December 19, 2010

A Bad Beat Bakes My Noodle

Oracle:  "I'd ask you to sit down, but, you're not going to anyway.  And don't worry about the vase."

Neo:  "What vase?"

[Neo turns to look for a vase, and as he does, he knocks over a vase of flowers, which shatters on the floor.]

Oracle:  "That vase."

Neo:  "I'm sorry."

Oracle:  "I said don't worry about it.  I'll get one of my kids to fix it."

Neo:  "How did you know?"

Oracle:  "Ohh, what's really going to bake your noodle later on is, would you still have broken it if I hadn't said anything?"

The Matrix

The weekend after Thanksgiving, I played a session at the Meadows ATM.  A lot of discussion at the table surrounded the bad beat jackpot (BBJ), which was at a record $113,000 and climbing (I'm not certain if the jackpot has been hit in the past couple of weeks, having instead been playing poker in Vegas).  Now Prairie Meadows has fairly liberal rules as far as BBJs go:  the losing hand need only be Aces full of Jacks or better (one ace playing from your hand for full houses), while quads can be a qualifying hand without a pocket pair, so long as the hole card plays as a kicker (e.g., A8 vs. JJ would qualify on a board of 8-8-8-J-J, while 98 vs. JJ would not qualify—though it would still be a sick beat).  So, getting a BBJ up over $50,000 or so is a rare event.

As is the usual case when BBJs get higher than normal, there were tons of stories flying around the table about BBJs previously hit, as well as the usual bad beat stories about BBJs nearly hit, or hit and disqualified (Prairie Meadows DQ'd one BBJ a few years ago because a player not in the hand saw the losing player about to muck and told him to table his hand).  My favorite near-miss story involves Fred, a local uber-nit (though I hasten to add that Fred is a decent fellow who has always been friendly with me).  About a year ago, Fred folded AdQd to a preflop 3-bet, and wound up missing out hitting a royal flush against another player's quads.  If you want to needle Fred, just muck AQs face up and say, "Fred, how would you play Ace-Queen suited?" with a completely straight face.  Hilarity will ensue!

The point of this post, however, is to look at a common talking point involving BBJs—whether players sitting out of a hand deserve a table share (or some financial reward) when a BBJ hits.  For those unfamiliar with BBJs, it is typical to divide the jackpot between the winning hand, the losing hand, and the other active players at the table (or even all active players in the room).  Prairie Meadows awards 50% of the jackpot to the losing hand, 25% to the winning hand, and divides the remaining 25% among all other players who were dealt into the hand (they also allow an absent player to be dealt into one hand after leaving the table, so long as they have chips behind).

It is common to hear players claim that, if a player sits out of the hand and a BBJ hits, they should still be given either a full table share, or at least a significant payoff from the winning and losing hands.  The theory behind these kinds of claims is that "the bad beat would never have occurred if Player X had been dealt into the hand, so Player X should be rewarded for causing the bad beat" (see this recent discussion thread over at All Vegas Poker (AVP) for a couple of examples of this argument).*  These kinds of claims are pure nonsense.

The implicit premise underlying this type of argument is that Player X caused the bad beat by deciding not to play the hand.  After all, if Player X did not cause the bad beat, he clearly has no moral claim to any share of the jackpot ("moral" here used in the sense of fairness or equity, as opposed to a technical claim to a share, which the player clearly does not have under the rules).

