End of passion play, crumbling away, I'm your source of self-destruction. Veins that pump with fear, sucking dark is clear, Leading on your death's construction.
Taste me you will see, More is all you need. Dedicated to How I'm killing you.
Come crawling faster. Obey your Master. Your life burns faster. Obey your Master. Master!
Master of Puppets I'm pulling your strings, Twisting your mind and smashing your dreams. Blinded by me, you can't see a thing. Just call my name, 'cause I'll hear you scream. Master! Master!
I've long been a huge Metallica fan, and have been to more of their concerts (five) than any other band. I first got hooked when their first video, for "One", debuted during my early college days. Of course, this led me to explore their earlier albums, and what song is more quintessentially Metallica than "Master of Puppets"? I suppose some would argue for the ubiquitous "Enter Sandman", but in my view, "Sad But True" was the best song off the Black Album. Of course, if we're talking best Metallica song, I might lean toward "Fade to Black" off Ride the Lightning or "Sanitarium" off Master of Puppets. If you need a song to rock out to when angry, to chill out with when down, or to pump you up on a long run, Metallica has plenty of music that will fit the bill.
In any event, the classic Metallica song "Master of Puppets" might as well be called "The Call of the Yaks" considering the feelings of anger and despair that often accompany playing pocket Yaks. As the saying goes, "There are three ways to play pocket Jacks; all of them wrong." Frankly, I've probably found more than three ways to misplay Yaks over the years, often using three misplays in a single session. But yesterday, at the Meadows, I finally discovered how to play Yaks. Yes, I became the Master of Yaks.
I went to the Meadows ATM for a short session, hoping to find good action after the noon tournament. While waiting for a spot to open, I watched the final table of the tourney. Down to the final three players, the blinds were 5K/10K, and the chip stacks were 165K, 5K, and 5K. Yes, the chip leader, Lori, had a 33:1:1 chip lead, with the small blind having a single 5K chip merely because he was rounded up during the chip race off that occurred when they went to three-handed play. The two short stacks were immediately all-in, then heads up play began. Lori got her money in as a huge favorite but lost with Q4s vs. 54o, Q8 vs. 85, and KQ vs. 62. In the first two hands, her opponent rivered a 5, while in the third hand, he flopped a duck. Finally, on Hand #4 of heads up, with the stacks nearly equal (95K to 80K), Lori ran her AcQc into 66, and despite not hitting a pair, a flush, or a straight, still won the tourney after finding a double-paired board to counterfeit the pocket 6s: K-T-T-K-4. Amazing showing by Lori, one of the nicest regulars at the Meadows, albeit a tough player.
About a half hour later, I finally get a spot on one of the 1/2 NLHE tables. I posted in behind the button. Then, three hands later, there is a straddle and a call to me in middle position. I find Commie Yaks, and decide to limp, expecting a raise from the straddler, and planning to reraise. Instead, the player on my left pops it to $17. Surprise! Even more surprising, there were five callers to me. Hmmmm, repop squeeze play? Call and set mine? The initial raiser had a pretty tight range for that raise, say {AA-99, AK, AQs}, so I wasn't thrilled about maybe walking into a big hand. Also, there were a couple of gamblers among the callers, so who knows if a squeeze play would work? I finally opted to set mine, to lower my risk of a big hit to my stack, while still fairly certain to get paid off big if I hit the flop.
Alrighty then, seven of us see the flop with ~$120 already in the pot. The flop came out Js-7c-6c. Donkey Kong! It checked to me, and I checked as well, certain there would be a bet. Sure enough, the preflop raiser made it $35 to go, and there were two callers to me. The pot was getting huge, and the board was draw heavy, so I just went ahead and pushed for ~$275 total. The preflop raiser agonized, then called, the next two guys folded, and the final guy called. The turn was the Kh. Preflop raiser pushed all-in for another $100, and seemed really happy. Ruh roh, Rooby! Did someone just hit a bigger set? Inquiring minds want to know! The river was a non-club Ten. Groovy, AcQc just got there. How lovely. But no, preflop raiser rolls over AcKc, while the other guy shows ... 54 offsuit?!?! Pac Man! The pot was ~$980 to me, giving me a triple up on my first orbit.
