Poker fans around the globe still can’t get enough of the WSOP Main Event, but what are the actual odds of winning the World Series of Poker? In this and the following blogs, I’ll be analyzing key hands and bad beats leading up to and including the “November Nine” and many of the principles covered in the poker-strategy sections of www.winnerinaweek.com. This post particularly applies to “bankroll management” and illustrates just how tough tournament poker and MTT variance can be … even for the pros! Briefly summarized …

The biggest live poker tournament of the year, the WSOP No-Limit Texas Holdem Main Event, is also the biggest long-shot!

There are numerous MTT luck factors in addition to compound probability of having to win big back-to-back-to-back that contribute to the long odds of winning the World Series of Poker, and even the best in the world can and do go broke when they don’t adhere to strict bankroll management in their regular games. For all of you out there who still might believe that the following rhetorical question from the movie Rounders represents poker reality, I’m here to tell you that nothing could be farther from the truth: “Why do you think the same five guys make it to the final table at the World Series of Poker … every single year? What are they, the luckiest guys in Las Vegas? It’s a skill game ….”

Poker is both a game of skill and a game of chance, and the “chance” aspect of the game should not be underestimated.

Brutal Bad Beat Hands at the WSOP Main Event

In the 2011, with 214 players remaining of the total 6,865 WSOP Main Event entrants (~3% of the entire field), an average stack size of $962,393, and the next pay-out increase at 162nd place, Daniel Negreanu moves all-in (AI) for 95K (approximately 6 big blinds): an open push from middle position with TT. Here’s his bad beat video as a 68% favorite vs. A7s (i.e., an ace and seven of the same suit)!

Welcome to the bitter truth of poker: even the best can and very often do lose due to “variance.”

[This video has unfortunately been removed from YouTube since the publication of this post.] https://youtu.be/9cQUQ-xA2ak?t=19m13s

Elder is big-stacked and “snap-calls” w/A7s … with four players left to act! This was a bad call for many reasons:

  1. First and foremost, any one of the remaining four players behind him could 3bet Squeeze this guy right out of his seat … knowing that he probably called “light” (i.e. with a less than premium hand) in order to potentially knock out one of the best remaining players in the field (see analysis below).
  2. Elder is a 40.25% dog if he puts Daniel on a relatively wide ~14% shove/push range (all-in) of any pair, A9s+, KQo and any suited broadway: 22+, A9s+, KTs+, QTs+, JTs, ATo+, KQo. He’s only getting pot odds of 1.44 :1 for this call, which means he needs 40.95% equity in order to only break even … without the bubble factor!
  3. Even if he puts Daniel on a push range of ~15% that contains any pair, almost all broadway hands and a couple of max-stretch suited connectors (e.g. 22+, ATs+, KTs+, QTs+, JTs, T9s, 98s, ATo+, KJo+), Elder’s Ad7d still only has 42.4% equity to the river.
  4. To make the problem for Elder even worse, if the player in the cut-off or on the button decides to over cold-call (also referred to as “calling flat” or “flatting”) vs. Daniel’s push, Elder will be playing out of position (OOP) on all post-flop streets.
  5. If the late positions fold, either the player in the small blind or the big blind also have the option to over cold-call and then “donk bet” (i.e. bet into the last pre-flop aggressor) on any non-ace flop. Even flops that have an ace are dangerous for Elder vs. another big-stacked player due to his weak 7 “kicker.”

Daniel’s push w/TTs given his stack-size is of course optimal play. Luckily he got someone to pay him off … unluckily, he suffered a huge bad beat, which sent him to the rail along with all of the other big names and previous champions who had also been eliminated (many far from the money) in the biggest live tournament of the year.

In Elder’s defense, his call was only ~6 big blinds, which wouldn’t harm his stack much at all in the case of a loss (or having to fold vs. a 3bet squeeze behind him), and it is arguably worth calling in some cases even when you know that you are behind if the pot odds are decent and you’ll be able to knock out one of the best players remaining in the field. As mentioned above, the huge risk of calling flat in Elder’s position (i.e., in the “hijack,” two seats right of the dealer button) is that any of the other players could have 3bet squeezed in order to knock Elder off his hand and be heads up with Daniel while only needing ~33% equity to break even (assuming Elder would fold 100% of his cold-calling range).

