Formula for Success

The Formula for Success is: Amount risked/ (Current Pot + Amount Risked)

Like many poker concepts, the Formula for Success is really just common sense given a name. But the naming of it helps solidify the idea, making it easier to understand much like "semibluffing," "stack to pot ratio" and a thousand other terms.

One of the most practical uses of the Formula for Success is to determine the percentage of the time a bluff needs to work to show a profit, as discussed in CardRunners' "Heads Up: Zero to Sixty in 15,5650 Seconds, Part 1 of 6."

For example, you can figure how often a continuation bet needs to get a fold to be successful, assuming you have 0 equity otherwise.

A pot-sized continuation bet needs to work: 50 percent of the time
3/4 pot c-bet: 42.86 percent
2/3 pot c-bet: 40 percent
1/2 pot c-bet: 33.33 percent

The formula works equally well when figuring how often a 4-bet needs to work, as discussed in DeucesCracked's Spaceman in a Cowboy Suit: Ep. 6.

In the DC example, a $93 raise/4-bet needs to get a fold about 64 percent of the time if there's $53 already in the pot.

Another way to use the formula is to figure out whether how often a call in an all-in pot needs to be profitable, which I referenced in my last post.

In that usage, calculating the amount of a call relative to the total pot size will determine how often you need to win the pot when you call. From there, you can do additional math to account for hand ranges, outs or other factors.

Warning: I make math mistakes sometimes. Please point out any errors if you see them.

Riverboat Gambling

That was a fantastic weekend vacation. I saw the Braves and Cardinals win one game each on Friday and Saturday, and then I drove to Kansas City to witness the home team beat the Tigers.

And I played in live casinos every day.

I met up with Kuro at Harrahs in St. Louis immediately after I arrived. It was cool to see signs at Harrahs supporting Dennis Phillips, who started his journey toward the World Series of Poker November Nine there in a $200 satellite.

I only had a little money on me, and I was looking to sit at a $1/2 NL table, but my name came up for a $2/5 table first. When I found my seat, it didn't take long to remember how juicy live poker can be: five players saw most flops, reraises were rare and people missed many obvious value bets on later streets.

I feel like it takes a little investment to beat these games sometimes. That's because you should be seeing many flops in position, and if you miss all the time, your stack is going to bleed away. The rake and jackpot fee don't help either. But I'm certain this kind of live game is overwhelmingly profitable over time. (I wish I could be dealt more than 30 hands an hour!)

Eventually, my stack dwindled to about $150, and I limp-raised all-in from under the gun with 77 after an MP player raised to $50 and four people called, putting more than $200 in the pot. I got called by the raiser, who wouldn't reveal his pocket 8s until after the river was dealt even after I turned over my hand immediately. Jackass grayhair.

I ended up losing more money at blackjack, but the real story of the trip is my roulette winnings at Casino Queen in Illinois and Isle of Capri in Kansas City.

I played a Martingale strategy, in which I placed near-break-even wagers on the outside, pocketing my winnings on small bets and doubling my bets when I lost.

In four sessions of roulette over four days this weekend, I walked away a solid winner every time.

The Martingale system isn't profitable over the long run, but it gives you the opportunity to book small wins and have fun at the table for several hours at a time. I'll play roulette this way all the time.

Cash stats

Tableratings.com has added many new features that allow you to search players' screennames to see how they have done in cash games on Full Tilt. (Thanks Bone Daddy for pointing it out).

This is an incredible tool cash players can use as they select the best games and the juiciest fish to play against. And even if you don't play cash games, it's fun to see how friends, poker bloggers and pros have been running.

As far as I can tell, the database is still young, dating back to March. Its data will grow more reliable in time. In addition, the site still has table selection tools to help you find the loosest and most passive games. It's still free for now, although I wonder if it will become a pay site in the future. The figures appear to fairly accurate, although some hands are missing.

Here's a sampling:

smizmiatch (me): $8,293 0.95 BB/100.
Phil Ivey: $416,863.50, 9.6 BB/100
Cole South: $-542,310.20, -2.35 BB/100
Brian Townsend: $-80,876.70, -6.93 BB/100
Mike Matusow: $-17,920.15, -1.4 BB/100

When are you pot committed to calling a preflop all-in with AK?

UPDATE: I'm pretty sure my original calculations were wrong, so I've revised this post throughout to reflect those changes. Thanks to Greylocks for his help, and I apologize for the mistake.