And that, dear readers, is how to play Yaks.
Yak with Mt. Everest in background (image source).
------------------------------------------------------------------ POSTSCRIPT: OK, in the interests of full disclosure, I did donk back some of the chips, mostly on one hand where a table maniac and I each flopped Kings up, only he had the better second pair. I also got run down in a couple of hands, but still carted home a full buy-in profit.
Unfortunately, I didn't play nearly as well Friday night in a home game with, among others, Ironman Mr. Chow, who channeled his inner crasian to run down my KK with QTo, flopping J-9-x, and turning his six-outer to the straight, at which point I promptly spewed my entire stack to him drawing dead. Eh, maybe I'll make Cowboys the next hand I master. I can see it now—Master of Cowboys—a blended sequel to Rounders and Brokeback Mountain. There will need to be a Tom Dwan cameo, obviously, and maybe an appearance by Zed and the Gimp ...
I played a very short session of poker last night at the Meadows ATM. I was driving back from a lengthy meeting with an expert witness at the University of Iowa medical center, and found my car taking the Meadows exit. Well, my car was right, it was Thursday night, with plenty of big action players and tourney players to fill the poker room. Problem was, management was essentially incompetent, as I stood around for nearly an hour while three—count 'em, three—floor folk stood around bickering about whether to open the 2/5 NLHE game, or a new 1/2 NLHE game. The blindingly obvious answer was to open the 2/5 game, which would in turn open up enough 1/2 seats to get nearly everyone into the game they wanted to play. Apparently, the sticking point was that a few guys in the 5/5 mixed game were on the 2/5 list (which was 18 deep), and wouldn't commit to opening the 2/5 game. This in turn caused angst among the mix game players who were worried about playing short-handed. Where is the floor with the backbone to tell these guys to stop bellyaching and just pick the damn game they wanted to play?
Anyway, I ended up playing only an hour and a half. My table had a couple of guys I figured would spew chips, and I was right. One guy was trying to be a table bully, but I quickly figured him out, letting him three barrel me with air. One hand, I held 65o, called him all the way down with fourth pair, and won. An orbit later, I held 54s, flopped the flush draw, and called his river bet after I missed with just bottom pair, and again raked the chips. Thank you! Come again!
The rest of the night was pretty standard for me, winning some pots with aggression, losing a couple on big draws that whiffed. On one hand, I called a preflop raise with 98s, the flop was A-K-9, and the preflop raiser bet big. I thought about raising, then decided it wasn't worth it. The other guy proudly slammed down 32o, and spent the next two orbits crowing about his huge win (of $15). Which leads to our hand of the night:
I was UTG, and found 32o. I figured, why not play it for a lark? Maybe a little poetic justice will result. Right on cue, big bluff guy raises to $17, a big bet at this table. Surprisingly, there are five callers to me. I call as well to close the action—that's right we had seven players to the flop for $17 in a 1/2 NL game. Crazy. Anyway, flop is 9-3-2 with two spades. Donkey Kong! I know there will be a bet, so I check, intending to check-raise all-in. Cue big bluffer, who overconfidently puts out $75. Couple of folds, then hell breaks loose. One guy raises all-in for a little over $150. Another plays calls all-in for around $120. I put both guys on flush draws, or maybe an overpair and a flush draw, so I push all-in as well. Despite the great odds, big bluffer insta-mucks (hah!). Sure enough, the other guys show QsTs and AsJs. Turn is a Queen to give me a little sweat, but the river was a beautiful, if unnecessary, trey of clubs. Canoe! I rake the ~$600, and a few hands later, rack up my profit and head home for some well-deserved wine.
CAUTION: The foregoing poker play was made by an expert (donkey) under controlled, statistically variant conditions. Please do not try this move at home. Remember, canoes can be hazardous to your health.
Twenty-odd years ago, I was a teen in a tiny farm town in western Nebraska. Video games were popular, but the only one in town was in the local bar, a place that was verboten to me. But on school trips and summer camps, I managed to sneak away with friends to the occasional arcade or hotel game room, where we'd pump quarters into all the classics: Pac-Man, Ms. Pac-Man, Donkey Kong, Centipede, Frogger, Defender, Galaga, Space Invaders, Missile Command, Mortal Kombat, Asteroids, Duck Hunt, Double Dragon, Street Fighter ... OK, so there were a lot of video games back in the day.
