Aug 21 2008

#5: Why are there so many bad beats?

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Royal flushes, straight flushes, full apartments, quads, and double-case-outs permeate the ULBPC events. When six or more players routinely go to the flop, statistics tell us one of them will probably connect hard, and he’ll usually find at least one player willing to show down at the river. Likewise, when so many players routinely call bets for the wrong price after the flop, statistics tell us some of them will get lucky and suck out.

If you look at it from a mathematical perspective, a loose player sucks out proportionately more often and a solid player wins proportionately more often. ULBPC events reek of loose play and therefore reek of suckouts. Check out this ongoing collection of amazing ULBPC poker hands if you need proof.

Good or bad luck is just the instantaneous manifestation of statistical probability

Good or bad luck is just the instantaneous manifestation of statistical probability

(Study this snapshot. Player "ashkh" flopped a flush with a gutshot to the king-high straight flush. The river completes her straight flush and only one card in the deck can beat her — the one that completes a royal flush. Imagine how that person must have felt. "I had a king-high straight flush but I lost to a one-outer royal flush on the river!")

So let’s do a little math. Let’s say six players invest 4xBB to see the flop. A suited T3 gets involved because it was suited, but he’s even more happy to flop 33T. This is bound to happen at some point given the high volume of players who see every flop. And once you nail trips or a set or a full house on the flop, there’s roughly a 5% chance you’ll go quad by the river!

Now let’s say the 4xBB raiser holds a suited AT. He’s got two pair on the flop. He bets out strongly, the full house calls, and now our guy thinks "did this idiot pay 4xBB with a 3 kicker?" The turn brings another T. "Aha, now I’ll screw that 3 into the ground," he thinks. Suited AT goes all in, suited T3 calls, and the river brings — you guessed it! — the case 3. Our guy screams about statistical improbabilities when in fact it’s all about (1) the sheer number of players who see the flop and (2) the sheer number of hands that insist on showing down at the river.

If you play ultra-tight in the ULBPC events, you’ll quickly discover you throw away a lot of amazing hands. I myself have thrown away three royal flushes before the flop, a few dozen straight flushes, countless quads, and countless other stone-cold-nuts hands. And those are just my hands! Again, it’s all about the sheer number of hands that show down at the river. "If I’d called all in with those pocket 5s in the big blind on the first hand, I would’ve made quads and I’d have taken four players’ stacks!"

Real-money games see fewer true "bad beats" because (a) fewer people see the flop and (b) even fewer hands get show down. Still, you’ll see all sorts of amazing beats on television. You just need to bring enough cameras to a tournament with thousands of players and you’ll see quad aces fall to a royal flush… This leads me to postulate Rosenberger’s Proclivity For Bad Beats:

  1. If you’re destined to lose, let it be to quads; and
  2. If you’re destined to lose, let it be with quads!

Bad play breeds bad beats

Here’s an all-too-typical example where you isolate on a calling station who’s been lucky so far, and you see a great flop, and you realize you’re going to double through, so you put a third of your stack in, and you get a call, and you get the rest of your chips in after the turn, and he flips over pocket deuces. You stare at his hand in awe — "what a stupid calling station!" — and then he spikes a two-outer on the river.

Here’s another all-too-typical example where you isolate on a calling station who’s been lucky so far, and you see a great flop, and you realize you’re going to bust the player, so you carefully get most of their chips into the pot after the flop & turn, and you get the player all in on the river, only to realize he chased a two-outer and caught it on the river.

A calling station is a loose player and a loose player will suck out proportionately more often. In other words, stupidity breeds bad beats. So on those occasions when I get sucked out, I say out loud "ah well, boo hoo" and then I find another school of fish. I know that good or bad luck is just the instan­ta­neous mani­fes­ta­tion of statis­ti­cal proba­bility.

An analysis of some crap shoots

PokerStars allows the use of poker calculators like the one I prefer at CardPlayer.com. I urge you to exploit any fair software & websites. With that said, let’s analyze some crap shoots and each player’s odds of winning:

  • Four players go all in pre-flop and pocket aces lose to a middle suited connector. Pre-flop, rockets are only 58% to win and 78RPM trails at 19%; the KT and Q9 hold live cards but they interfere with each other’s straight possibilities. After the flop, the suited connector jumps to 60% and rockets drop to 24%. After the turn, the suited connector rises to 80%, rockets drops to 20%, and the other two hands go bust.
  • Four players go all in pre-flop and they all chop to a straight. Pre-flop, we see two players holding a queen, yet popeye only has a 29% chance versus 33% for the suited big chick. After the flop, popeye jumps to 53%, big chick plunges to 17%, and the suited J8 gains +1% with a pair and a backdoor flush draw. After the turn, popeye makes trips and jumps to 67%, big chick holds steady at 17% thanks to a flush draw, J8 plunges to 7% — and the royal marriage can only pray for a 7.5% chop.
  • Two players go all in pre-flop and rockets defeat popeye. Pre-flop, rockets is 81% to win versus 19%. After the flop, popeye drops to 13% but gets a backdoor flush draw. After the turn, rockets makes trips but popeye jumps to 18% with a flush draw.
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