Calling all-in with AK with 100BB effective stack sizes is not a leak in cash games against an opponent who will push with QQ or better and you've already invested only 21BB.

That's my conclusion after running some numbers based on a recent hand in which I had 4-bet raised to $400 preflop (40BB) with AK and then got pushed on in a 5/10 game. I had to call $600 to win $1,400 in the pot. I was up against KK, failed to spike an Ace and lost a buy-in.

The hand got me wondering whether my call was correct against a villain's hand range of AA, KK, AK and QQ.

When am I committed to calling all-in?

AK is about a 60-40 dog against a range of AA, KK, AK and QQ, according to PokerStove:

equity win tie pots won pots tied
Hand 0: 39.594% 19.26% 20.33% 110831016 116968584.00 { AKs, AKo }
Hand 1: 60.406% 40.08% 20.33% 230565960 116968584.00 { QQ+, AKs, AKo }

The break-even point for calling comes when your opponent shoves for 121BB, and you have to call 79BB more:

0.395(121) - .605(79) = 0

100-79=21

Therefore, against this range, I have to call after only putting in 1/5 of my stack (21 BB) with AK.

What if my opponent's range is AA, KK or AK?

Then my equity drops to 38-62, and I become committed after investing 24BB.

What if my opponent's range is only AA and KK?

Then my equity drops to 20-80, and I'm not committed unless I've already invested 60BB.

Calling an all-in with AK is far easier against someone with a wider preflop pushing range. That changes the odds substantially.

These numbers show me how hard it is to get away from AK preflop against anything but tight players. Against a wider range, I lose the option of folding unless I have a strong read or I'm deeper-stacked.

One more time

I was really bored and couldn't sleep on the flight back from Phoenix to Honolulu, so I ended up doing some lengthy poker math.

Here's what I wanted to find out: When you hold QQ in the big blind against a late position raiser and a small blind re-raiser in a 5/10 shorthanded game, is it better to call or push?

I addressed the first part of this question in a few previous posts, where I estimated the EV of calling with QQ and pushing any flop without an Ace or King. The number I came up with was $180.12, which is a high estimate because it doesn't consider the ~7:1 chance of my opponent flopping a set. But I think it's safe to say that making this play is well in positive figures.

So on the plane, I figured the EV of pushing with QQ in that same situation. The results were much worse: -$40.90.

Pushing with QQ preflop against two raisers is a donkey move. Call and push any undercard flop in this specific situation.

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The Math:

(Chance that both LP and SB will fold * winnings) + (Chance that LP will fold and SB will call with QQ * winnings) + (Chance that LP will fold and SB will call and be ahead * losses) + (Chance of LP or SB calling when ahead but QQ sucking out * winnings) + (Chance of both LP and SB calling when ahead but QQ sucking out * winnings) + (Chance of both LP and SB calling when ahead and QQ losing * losses) + (Chance that SB will fold and LP will call when behind * winnings) + (Chance that SB will fold and LP will call with QQ * equity * winnings) + (Chance that SB will fold and LP will call when ahead * equity * losses) =

(.75 * $145) + (.016 * $17) + (.16175 * -$1,000) + (.03325 * $1,035) + (.0075 * .15 * $2,000) + (.0075 * .85 * -$1,000) + (.0315 * .15 * $1,110) + (.0315 * .04 * $55) + (.0315 * -$1,000 * .81) =

-$40.90

More math...you know you love it

Picking up from yesterday, it would appear that making an all-in move on any undercard flop with JJ in that situation was a break-even play at best.

Dustin, a commenter, pointed out that I failed to account for times when JJ will suck out on the turn or river in this situation, which will happen about 8 percent of the time. To fix this:

(.55 * -$140) + [.12 * (.92 * -$1,000)] + (.33 * $580) = -$77 - $110.40 + $191.40 = $4.

But even though we get a positive number, this equation still doesn't account for the times the LP player hits his hand and busts the JJ. So I still don't think this play is +EV.

It's interesting to note that this play becomes more favorable for the JJ player if he's playing a smaller stack, and worse when playing a bigger stack.

After all these calculations, I'm thinking that it might make more sense to make this play with QQ from the big blind against two raises. Personally, I don't like pushing all-in or 4-betting preflop with QQ unless I have a strong read, but I also hate folding what may be the best hand in this situation.

So let's run the same scenario with QQ, assuming that the QQ player in the big blind will cold call the reraise preflop, fold if an Ace or King flops, and push all in on any undercard board.

Six combinations of AA and KK will call and be way ahead, one combination of QQ will call and be tied for a $70 profit, while 44 combinations of AK (16), AQ (8), KQs (2), JJ (6), TT (6) and 99 (6) will fold. An Ace or King will flop about 40 percent of the time.

(.40 * -$140) + {[.60 * (6/51)] * -$920} + {[.60 * (1/51)] * $70} + {[.60 * (44/51)] * $580}= -$56 - $64.94 + $0.82 + $300.24 = $180.12

Again, this equation is flawed because it ignores the chance that the LP player will flop a big hand. But it's pretty amazing that QQ seems to do so well under these circumstances.

Based on this math, I believe that when there's a late position raiser and a small blind reraiser, calling with QQ and pushing any undercard flop is often the best play.

More on Hand Combos

Every poker player has been in this spot before: A late position player raises, and you get dealt a monster like KK and raise it up from the small blind. The big blind and late position player both call. When rags flop, you continuation bet, and the big blind pushes all in. The late position player folds, and you need to decide what to do.

Sure the big blind could have flopped a set, but you can't always fold because you're afraid of a hidden set on a somewhat uncoordinated board. It's more likely that the big blind is pushing an overpair like JJ, and you call and take his stack. A set would usually smooth call or put in a smaller raise.

So if I'm holding KK, I'm going to call most of the time unless I have a read or a feeling that someone is overbetting their set for value.

But what about from the big blind's perspective? Sure he'll lose when I have AA, KK or QQ, but he'll win any time I was raising preflop and continuation betting with AK, AQ, KQs, JJ, TT or 99, which is a pretty accurate list of my 3-betting range from the small blind (except for times when I'm making a play, but let's not delve into that).

I want to find out if it's possible that the big blind is right to push with a hand like JJ, knowing that he'll lose to a higher overpair but also knowing I'll fold lots of hands that he beats. Using hand ranges and EV calculations, I'm going to dissect this kind of hand.

Here's the hand:

5/10
Hero posts small blind $5
Villain posts big blind $10
Villain has $1,000, Hero has him covered
*** Dealing down cards ***
Hero is dealt Ks Kc
Villain is dealt Js, Jd
LP raises $45
Hero raises $140
BB calls $135
LP calls $100
Pot: $420
*** Dealing Flop *** [ 2s, 6h, 7c ]
Hero bets $300
Villain is all-in for $860.
LP folds.
Hero calls all-in for $560.
*** Dealing Turn *** [ 6d ]
*** Dealing River *** [ Qs ]
Hero wins $2,140 with two pairs, Kings and Sixes.

Let's assume that the big blind will push all in on any undercard flop and I will call 100 percent of the time with AA, KK and QQ. Let's also assume that I'll fold AK, AQ, KQs, JJ, TT and 99 100 percent of the time. Up until the point the Villain goes all in, there are many times when I would have played that range identically, as well as had a strong read on him that he had a hand like JJ.

AA, KK and QQ add up to 18 possible combinations that have my opponent slaughtered (6 combinations of each).

AK, AQ, KQs, JJ, TT and 99 add up to 16+16+4+1+6+6 combinations, which equals 49 hand combinations that I'll fold.

If my math is right (and it may be totally wrong, in which case I would appreciate being corrected):

There's a 27 percent chance (18/67) that my opponent will lose his stack by making this play, and a 73 percent chance (49/67) that he'll win what's already in the pot.

.27 * -$1,000 = -$-270
.73 * $580 ($140+$140+$300)= $423.40
EV = $153.40

This initial calculation makes it look like this is a profitable play to make with JJ.

But wait. What about those times that an A, K or Q flops, and the JJ has to fold to a continuation bet? I did the math for this once before, and the odds of any one of any three cards flopping is 55.3 percent. That means there's a 55 percent chance that my opponent will lose what's already invested in this pot, if we assume he folds 100 percent of the time an overcard flops:

.55 * -$140 = -$77

And he'll push the other 45 percent of the time (12 percent of the which he gets busted [.45 * .27], and 33 percent on the time he'll win what's already in the pot [.45 * .73]):

.12 * -$1,000 = -$120
.33 * $580 = $191.40

Grand Total:

-$77 - $120 + $191.40 = -$5.60.

