Good Guy, Bad Guy

The phrase “Good Guy, Bad Guy” generally refers to a negotiating tactic whereby two people on the team team play very different roles.  One negotiator is the “Bad Guy” who bullies, uses anger and threatens to walk away from the negotiating table.  The other negotiator is the “Good Guy” who comes to rescue the negotiation by being considerate and understanding.  The Good Guy blames the Bad Guy for all the difficulties while telling the other side that if they will only concede certain negotiating points (the most important ones, of course), he’ll try to get the deal back on track.

This comes to mind in thinking through an interesting poker hand I recently played.  In this case, the actual sequence is Bad Play, Worse Play, Good Play, Bad Outcome.

I’m in a $1/2 no limit home game, and the player to my left – with whom I have played quite a bit (I’ll call him “Russ”) – has sucked out on me twice already.  Once I flopped middle set v. his top pair/medium kicker.  The turn gave him trips (i.e., paired the top card on the board) while also giving me a full house.  The river paired up with his kicker, giving him a better full house.

And very recently, I flopped top pair/top kicker and he had a flush draw.  Both the turn and river cards looked like bricks but actually gave Russ a back-door, well concealed straight.

So my stack is down to $112, and my emotional state is sub-par as well.

Another player (“Jason” from this post) puts up a $5 live straddle, and I look down at 5s 3s one or two seats to the right of the button.  This is an easy fold, almost always.  Bad Play:  I call.  Maybe it’s my turn to hit some kind of well-concealed bullshit hand.  In reality, WTF am I doing here?  Not folding is a sure sign of the onset of my C-game.

Then Russ raises to $15.  Another player calls and Jason also calls.  I feel like I’m getting a good price to continue.  Now there is $53 in the pot (including the blinds) and $1o more for me to call.  Maybe they all have high cards, leaving the deck loaded with lots of low cards to come out on the flop and connect with my hand.  Worse Play:  I call again.  At least my cards are so bad that I should be able to get away from them easily on the flop.  WTF again?  my stack is not deep enough for this sort of highly speculative call, where I’ll be out-of-position with respect to the aggressor post-flop.

Flop ($63):  Ts 7h 4s.  I have a flush draw and gutshot straight draw.  12 outs for a very strong hand.

Russ leads out for $50.  Sure looks like he has a big pair, and would be perfectly happy to take this pot down right now, or at least charge a high price to any draws.

After one fold, Jason then goes all-in for $35.  He could be calling with any hand that hit any part of this flop, or any draw.  I’ve played with Jason enough to know he will stick it all-in when he has a short stack with a very wide range that gives him any amount of hope, so there is no reason to assume this means great strength.

I have $97 remaining, and Russ has much, much more.  I can fold, in which case I’ll still have $97.  I can call, but that would be very stupid.  If I’m going to continue, I need to be sure I will see both the turn and river cards.  Yet… surely if I raise, Russ will call even if just two over cards to the board.  I cannot count on any fold equity.  What does the math tell me if I shove?

At the table, I use the simple “rule of 4.”  With two cards to come, simply multiple the number of outs by 4 and the result is the percentage of times you will hit one of your outs if you are able to see both the turn and river cards.  I have 12 outs (9 spades to make a flush, plus 3 non-spade sixes to make a straight = 12).  12 x 4 = 48%.  One small adjustment still needs to be made:  since I have more than 8 outs, I have to subtract the excess over 8.  12 – 8 = 4.  Subtract 4% and voila… 48% – 4% = 44%.  If I shove and Russ calls, I should have approx. 44% equity in the pot.

If Russ indeed has an overpair, and Jason has something other than a bigger flush draw, this should be pretty close.  Note that I’m not overly concerned about putting either Russ or Jason on a range.  I need to hit one of my outs, and if I do my hand will win.  If not, I will lose.  The only exception is where one of the villains (more likely to be Jason than Russ) has a higher flush draw.  For now, my hand is 5-high.  I know I’m behind 100% of both of their ranges and don’t need to worry about constructing the range to make my decision.  I need to worry about outs and pot odds.

I assume that if I go all-in, Russ will call.  Jason is already all-in.  The main pot will be $168 ($63 from the pre-flop action, plus $35 from each player).  There will be a side pot of $124 (the rest of my chips and enough from Russ to call my raise).

So my EV is 44% x (168 + 124) = $128.

Compare that to my stack size if I fold, which is $97.  Going all-in has an EV of $31, the increase in my stack (i.e., on average if we were to play out this exact scenario thousands of times) that results from calling.

Good Play:  I go all-in, and Russ calls, whilst shaking his head and saying he knows he is about to get ****’d.

Russ turns over QQ (with the Q of spades).  Jason turns over J8 (with the 8 of spades).  Dammit, there goes two of my outs.

Now that I am at home, I can do the math again based on their actual hands, both of which are pretty close to what I expected.  I’m 41.5% against Russ heads up for the side pot, and about 40% against the two of them for the main pot.  Note how close this is to my “rule of 4” calculations at the table.  I’m slightly weaker than I thought after taking their combined 4 cards out of the deck, including 2 of my flush outs.  My theoretical stack size after the hand would be $119, further reduced to $112 after the house rake and dealer tip, making the play a +EV of $15.  Lower than my rule of 4 calculation due to the impact of Russ and Jason each holding one of my out cards, plus the rake/tip, yet calling still is correct.

To reduce the variance a bit, Russ and I agree to “run it three times” for the side pot.  (This means the side pot is divided into thirds.  We’ll have a turn and river card for 1/3 of the pot, then a new turn and river card for the next 1/3 of the pot.  And a final turn and river card for the remaining 1/3 of the pot.)  Since there are 3 players in the main pot, we cannot run it more than once, so only the first turn and river will apply.

Bad Outcome:  I miss my outs on the first turn and river, and Russ wins the main pot and 1/3 of the side pot.  The big money is quickly gone.  I miss again on the next two board run outs and decide to go home and eat some ice cream.

Ice cream always cheers you up a little bit when you’re feeling bad, doesn’t it?