One of my personal favorites was Gauntlet, a multiplayer game with a Dungeons & Dragons-esque theme. Up to four people could play at once, with each player selecting his or her own type of character: Wizard, Warrior, Elf, or Valkyrie. Each type of player had its own strengths and weaknesses, and the players needed to work as a group to be successful. There really was no ultimate objective, just lots of killing of ghosts and demons, avoiding the Death wraiths, collecting treasure, and trying to eat food to stay alive for another level (though the game would helpfully take more quarters if you couldn't find a snack onscreen). One of the alternately cool and obnoxious parts of the game was an announcer with a deep and oddly-accented computerized voice that would intone various warnings:
"Blue Wizard needs food, badly!"
"Do not shoot the food!"
"Use magic to kill Death!"
"Red Warrior is about to die!"
I got to thinking about Gauntlet recently because I have noticed a marked uptick in bad players in the low-stakes cash games I play. Although my poker buds and I have generally observed games getting tougher the past couple of years, recently there has been a notable—and welcome—influx of new bad players. So what's the Gauntlet connection? Well, most of these bad players seem to be "Pay Off Wizards"—players who simply feel compelled to call value bets, particularly on the turn and river, even though they know they are likely to be behind. Pay Off Wizards seem to play in mortal fear of being bluffed off a hand, often convincing themselves their modest holding has a real chance of winning. Here are just a handful of the most egregious examples I've collected over the past three cash game sessions:
I flopped the Queen-high flush (in clubs, natch). I was called down for pot-sized bets on all three streets by ... AhJh for Ace-high.
I hold ATs, flop trips on a T-T-7 board, turn is a small blank, river is a 7, and I get called down on all three streets ($75 turn and $125 river) by .... 72o.
I turned the nut straight, got called. I bet the river, was raised, and then had my reraise all-in called by ... second pair, no kicker.
I play 87 sooooted, flop the stone cold nuts with 4-5-6 rainbow. I got called on the flop and turn in three spots, and got two players to call all-in on the river trey with ... K7o and J7s.
I flop a flush draw with A3s, miss, but hit a trey on the river. I bluff a 3/4 pot-size bet, and get called by .... AK unimproved.
I flop a flush draw with A5s, miss, but turn a 5. I bluff the river and get paid off by ... KQ unimproved.
I play 64 sooooted OTB for a raise. Player calls me on blank flop. I turn a flush draw and keep firing; only a call. I river the flush, bet the pot, get called by .... second pair.
I play A6 soooted, float the flop in position with bottom pair. Turn trips, raise the turn and bet the river, get called by ... TPTK.
I raise OTB with pocket ducks, flop a set on an Ace-high board. I get called in two spots all the way to showdown ... by A9 (rivered two pair) and A5 (top pair no kicker).
It's not just me and my weird LAG playing style, either. I've seen similar payoffs in favor of other players as well, including bizarre calls of river value bets by rocks and nits who wouldn't voluntarily risk a redbird without having the near-nuts. Well, I'm not one to object to draining players of their cash (and life force). Just call me Poker Death.
"Pay Off Wizard is about to rebuy!"
--------------------------------------------------------
Here's a Poker After Dark episode where Phil Laak acknowledges his extraordinary Pay Off Wizard skills:
Medical students are taught to "think horses, not zebras" to remind them that in most patients, a common diagnosis is more likely than a rare condition. This concept occurred to me recently when I saw a couple of hands posted in the strategy forum over at All Vegas Poker (AVP), and a similar hand on Vegas Poker Now (VPN). In one hand, a player flopped a baby flush and ran into a bigger flopped flush, and in the other two hands, a player flopped the idiot end of a straight. Of course, in each thread, the poster wanted to know how to avoid these potential coolers (well, other than by folding preflop, natch).