Brief side-note: both Daniel and Phil Helmuth commented on the so-called “table-talk” or “Jamie Gold Rule,” which is a huge topic that I’ve covered in a separate post.

Here’s the breakdown of this hand seen from the perspective of Robinson’s “decision tree” (the player in the big blind holding 44). He can either:

  1. Fold (which he decided to do … entirely too quickly)
  2. Over cold-call for “set value” (i.e. looking to flop a third 4 to give him a monster 3-of-a-kind hand, which only happens once every 7.5 flops). If he doesn’t flop a set or better, he can donk bet any non-ace flop or turn to potentially push Elder off his hand post-flop.
  3. 3-bet squeeze: either a normal re-raise amount (if big stacked) or a direct shove “over the top.”

Blinds: $8K/$16K; Ante: $2K; 9 players

  • Pot amount prior to Daniel’s shove: $42,000 (i.e. only the blinds and antes, a.k.a the “orbit cost” per player, which in this case is 2.625 big blinds every 9 hands played)
  • Daniel’s open push amount: $95K (5.94 BBs)
  • Pot size with Daniel’s push: $137K (8.56 BBs)
  • Pot size with Elder’s cold call (CC): $232,000 (14.5 BBs)
  • And now Robinson has to make a decision.

Since it wasn’t possible to see what Robinson’s stack size was, I’ll assume a stack size of of $450K (~28 BBs) after he posted the big blind and ante ($18K). If Robinson thinks that Elder will never fold to his pre-flop re-raise, and since Robinson is “closing the betting round” and also getting decent odds for the call at 2.44 to 1 (or 29%), the potentially safer line for Robinson (as opposed to 3-bet squeezing) would be option 2 above, followed by the possible donk bet on a non-ace board or a slow play with a flopped set or better; he could also “get creative” on low flops with a check/raise push vs. Elder:

Pre-flop pot (including bets)

Robinson’s cold-call amount (~6 big blinds)

$232,000.00

$95,000.00

Robinson’s pot odds:

2.44 :1

Break even (BE) equity (%) needed if calling all in:

29.05%
(just over 33% with a bubble factor of 1.2)

Robinson’s over cold-call as a % of the pot:

40.95%

Pot size on the flop if Robinson over-cold calls:

$327,000.00
~20.44 BBs

As the table above indicates, if Robinson re-raises (“squeezes”) here, and Elder folds, Robinson will only need ~33% equity against Daniel’s open-shove range because of all of the “dead money” already in the pot … even with a bubble factor of 1.2. With a bubble factor of 1.5, he would only need 38% equity vs. Daniel’s open-push range in order to break even. Does Robinson have the required 33% “b.e. equity” against Daniel in a heads-up pot?

Yes (more than likely), given the fact that Daniel only had 6 big blinds remaining in his stack and would probably be shoving from middle position with a much wider range of hands than even the example ranges below. Expert players do not judge the validity of their decisions “ad hoc,” i.e. based on the result of any specific hand in a poker session, rather on whether the decision made was correct, given the total set of estimated hands that their opponent(s) could be playing in that way in that position. Robinson’s respective equities in heads up with 44 are as follows:

  • 22+,A9s+,KTs+,QTs+,JTs,ATo+,KQo = 42.62%
  • 77+,A9s+,KJs+,AJo+,KQo = 39.4%
  • 99+,ATs+,KQs,AJo+,KQo = 40.9%
  • TT+,ATs+,AJo+ = 40.4%

Here’s a detailed look at the very tricky option 3 above: the most advanced and aggressive move.  Is it wise for Robinson to 3-bet squeeze all-in with 44 in this spot?

The correct answer depends on a few key questions:

  1. What is Robinson’s total stack size (which wasn’t viewable in this video), especially in relation to Elder’s remaining stack? That’s to say, how afraid should Elder be if Robinson decides to get involved in this pot (either aggressively by 3-betting or passively by over cold-calling)? The deeper the effective stacks are, the more Robinson should tend to over cold-call for set value in this spot and the more Elder should fear any bets made by him post-flop.
  2. What percentage of Robinson’s stack size is the $95K needed to over cold-call and see the flop (i.e. how much is he risking to make the call and potentially a post-flop move at this pot)? If the call will commit over 1/5 of Robinson’s stack, he should probably either push or fold (in this spot).
  3. What percentage of Elder’s cold-calling range will he fold vs. a 3-bet from Robinson: i.e. what is Robinson’s assumed fold equity?

