4 = 54 total reraising combinations
And the hands he’s going all in with: AhKh, AhQh, JhTh, QQ-AA, or 18 + 3 = 21 stacking off combinations. Thus, the number of folding combinations is 33 (54-21). Our folding equity then is 33/54 = 61.11%!!!!!
Wait, what? That means my play wasn’t spewy at all! In fact, its slightly +EV. We can find this out by putting our actual fold equity in place of X:
EV = 80.4X - 46.9
X = 61.11%
EV = 80.4*.6111 - 46.99
EV = $2.14
It isn’t exactly the most +EV of plays, but it isn’t -EV either. We get most of our equity when he folds his overcard-type hands, plus if we had a flush draw/open ended straight draw it would be a lot more profitable. I prefer to not risk a stack to win 2BB in EV, as that is something that will increase your variance. Granted, if he ever reraises me with more than he does then its even more profitable.
What happens when he never has JTs here and only does it for value? Then his total reraising combinations is 50 (AQ, Ak, QQ+), and calling reraise range with 20 (QQ+, AhKh, AhQh). And (50-20)/50 = 60% Fold Equity, or exactly 0 EV, which puts it at the same level as folding (ignoring metagame effects).
Wow, this was fun. It wasn’t as spewy as I thought. Yay!