If you play poker regularly, you will run into the occasional monster cooler, something tougher to lay down than two pair versus a better two pair. Sometimes you win, sometimes you lose, and sometimes you get to enjoy the slow motion carnage as a bystander to the train wreck. The thing is, coolers tend to be memorable:
In Confessions of a Winning Poker Player, Jack King said, "Few players recall big pots they have won, strange as it seems, but every player can remember with remarkable accuracy the outstanding tough beats of his career." It seems true to me, 'cause walking in here, I can hardly remember how I built my bankroll, but I can't stop thinking of how I lost it.
Although set over set is bad enough, I have seen flopped set-over-set-over-set on two occasions, once with me involved; in both cases, bottom set turned quads for the win. In a memorable stretch of runbad last fall, I got stacked three times in a single session of 2/5 NLHE, with a flopped King-high flush versus a flopped Ace-high flush twice, and a flopped set over set on the third hand. Or, on my Festivus trip to Vegas last winter, I was involved in a hilarious hand with a couple of total yahoos, flopping a Yak-high flush against BWoP'sLe Dawn-ed flush, and Poker Grump's Set O' Presto. My hand did finish in a strong second place; unfortunately, I had bet the win, rather than the exacta box.
In any event, although weird coolers seem to happen frequently in poker, I decided to figure out the actual odds for the most common coolers: set over set, flush over flush, and straight over straight. Here's the executive summary (the "show your work" segment is below the jump). Now, there are actually a couple of different ways of looking at the probability problem, with different relevance to our decision-making at the table:
The "Perfect Storm" calculation—Determining the odds that, as a deal begins, the right confluence of events will occur to create a cooler hand that will sink us or our opponent (or any two players at the table).
The "Doomswitch / Boomswitch" calculation—Determining the odds that, upon hitting a monster flop, an opponent has the necessary hole cards to complete the cooler hand.
Note that the odds below are "pure" odds, calculated without regard to player hand selection. So, assuming players tend to muck certain hands preflop (e.g., J2s, 74, 43) as "junk", or fold small pairs to preflop raises, the realistic odds of flopped coolers are much longer. Also, the odds below are merely a calculation of how often we will find ourselves in these flopped cooler situations, not how often we will be on the top or bottom side of these cooler flops. The relative tightness/looseness of our and our opponent's starting hand ranges will dramatically affect how often we are winning or losing in these situations.
Set over set:
Perfect storm odds—Thankfully, Brian Alspach has already calculated these probabilities in great detail for a Poker Digest article. The perfect storm probabilities for a set over set situation vary somewhat based on the number of players in a hand, as more players mean a higher probability of players being dealt pocket pairs. However, for a ten-handed game where all players take pocket pairs to the flop, flopped set over set should occur in roughly 1 out of every 167 hands. Since we will only be dealt a pocket pair once every 17 hands, the odds we will be involved in a flopped set over set situation (assuming all pocket pairs see the flop) are 1 in 2,839.
Doomswitch / Boomswitch odds—We flopped a set, so what are the odds our opponent's random hand also flopped a set?—are 1 in 90.
NOTE: Not all flopped set over set hands will wind up as coolers. There will be cases where a draw heavy board will slow down the action. I haven’t factored these situations out of the calculations above, because those hands typically will still end up as coolers if both players play their sets aggressively versus draws. Also, there will be rare cases where the flop will be full house versus quads, which again are not factored out, as they are also coolers (just much colder).
Flush over flush:
Perfect storm odds—Unlike with sets, where more players in a hand mean more possible pocket pairs, which increases the odds of a flopped set over set situation, the odds of flush over flush situations decrease with more players, as more cards of the suit in question will be distributed to players, rather than being available for the flop. To put it another way, having more than one opponent with suited hole cards decreases the odds of a flush flopping, while having more than one opponent with distinct pocket pairs increases the odds of sets flopping. So, we need to look at the perfect storm odds of two players with random hands flopping flushes—1 in 19,491.
Doomswitch / Boomswitch odds—We flopped a flush, so what are the odds our opponent's random hand also flopped a flush?—1 in 39.
NOTE: Not all flopped flush over flush hands will wind up as coolers. There will be a few rare cases where the lower flush will in fact flop a straight flush or open-ended straight flush draw. I haven’t factored these situations out of the calculations above, because those hands typically will still end up as coolers.