We have seen that Robinson does have the needed equity in a heads-up pot against Daniel in order to break even in the long run, but the problem is that Elder might not fold vs. Robinson’s re-raise push. Let’s assume the following:

  • Daniel open pushes (all-in) with 6 big blinds on a 39% hand range of 55+,A9s+,KJs+,ATo+,KQo.
  • Elder cold-calls Daniel here with an ~11% range: 77+, A9s+, KTs+, QTs+, ATo+, KQo (i.e. 148 of all possible 1,326 pre-flop hands in Texas Hold ‘em).
  • Elder will only call vs. Robinson’s 3-bet squeeze with the ~top 4%: TT+, AQs+, AKo (i.e. 50 hands).
  • Robinson’s assumed “fold equity” here (i.e. the likelihood that Elder will fold after his cold-call) is: 1-50/148 = 66.2%!

Robinson’s approximate chip expected value (cEV), with an assumed remaining stack of $450K (~28 big blinds) after posting the big blind and ante ($18K) and based on these very reasonable parameters, is determined using our “push calculator” (available in the poker-strategy shop now), adjusted for the respective 3-way or 2-way pot equities as follows:

Robinson’s loss in BBs

Chip expected value (cEV)

-2.553

-$40,843.93

I won’t bore you with the exact cEV calculation as it is quite complicated and beyond the scope of this post, but you should know that Robinson’s assumed equity was calculated using the program PokerStove for the 3-way pot (i.e. in the case that Elder calls the 3-bet push from Robinson) and the heads-up pot (in the case that Elder folds) as follows:

 3-way all-in pot

Equity

Win%

Tie%

Assumed ranges

Daniel’s open-push range (small stacked):

30.12%

29.09%

1.03%

55+, A9s+, KJs+, ATo+, KQo

Elder has a hand within his 3-bet calling range:

46.66%

45.63%

1.03%

TT+, AQs+, AKo

Robinson’s equity if Elder calls his “3-bet squeeze” from the big blind:

23.22%

23.10%

0.12%

44

 If Elder folds vs. the 3-bet from Robinson:

Equity

Win%

Tie%

Assumed range

Daniel’s open-push range (small stacked):

61.17%

60.80%

0.36%

55+, A9s+, KJs+, ATo+, KQo

Robinson’s equity if Elder folds vs. his “squeeze”

38.83%

38.47%

0.36%

44

 

To determine the odds of winning the World Series of Poker, we’ll look into the main WSOP luck factors in greater detail in the following blogs, and I’ll give you a comprehensive analysis of the “Nash push/fold/call Equilibrium” for the November Nine as well as their respective “bubble factors.”

Till next time … all the best, and best of luck at the tables!
Dylan

 

P.S. Whenever you sit down to play your next tournament, remember the following hypothetical scenario. If you’re “small/mid-stacked” in the big blind  vs. one aggressive opponent who likes to raise with a very wide range of hands from the later positions, seriously consider a “re-raise push” with most pairs (and even A9+ hands) … if this opponent is also able to fold! If she or he is a loose/calling station, this move may or may not be profitable, as it is highly dependent on the fold equity your push will effect.

Assume Elder had made the same open raise to $95K instead of Negreanu. If Robinson were only playing Elder in a heads-up pot (i.e. if Daniel weren’t all-in and could not therefore potentially win the pot after Elder folds to Robinson’s 3-bet), Robinson’s re-raise push (given the same ranges and fold equity parameters), would be a “positive EV move” … even with 44!

Pot (total)
(when Robinson “3-bet pushes” only vs. Elder)

Effective stack
(including blind & ante)

Dead money
(which doesn’t include Elder’s large ~6BB bet)

Robinson’s equity
(when Elder has a hand in his 3bet calling range)

~Fold equity

(chip)EV
(for a 3-bet shove)

$137,000
8.56 BBs

$468,000
29.25 BBs

$42,000
2.63 BBs

32.55%

66.20%

~$44,203
~2.8BBs

 

Equity

Win%

Tie%

Assumed range

A late open-raise range of ~11% (this can be up to 40% or more in loose games):

77+, A9s+, KTs+, QTs+, ATo+, KQo

Relatively tight 3-bet calling range:

67.45%

67.21%

00.24%

TT+, AQs+, AKo

Your equity if called in a heads-up pot:

32.55%

32.31%

00.24%

44

 

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