In order to analyze whether a player sitting out of a hand can be said to have caused the bad beat, let's first consider all the factors that require perfect coordination to bring about a particular bad beat:
  • First, the deck must be shuffled to permit a bad beat to occur.  That is, the deck must contain a series of cards that, when cut in the proper spot and dealt to the proper number of players, will result in a qualifying bad beat.  It is theoretically possible for some decks—likely most decks—to be shuffled so that no bad beat can occur.  It is also theoretically possible for a deck to be shuffled to permit more than one bad beat to be dealt, depending on the cut and the number of players.  Let's call a deck with at least one potential bad beat lurking in it a qualifying deck ("QD").
  • Next, the deck must be cut in the correct spot to bring the QD's potential bad beat into play. There is theoretically a 1/51 chance of the deck being properly cut to bring the bad beat into play.  However, because most dealers do not cut close to the top or bottom of the deck, a certain percentage of potential bad beats never have a chance of being dealt out of an otherwise QD.
  • Once the deck is cut in the correct spot, the proper number of players must be dealt into the hand.
  • Once the players are dealt in, the betting must proceed in a fashion that permits the two qualifying hands to make it to the river.  For example, a hand like 22 or 96s might be driven out by a preflop raise, or a hand like 88 might fold to a flop bet on an eventual board of Q-Q-J-8-8.
  • Player betting decisions may be determined by external factors.  A player holding a potentially qualifying bad beat hand may fold because of a large raise from a player who seems likely to hold a strong hand based on playing style or physical tells.  Or a player with a potentially qualifying bad beat hand may fold because they just lost a big pot and are looking to play only the strongest starting hands, or because another player in the hand is short-stacked and doesn't offer correct implied odds to play a suited gapper starting hand.
  • During the entire hand, there must not be a dealer error that affects the two qualifying pocket hands, nor the qualifying final board (e.g., no flashed cards, no premature burn and turn, etc.).  Note that there will be a certain number of non-QDs that can become a QD as the result of a dealer error which is corrected in the normal course of play (e.g., a flashed pocket card is replaced, a boxed card is discarded, a premature river card is replaced) (let's call these "near-QDs").  Bonus noodle baking—Should a player sitting out of a hand still get credit for "causing" a bad beat if the bad beat would never have occurred but for the subsequent dealer error?
Notice that out of all of the necessary conditions for a particular bad beat, a player's decision whether to play a hand only affects one of them—the number of players initially dealt into a hand.  But an individual player's decision whether to play a hand is only one small factor in determining the final number of players dealt into a hand.  Let's consider a few common situations that affect player decisions whether to play a particular hand:
  • Player 1 is new to the table and must decide whether to post in (or take the blinds in Vegas), or to sit out and wait for the blinds to hit (or for the blinds to pass in Vegas).
  • Player 2 gets a phone call from his spouse.  He has to decide whether to take the call and be dealt out, or ignore the call and play the hand.
  • Player 3 is racking up to head home, and has to decide whether to see another hand.
  • Player 4 is supposed to meet his buddy for dinner.  His buddy drops by or texts to tell him either to leave immediately, or to play a few more hands, based on how well his buddy is doing at table games or in the sportsbook.
  • Player 5 is a nicotine-addict and has to decide whether to take a cigarette break or play.
  • Player 6 has to decide whether to take a restroom break or play.
  • Player 7 sees a friend across the room and has to decide whether to go greet him or play.
  • Player 8 is called to a new game or is given his table change request.  He has to decide whether to take a hand or move immediately.
  • Player 9 has been absent from the table and has to decide between paying his missed blinds and waiting for the blinds.
  • Player 10 just busted out and has to decide between buying back in short, locking up his spot while he hits the ATM to reload for a full buy-in, or calling it a night and letting a new player sit down.
  • In the case of one or more empty seats, there is an added decision by the floorperson whether to fill the empty seat(s) from the list, from a table change request, or from a table break, or whether to leave the seat(s) empty.  The floor decision is then followed either by a dealer decision to deal or wait for the new player(s), followed by the decision of the new player(s) to play or sit out that hand.
Notice that, in a situation where a QD is in play, there will be up to ten relevant player decisions that affect whether the proper number of players are in a hand so that the potential bad beat may actually be dealt.  But, no one individual player decision, in and of itself, determines whether the bad beat occurs.  Rather, it is the aggregate of the decisions that ultimately matters.  After all, once a QD is in play, it doesn't matter whether a particular player is in a hand, it only matters that the correct total number of players are in the hand.  Thus, an individual player's decision to sit out of a hand is no more and no less important than the independent decisions of all the other players at the table to play or sit out of the hand.  However, the sum total of all of those independent player decisions are interdependent in creating the final conditions for determining whether the potential bad beat will be dealt.

To think about the situation a little more deeply, let's say that a QD is in play, and exactly eight players are needed to be dealt into the hand in order for the bad beat to hit.  Six players are clearly going to take hands, but four players are making legitimate decisions whether to play.  If two of the four "on the fence" players sit out and two play, did the two that sat out "cause" the bad beat any more than the two that chose to play?  Did the two that chose to play that particular hand "cause" the bad beat any more than the six players who were going to play the hand regardless?  What if two of the players making decisions are friends who rode together; if one chooses not to play and his friend goes along with the decision, did the player who made the decision to leave "cause" the bad beat while his friend who acquiesced in the decision did not do so?

Let's look at the same situation from a different angle.  Let's assume there is a QD in play. All that is needed is for exactly six players to play the hand.  But, because of various player decisions, eight players take hands and the bad beat is not hit.  Which two players do we "blame" for "causing" the bad beat to miss?  If that question strikes you as nonsensical, isn't it equally nonsensical to credit a player who sits out of a hand with "causing" a bad beat that hits?

Just to be thorough, let's examine bad beats in online play (but first, you may want to take a quick look at these discussions by Shamus—Part 1 and Part 2—and Poker Grump regarding online card randomization processes).  According to PokerStars, they use a truly random shuffle to "set" an entire deck at the beginning of a hand.  PokerStars also utilizes "user input, including summary of mouse movements and events timing, collected from client software" as one source of entropy to ensure a truly random shuffle.  Based on this method of shuffling, should we consider each player whose "user input" contributed to the shuffle that results in a QD to be a "cause" of the bad beat?

Now, to really bake your noodle, let's look at Full Tilt where, instead of "setting" an entire deck at the beginning of a hand, the software instead waits until a card is needed to be dealt to a player or to the board to randomly select a card from the remaining "deck" of undealt cards.  Since there will never be a QD in play (since there is no deck), can we ever claim that player decisions to sit out or take a hand "cause" a bad beat?  If one player's decision to auto-fold or mull over his playing decision causes the next random card to be drawn to "change" (i.e., be different), and the resulting card results in a bad beat, did the player's decision how fast to play his hand "cause" the bad beat?  More to the point, using Full Tilt's card randomization process, can we ever meaningfully consider any player decision to be the "cause" of a bad beat?

The assertion that one player's decision whether to play or not play a hand "caused" a bad beat reminds me of the classic "Horseshoe Nail" proverb:

For want of a nail the shoe was lost.
For want of a shoe the horse was lost.
For want of a horse the rider was lost.
For want of a rider the battle was lost.
For want of a battle the kingdom was lost.
And all for the want of a horseshoe nail.

Of course, for something as significant and subject to as many independent factors and decisions as the outcome of a large-scale battle, it is nonsensical to attempt to trace the root "cause" to something as minor and as remote as whether a horseshoe nail was in place. In reality, there were almost certainly hundreds of independent factors and decisions at play that contributed to the outcome of the battle.  Similarly, a poker bad beat hand is never dependent on one or even a few factors and decisions, and it is equally nonsensical to describe any one individual decision or factor as the "cause" or even a "cause".

Perhaps the best way to analytically describe poker bad beats is to regard a hand of poker as an example of chaos.  Chaos theory describes:

"dynamical systems that are highly sensitive to initial conditions" where "[s]mall differences in initial conditions ... yield widely diverging outcomes ... rendering long-term prediction impossible in general.  This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved.  In other words, the deterministic nature of these systems does not make them predictable."