Straight over straight:
Perfect storm odds—To keep consistent with our flush odds calculation, what are the odds of two players with random hands flopping straight over straight? This takes a little more thought, as there are three ways two players can get straight over straight—"bookend" straights with connectors (e.g., 34 vs. 89 on a 567 flop); "gapper" straights with a shared middle card (e.g., 35 vs. 58 on a 4-6-7 flop); and "bookend-gapper" straights with a shared middle card (e.g., 34 vs. 48 on a 5-6-7 flop, or 37 vs. 78 on a 4-5-6 flop). The final odds—1 in 24,038.
Doomswitch / Boomswitch odds—We flopped a straight, so what are the odds our opponent's random hand also flopped a straight?—1 in 82.
NOTE: Not all flopped straight over straight hands will wind up as coolers. A monochrome flop may easily slow down one or both players. Also, in the shared middle card straights, there will be a few rare cases where the lower straight will in fact flop a straight flush or open-ended straight flush draw. I haven’t factored these situations out of the calculations above, but it does mitigate somewhat the effect of straight over straight coolers.
Conclusions:
Realistically, the Doomswitch / Boomswitch odds are the ones we care about the most, since we rarely think about cooler hands if we aren't already in a potential cooler situation. So, what can we conclude from these odds?
Flopped cooler hands are quite rare. Flopping bottom/middle set, a small flush, or the idiot straight should be a happy occasion, not a time to start seeing monsters under the bed.
It is much more likely to see a flopped set over set situation, both because it is easier to hit the requisite perfect storm situation, and because player self-selection makes it more likely players will play pocket pairs to the flop, while many suited or connected/gapped cards get folded preflop as "junk" (e.g., J2s, 74o, 43).
Because flopped cooler hands are rare, if we encounter aggression after flopping bottom/middle set, a small flush, or the idiot straight, we are most likely up against a hand we can beat. If we flopped a set, we are usually looking at two pair or a draw. If we flopped a straight or flush, we are usually up against two pair, a set, or a draw (including pair-plus and combo draws).
Because we are usually ahead on the flop with these hands, it might make sense, absent truly deep stacks, to play fast and aggressive with smaller sets, straights, and flushes.
Conversely, with top sets, nut/big flushes, and nut/big straights, it may pay to raise smaller for value, or to slowplay, hoping our opponent will commit more chips on a safe turn card. If our opponent in fact is on the wrong side of a cooler, he will likely let us know by getting his chips in on the flop without our help.
Although flopped coolers are rare, the odds of a cooler materializing greatly increase as the turn and river change the board texture. Although we may flop the best hand, if the chips don't go in on the flop, we may well get run down on later streets.
Now, although the numbers tell us that flopped coolers are rare, sometimes those hoofbeats you hear are in fact from a herd of zebras. Or gazelles. Maybe wildebeests. Anyway, good poker intuition can still play a valuable role in helping sniff out the trap hands where you seem destined to go broke. For example, about a year ago I was playing $2/5 NLHE at the Meadows ATM. There were a few limpers, and one of the regular maniacs raised to $25. There were a couple of callers, all standard. I found Yaks in the BB, so I popped it to $150 straight. To my surprise, a young guy UTG smooth called, as did the original raiser. The flop came out Qh-Jh-7d. Yahtzee! But, it was a busy board, so I decided to play aggressively, and bet $350. The young guy UTG thought, then pushed all-in, and the maniac snap-folded. Now, the young guy is a regular, and a solid player. He isn't necessarily rock-tight, but his play smelled a lot like QQ. I just couldn't see him playing 77 for $150 preflop, and I would have expected him to reraise with AA/KK. AhKh made some sense, while AQ and QJs were longshots. On the other hand, he is capable of a big move if he smelled weakness, though I couldn't think of a hand he might think I had that I would lay down, other than AK or an underpair. We were each pretty deep, around $1,500 at the start of the hand. So, calling would cost me ~$1,000. My heart told me I was beat, but in the end, I just couldn't lay down the Yaks. Sure enough, he rolled over QQ, and it was "good hand, good night" time for me.
