by Tony Guerrera

 IGT has a heads-up limit bot that can be found now on many casino floors in Las Vegas (most of the time, you’ll find a bank near the poker room). I’ve witnessed some obvious mistakes from this bot. For example, I played a hand where I raised my button preflop, and the bot folded A-8o. Seeing an obvious mistake is one thing—recognizing the true value of that mistake is an entirely different issue.

by Tony Guerrera

One evening during the 2011 WSOP, I played racquetball with Collin Moshman and his wife, Katie Dozier. Afterwards, while hanging out in the steam room, we got into some quality poker debate. Since I have a reputation for being a math guy, here’s an equation for you: racquetball + steam room + poker debate = the nuts!

 The topic of our debate was heads-up last-longer bets in the WSOP single table satellites—and more generally, heads-up lastlonger bets in winner-take-all tournaments. Are they sucker bets because:

 • Optimizing performance in heads-up last-longers involves making decisions that are suboptimal with respect to the winner- take-all part of the tournament.

 • Optimizing performance in a winner-take-all tournament involves making decisions that are suboptimal with respect heads-up last-longers.

 Engaging in heads-up last-longers creates potentially conflicting incentives. However, how much expected value ($EV) gets shifted from one bucket to the other if you were to play the same tournament a bunch of times? By taking a heads-up last longer, is overall $EV conserved, or is it somehow possible for your overall $EV to be lower by taking a heads-up last longer? In a winner-take-all satellite, proper strategy is to play close to chip EV, where playing with respect to chip EV means maximizing your expected chip count in every hand. Survival doesn’t mean much. Meanwhile, when engaged in a heads-up last-longer bet, specific situations arise where maximizing your probability of surviving is at odds with maximizing your expected chip count.

 For example, you’re in the big blind with a hand that’s a marginally profitable call with respect to chips. A big stack goes all-in, your last-longer opponent calls with fewer chips than the big stack. You have fewer chips than the big stack and your last-longer opponent. Folding in this spot can sometimes be best when thinking only of the last longer bet.

 I say “sometimes,” because many assume that folding here is always best. Those making this assumption fail to account properly for the last-longer opponent’s chance of winning, what the new relative stacks will be if the last-longer opponent wins, and the winner-take-all $EV that’s being sacrificed. Folding here is only best if the gain in last-longer $EV exceeds the loss of winner-take-all $EV.

 It’s easy to get lost in a forest of specific situations, so let’s back up and take a more macro view of poker tournaments. Does playing close to chip EV every hand result in a lower median finish than avoiding situations that are marginally profitable with respect to chips? Most players make a hasty assumption here—that playing survival results in a higher median finish but lower $EV. But because of blinds and antes, it’s at least possible that playing survival results in a lower median finish and lower $EV—especially since many plays that are profitable with respect to chips early in a tournament involve only small fractions of one’s stack.

[Editor’s Note: Poker Player Newspaper is glad to welcome back Tony Guerrera to its pages on a part time basis, beginning this issue. —Lou Krieger]
 
Very early on March 26, 2005, cash game action on the Party Poker Million IV cruise was reaching its end. Holland America’s Oosterdam was approaching the San Diego waters from which it had departed a week earlier. I was playing in a $2-$5 no-limit hold’em game. The action was fast and furious as it had been all week, but things were about to go into overdrive…
 
I was UTG+3 at a full handed table with approximately $800 in front of me, and was dealt A-A. Chaos ensued. UTG opened to $25. UTG+1 flatted. UTG+2 re-raised to $75. I four-bet to $150. Four or five players cold-called—I’m pretty sure it was five, but this hand happened a long time ago, so forgive me if it was only four.
 

[Editor's Note: This is Tony Guererra's final column for Poker Player Newspaper. Tony has always worked to advance the state of poker theory and we appreciate his contributions to this paper. We wish him all the best in his future endeavors.]

"We live in a black-box society. What I mean by this is that we do not know how many things work; we simply know how to use them. TVs, computers, cars, cell phones, and microwaves are just a few of the myriad black-boxes that we take for granted." (Killer Poker by the Numbers, p. xix)

A few months ago, John Vorhaus, who coauthored Killer Poker Shorthanded with me, and I hit Hawaiian Gardens for a quick session. Other than that, I can't remember the last time I played live poker. LA has great poker rooms and I've spent plenty of time in them, but one table of 9-handed action is now brutally slow for my taste.

NFL teams play predetermined schedules. NBA teams play predetermined schedules. NHL teams play predetermined schedules. Teams in these leagues don't get to choose their opposition. Their schedules are set by the league and the teams play it. Thriving in such an environment requires being the best.

Poker is much different. If you're a cash game player, you can enter or leave games as you wish. As a result, it's possible to be a winning player in the long-run even if you're the ninth worst player in the world. Simply sit in games exclusively featuring the eight worst players in the world.

You're playing some shorthanded no-limit hold 'em. Action folds to you and you raise on the button. The blinds fold. An orbit later, action folds to you, you raise on the button, the blinds fold. The same pattern emerges orbit after orbit. In fact, you're not even looking at your hole cards. You're exploiting foes who play too few hands, and you're running over the table.

Double-ups, triple-ups, and quadruple-ups are far from the only components of tournament poker, but playing all-in situations properly is essential if you're to become a top tournament player. Whether you or your opponent faces elimination in a particular hand, the following process will ensure that you're considering all relevant factors in such situations.

Step 1 (Pot Odds): Figure out the ratio of how many chips you stand to win versus how many chips you have to call. Remember that if your opponent has you covered, his extra chips don't factor into your pot odds.

In The Theory of Poker, David Sklansky introduced his now famous Fundamental Theorem of Poker: