The Oracle's Corner

This is my first column for Card Player magazine. I'd like to thank those of you who have followed my blog on CardPlayer.com, and to those of you who haven't, what's up with that? This column will discuss interesting hands from both tournaments and cash games that are somewhat controversial. The column will present multiple viewpoints from different pro players. I will be collaborating with Michael Binger, who will discuss the mathematical analysis of each hand. In addition, the player involved in the hand will discuss his play. This hand was played by Noah Schwartz, who began as an online player (he won the PokerStars Sunday Million last year) and has been on fire in live events recently.







My initial thought preflop when I looked down at two red tens, taking into account that the pot was opened by a relatively tight player who was under the gun, was to smooth-call. The raiser had been involved in only one other pot during the last two levels, and was slowly getting blinded away. The pot he was involved in was just two hands prior, when he open-shoved K-J from the cutoff for 96,000. I was in the small blind with A-K and called, only to get outdrawn. I also had several big stacks behind me, including Erik Seidel and Erick Lindgren, so I decided that I could easily get away from the hand preflop should someone come over the top. So, I called the 23,000, the action was folded around to the big blind, who completed for another 15,000. So, going to the flop, there was 83,000 in the pot. With the flop of J 10 7, it was checked around to me, and I opened for 60,000, which was three-fourths of the pot. The big blind flat-called, and the under-the-gun raiser folded. The turn was the 2, and the big blind led for 80,000 into the 200,000 pot, which at the time seemed to be quite peculiar, as he had a pattern of overbetting, which he did in consecutive hands against Erick Lindgren. So, I had predetermined that if he led into me, I was going to represent a monster, leaving him plenty of fold equity with 320,000 in chips remaining. He instantly called my shove, and I saw that although I was in bad shape, I had 17 outs with one card to come. But the 3 on the river ended my tournament.



Preflop: Given the stack sizes, calling is the optimal play against a tight under-the-gun raiser. A reraise simply turns your hand into a bluff and puts you in a very difficult spot if you are reraised all in. Let's look at this in detail. The under-the-gun player opened for 23,000, so a normal-sized reraise by Noah is to about 70,000. Let's assume that the under-the-gun player will reraise all in only with J-J, A-A, and A-K. When facing this all-in bet, Noah will have to call 155,000 to win 316,000, while his chip equity against the under-the-gun player's all-in range is about 34 percent. From purely a chip-equity point of view, Noah would be getting barely the right price to call. However, since tournament-chip expected value overestimates real-money expected value, Noah's best play is to fold to the under-the-gun player's all-in bet. Since your cards are never shown, your 10-10 becomes a bluff.

Now I'll show that a preflop reraise by Noah is a negative expected-value play. The under-the-gun player is described as tight, which we assume means that his under-the-gun raising range is 8-8+, A-K, A-Q, A-J, and K-Q. Given this, the under-the-gun player will reraise (RR) all in with probability P(RR) = 0.396, and the expected value (EV) of Noah's reraise is: EV = P(RR) x (-70k) + (1-P(RR)) x (+44k) = -1,148. Since the chip expected value is slightly negative, the real-money expected value will definitely be negative. Thus, folding preflop (EV(fold) =0) is better than reraising with 10-10! However, calling the 23,000 bet is the best option, with a positive expected value that depends on the assumptions you make about post-flop play.

Also, when you call preflop, you might pick off a short stack that makes a move. Meanwhile, your reraise makes you vulnerable not just to the under-the-gun raiser, but also to anyone behind you who wakes up with a big hand.

Flop: I agree with Schwartz's original action in the hand. A bet of 60,000 into the 83,000 pot seems like just the right amount. When you flop a set, you want callers; you don't want to scare everybody away. Ideally, someone has A-J, K-J, or Q-J, and thinks he has the best hand and that you are stealing. Also, you have charged draws enough to make it wrong for them to call.

Let's verify that claim by calculating the expected value of the big blind on the flop, and see that it is negative. The big blind has an 8/45 chance of hitting a flush on the turn. If he doesn't hit on the turn, Schwartz will bet enough that the big blind cannot justify calling. If the big blind hits the turn, Noah can still hit his bigger flush (seven outs) or full house (10 outs) on the river. This means that the probability of the big blind winning the pot is only 8/45 x 27/44 = 11 percent. When the flush card hits the turn, let x equal the river bet that Noah calls when the river bricks out, y equal the river bet the big blind check-calls when the river is a fourth diamond, and z equal the river bet that the big blind check-calls when the board pairs. With these definitions, we find the big blind's EV = 37/45 x (-60) + 8/45 x (27/44 x (82 + 60 + 80 + x) + 7/44 x (-60 - 80 - y) + 10/44 x (-60 -80 -z)). For the reasonable values of x = 0, y = 0, and z = 120,000, the big blind's EV is -39,600. Any other reasonable assumptions for x, y, and z also lead to negative expected value for the big blind, thus justifying the claim that Noah's 60,000 flop bet has effectively priced the big blind out of profitably calling on a draw.

Turn: Calling the 80,000 bet by the big blind is far better than moving all in. I assure you that this claim is backed up by a mathematical calculation that compares the expected value of calling versus the expected value of raising all in, but I'll spare you the details. The point is, when the big blind is bluffing or semibluffing, you accomplish little by moving all in, whereas when the big blind has a made flush (usually the case), you risk going broke unless you draw out on the river. Since the big blind was kind enough to bet only 80,000 into a 200,000 pot, you are easily priced into calling.



Preflop: I would more often than not reraise. Pocket tens are a premium hand, the pot has been opened, and with the antes, blinds, and the 23,000 raise, this represents enough value. I would factor in my read on the player who opened the pot, as well.

Flop play: I don't love Schwartz's flop bet; he made it too cheap, perhaps hoping to get to the turn without a diamond, and then make it expensive to see the river. Although mathematically priced out of calling, the big blind did call, and got paid off huge when he hit on the turn. Binger wanted maximum value, and I want to take it down right here with a board like this.

Turn: My biggest problem with the hand is Schwartz's shove. If you are going to play the hand slower, you must be able to get away from it. When the diamond comes, I see his only options as call or fold. If he calls, he is hoping for the board to pair. With that flop, I would have opened for at least a full pot-sized bet, to make it expensive for the flush draw. Let's not forget that 9-8 makes a straight, and is certainly a possible hand, although unlikely.
Tournaments are about survival. Schwartz still would have been above average in chips if he had laid the hand down on the turn, and slightly below average if he had smooth-called the turn and realized that he was beat and folded to a bet on the river. Additionally, with a 5-high flush, if the board did pair on the river, is Schwartz going to get paid off? I don't think so, but who knows, as Schwartz paid him off after he made the flush.

River: Get the board to pair; use Jedi mind control, or whatever it takes.

Noah Schwartz's Rebuttal: I agree with Roy's analysis of the hand that reraising preflop instead of taking a more passive approach, particularly late in the tournament, would most likely have forced out a 5-4 suited. With the texture and coordination of the board, I should have led more on the flop, to avoid giving the big blind the implied odds to call with a 5-high flush draw.

Pro Conclusions
Michael Binger: Schwartz correctly called preflop, bet the correct amount on the flop (60,000), and should have called the 80,000 bet on the turn and not moved all in.

Roy Winston: Schwartz should have considered a reraise preflop, and the flop could have been played more aggressively. If you are going to slow-play, you must be able to get away from the hand.