A similar hand occurred at the 2009 WSOP, the infamous Billy Kopp blowup hand. Essentially, Kopp went from being one of the dominating top three stacks with the final table bubble in sight, to busting out short of the final table, thanks mostly to gacking off a huge stack to Darvin Moon when both players flopped flushes. Although there are many better poker players who have dissected and analyzed that pivotal hand, it seems to me that the idea the Moon had flopped a higher flush never even occurred to Kopp. Although flush over flush was improbable, once Moon showed serious interest in the hand on the flop and the turn, alarm bells should have been going off. I'm not saying Kopp should have laid his hand down, but at some point, a baby flush turns into a bluff catcher, and a deep stacked player needs to think about protecting his stack.
So, even though we should expect horses, not zebras, it pays to remember that sometimes:
Detailed, boring math below the jump (feel free to point out math errors in the comments or via email!):
Set over set:
The basic calculations for the "perfect storm" odds are in the Alspach article. Simply multiply the odds of any two players flopping sets (1/167) by the odds we will be dealt a pocket pair (1/17) to get the odds we will find ourselves in a flopped set over set situation—1 in 2,839.
Now, for the "doomswitch / boomswitch" odds, we need to: a) assume we flopped a set, and b) calculate the odds our opponent has a pocket pair that also made a set on the same board. Since we made a set with one of the board cards, our opponent must have a pocket pair that matched the rank of either of the remaining board cards (assuming they are distinct ranks). Let's say the flop is J-9-5, and we have a set of 5s. Our opponent can have JJ or 99 to be ahead. Once this board flops, there are 6 ways for our opponent to hold a pocket pair of Js, and 6 ways for him to hold a pocket pair of 9s. There are C(47,2) possible starting hands (after we know our hole cards and the flop), so the odds of our opponent holding a pocket pair that also flopped a set is:
Chances of being dealt 2 suited cards = 312/1326 = 23.53%
Once you have 2 suited cards chances of seeing a flop that gives you a made flush:
Number of possible flop combinations: = C(50,3) = 19,600
Flop combinations containing all of your suit = C(11,3) = 165
165/19600 = 0.008418367347 or about .84%
So, assuming you play any 2 suited cards, chances you'll get a flopped flush would be 312/1326 * 165/19600 =0.00198079232 or, as you figured, about .2%
The more important number here is the .84% chance that you'll get a flopped flush.
To adapt this methodology to two flopped flushes, just work in the odds for a second hand having been dealt two suited cards of your same suit out of the remaining 50 cards:
However, once you flopped a flush, what are the odds your opponent with a random hand also flopped a flush? This is a little easier. There are 8 cards of our suit remaining after we flop our flush. To get two hole cards dealt of our suit, we calculate:
(8/47) * (7/46) = 0.0259 = 2.59% = 1 in 39
Straight over straight:
First off, there are only 8 ways to make a “bookend” straight vs. straight (ignoring suits for the moment):
Low Hand / Flop / High Hand
A2 / 3-4-5 / 67
23 / 4-5-6 / 78
…
89 / T-J-Q / KA
Let’s start by finding the odds of being dealt the low side of one of these straights—“low bookend connectors”. Now, the ranks 2-8 each work in two starting hand combos, while the Ace and 9 only work in one combo each. There are 9 ranks for the first card, with four suits for each rank, giving us 9*4 = 36/52 odds of being dealt a qualifying first card. Then, for each qualifying first card 2-7, there are 8 corresponding second cards that will give us connectors able to make a low bookend straight, while for the Ace and 9 there are 4 corresponding second cards that will give us connectors able to make a low bookend straight. Thus, the odds of getting a connecting card for the second card is 7/9(8/51) + 2/9(4/51) = [(7*8) + (2*4)] / (9 * 51) = 64/459. This gives us odds for getting low bookend connectors of (36/52 * 64/459) = 0.0965 = 9.65% = ~1 in 10.4.
Next we need our opponent to get the corresponding high bookend connectors, which fortunately are exactly one hand (disregarding suits). So, for their first card, they can be dealt any of the eight available cards that will make the corresponding high bookend connectors (8/50), and the second card dealt to complete the high bookend set must be one of the four cards of the other rank (4/49). So, the odds of our opponent getting dealt the high bookend connectors that match our low end are (8/50 * 4/49) = 0.0131 = 1.31% = ~1 in 77.