So it would appear that given this range, calling from the big blind with JJ and the intent of making this play will lose you money in the long run, but not much -- only $5.60 on average -- as long as the LP player folds (which may be a big "if").

I'm not going to do the math all over again right now, but I would think widening the SB's hand range and changing the BB's holding to QQ would be enough to put this play into +EV territory.

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For a different hand combo example, here's an old 2+2 hand that I referred to in the last post's comments: 3/6 Set Kings turn play.

New Layout and HOTD

I've felt very comfortable with my revised PokerAce layout. It's similar to my old layout, but I've removed both total Aggression Factor and Aggression Frequency, and I've added Aggression Frequency by street.

Here's what it looks like (although the colors aren't as bright as they actually appear on-screen). Click on it for a larger image:



Key:
Left hand column: Flop aggression frequency, turn aggression frequency, river aggression frequency
Middle column: VP$IP and Folds to Continuation Bet (purple)
Right column: PFR, Went to Showdown (yellow) and Total Hands (Blue)

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And now for a Hand of the Day! This was fun because of my opponent's overbet, which definitely NOT for value.

Hero is dealt [As Ah] in SB
Villain raises to $35
Hero raises to $100
Villain calls $65 (his first mistake)
FLOP [Kc Jd Jh]
Hero bets $150
Villain calls $150 (I guess he could have a Jack, but AK or a draw is more likely)
TURN [Kc Jd Jh][3h]
Hero checks (I decide that it's very probable that I'm ahead, and I want to see what Villain does)
Villain bets $774 and is all-in (Now I know for sure I'm good. I can't see him playing trip Jacks like this unless he's smarter than I give him credit for)
Hero calls $774
RIVER [Kc Jd Jh 3h][9h]
SHOW DOWN
Villain shows [Ac Th] (A Pair of Jacks, Ace high) (Nice hand, genius)
Hero shows [As Ah] (Two Pairs, Aces and Jacks, King high)
Hero collected $2055 from Main pot

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I'm feeling pretty optimistic about the poker world now.

Sure, Barney Frank's UIGEA repeal legislation is a longshot, but it's progress. And now that Yahoo! is entering the real money poker world on the BOSS network, that's a mainstream sign from a big business that isn't as afraid of the recent U.S. actions against gambling. Of course, U.S. players can't play on Yahoo!, but I would have thought Yahoo!'s executives would have feared prosecution.

These are not the LAGs you're looking for

I got a question asking how successful I have been in integrating the Cardrunners offense into my game. Specifically, was I able to transition from tight-aggressive play to loose-aggressive in shorthanded games?

The easy answer is, "not really."

I've tried to loosen up, especially in position, but I find that it's very difficult (read: unprofitable) when I try to play the role of the LAGgy pro. I know it works for Taylor Caby, but I'm not there yet.

That said, adapting the mentality of LAG play has absolutely helped my play, even if it doesn't necessarily work out in reality. I place more importance than ever on playing from position, and I try more steals from late position. While tightening up a lot from the blinds, I feel pretty comfortable raising with a wide range of hands when I have the positional edge.

Let's look at some stats. These are my Full Tilt numbers in shorthanded games only:

October:
VP$IP: 22
PFR: 13
WSD: 17
W$SD: 59

November:
VP$IP: 23
PFR: 15
WSD: 17
W$SD: 55

December:
VP$IP: 23
PFR: 12
WSD: 18
W$SD: 52

I don't know if much insight can be gleaned from those numbers. They're still fairly tight -- by comparison, my full ring VP$IP during those three months was 19.

I can think of a couple of conclusions:

1) I'm still a tight-ass, but it doesn't really matter. These are just numbers, and they don't really describe my postflop play, which is more important anyway. A couple of months ago, I posted about how I was worried that the blinds were killing me. In retrospect, I believe I was wrong. The blinds always and forever will suck money from my stack, but they'll never cause me to go bust. Loose calls out of position are a much more severe evil.

2) I call too much on the river (see November and December W$SD). I'm not sure what the ideal winning percentage at showdown is, but my results seem to reflect that I make more money when I call slightly less. Interestingly, my losses over the last three days seem to be in part caused by shoddy river play: 20 percent WSD and 45 percent W$SD.

You don't have to be this great LAG player in 6-max games who can make ungodly reads and bluff people off their Aces at will. I aim for a looser game, but tight play still works well.

Thanks to easyE for the comment.