Any poker hand is "deterministic" in the sense that it plays out in a predictable manner pursuant to a consistent set of rules.  However, every poker hand is also highly sensitive to initial conditions, including the deck shuffle, the cut, player decisions and actions, dealer decisions and actions, floor decisions and actions, and even the decisions and actions of persons remote from the game itself (e.g., the decision of a player's spouse to eat dinner or keep playing slots).  Alter one or more of the initial conditions for a given poker hand, and the hand will likely play out in a significantly different manner with a substantially different outcome (the proverbial "butterfly effect").

Viewed in this manner, any single player decision to play or not to play a particular hand is merely one of a large number of initial conditions for a given poker hand.  From time to time, there will be a very small subset of initial conditions for a given hand that may lead to a bad beat jackpot, but hitting the bad beat jackpot even in those situations requires the fortuitous combination of precisely the right subset of initial conditions.  Any one player's decision whether to play or not play a particular hand is no more significant than any of the other relevant initial conditions.  Although a player's decision to sit out of a hand may set up a relevant initial factor for the subsequent play of the hand, he has no more caused the resulting bad beat than has a butterfly flapping its wings in China caused a tornado half the world away in Nebraska.

So, there's no logical reason to give any player at a table credit for "causing" a bad beat just because they made a routine poker decision.  After all, poker isn't craps.  Same dice!


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* Similar arguments apply to any "cooler" type of hand (e.g., AA vs. KK, or set over set), in which the hand would never have occurred but for various player decisions to play or sit out the hand in question.  But, the argument is most commonly raised in discussing bad beat jackpot hands.

8 comments:

  1. Excellent breakdown of bad-beat theory, good sir! I've actually witnessed this situation occur. I was at a bad-beat table in November '08 that hit while one of our players was taking a break. Payout for players not claiming the two big chunks of the jackpot was around $800, and everybody tipped $25 or so to the absent player, which I think was a sound and generous gesture. Saying the person sitting out deserves some kind of equal cut, though? That's lunacy!

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  2. BB was at $130k yesterday, I believe.

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  3. I'm with Bob. I've seen the tipping of absent players, too.

    Here's my bad beat. Playing 20/40 at the Muckleshoot, I passed up a 10/20 seat which was taken by my buddy Don. Two hands later he's dealt JJ. Quads on the river is snapped by a royal flush. He pockets $100K. He tipped the dealer $13,000. Me? Nada.

    -DrC

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  4. @ Bob: Yeah, I've seen and heard of tipping absent players. Like you, I have no problem with tipping those players, but I just have a problem when they claim they deserve a share.

    @ Dr. Chako: But if you had sat in the game, would the bad beat still have been dealt? Would the deck have been set the same? Would the dealer have cut the cards the same? Pardon me for baking your noodle ... :-)

    FWIW, I think your friend at least owed you a very nice steak dinner with a top notch bottle of wine. Maybe a good vintage of Grange, even.

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  5. Yeah, good call on Chaos Theory, Grange.

    If Chako would have been at the table, he likely would have played some earlier hands different from his buddy (folding instead of calling, calling instead of folding, etc.) ... which would have rearranged the card positioning on the table when the dealer pulled the deck in ... which would have meant the cards went into the shuffler in a different order ... which means that particular bad-beat hand would have almost certainly not occurred.

    Hell, if Chako only mucks his cards differently than his buddy, it still could have completely rewritten the chain of events.

    Butterfly wings ... butterfly wings ....

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  6. Yeah, but in my fantasy world, that jackpot was mine, baby. Mine!

    -DrC

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  7. Although now I realize that you said it happened on just the second hand played, DrC. Hmm ... just how powerful are those butterfly wings?

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  8. Harrah's in AC used to pay the table share to anyone with chips on the table who had not missed posting a blind. This seems like a good solution to avoid this argument. In a place with multiple poker rooms, you don't want to lose a customer because he feels like he paid $10k for using the bathroom.

    I am not sure what the current rule is now that everyone playing at a CET table in AC gets a share of the BBJ. I haven't been quite nitty enough to ask.

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