Finally, we need the gin flop, with cards of exactly the three ranks needed to complete the straight for both sets of bookend connectors. Needing one card out four from each of three ranks on the flop, means there are 64 (4*4*4) flop combinations (order doesn’t matter) that can complete the bookend straight. There are C(48,3) total flops = 17,296, giving us odds for hitting a gin flop of 64/17,296 = 0.0037 = 0.37% = ~1 in 270 (note: you could also calculate the flop odds as (12/48)*(8/47)*(4/46) = 0.0037).
Thus, the final odds for flopping the idiot end of bookend connector straights: 0.0965 * 0.0131 * 0.0037 = 0.0000047 = 0.00047% = ~1 in 213,796.
But wait, there’s more! (actually, a LOT more). There are also straights where the two starting hands share a middle card and flop straight over straight. These straights occur in the following pattern:
9T / J-Q-K / TA
9J / T-Q-K / JA
9Q / T-J-K / QA
9K / T-J-Q / KA
So, ignoring suits, for each rank Ace (one) through 9, there are 4 starting hands that can flop the idiot end of a straight over straight (note that half are gapper vs. gapper, while the other half are gapper vs. connector, though each version has a shared middle card, so the distinction is not important). So, we have 36 starting hands in total, without reference to suit. Adding in suits, there are 16 (4*4) ways to be dealt each starting hand, and there are a total of C(52,2) = 1,326 starting hands, so the odds of being dealt an eligible idiot straight hand is (16*36)/1,326 = 0.4344 = 43.44% = ~1 in 2.3.
Now, for the high hand. Once the low hand is set, our opponent needs the exact matching high hand. These odds are slightly lower than with the bookend connectors, as there is one shared middle card between the low and high hands. So, the odds of our opponent getting dealt the matching high hand is (7/50 * 3.5/49) = 0.0100 = 1.00% = 1 in 10.
Finally, we again need the gin flop, with cards of exactly the three ranks needed to complete the straight for both hands. The flop odds calculation is identical to the flop odds we calculated for the bookend connectors: there are 64 (4*4*4) flop combinations (order doesn’t matter) that can complete the straight, and there are C(48,3) total flops = 17,296, giving us 64/17,296 = 0.0037 = 0.37% = ~1 in 270.
So, the odds for a flopped straight over straight where both hands share a middle card is: 0.4344 * 0.0100 * 0.0037 = 0.0000161 = 0.00161% = ~1 in 62,217.
Finally, to get the total odds of a flopped straight over straight, we add the bookend straights to the shared-middle card straights, and get 0.0000047 + 0.0000161 = 0.0000208 = 0.00208% = ~1 in 48,077. But, this was calculated as merely being on the idiot end of straight over straight. We could just as easily be on the high end of the equation, so we need to double these figures to get the final odds for being in any hand with a flopped straight over straight: 0.0000208 * 2 = 0.0000416 = 0.00416% = 1 in 24,038.
Onto the doomswitch/boomswitch odds—if we flop a straight, what are the odds our opponent has also flopped a higher or lower straight (identical straights are not included, only the coolers)? Depending on whether it is a bookend vs. bookend situation, or a shared middle card situation, our opponent can have either 8 or 7 cards for the first hole card, and either 4 or 3 cards for the second hole card. So, the odds become (7.5/47) * (3.5/46) = 0.0121 = 1.21% = 1 in 82. For a bookend vs. bookend situation, the odds are slightly better: (8/47) * (4/46) = 0.0148 = 1.48% = 1 in 68. If a gapper straight is involved, the odds are: (7/47) * (3.5/46) = 0.0113 = 1.13% = 1 in 88.
Now, why are the odds of a flopped straight over straight so much lower than the odds of a flopped flush over flush? There are several factors in play. First, it is easier to get an eligible straight starting hand than flush starting hand. Conversely, it is easier for our opponent to get an eligible flush hand than it is to get an eligible higher straight hand. But the real kicker is that the gin flop is easier (nearly 24% easier) to hit in a flush over flush hand than in a straight over straight hand: 84/17,296 flush flops rather than 64/17,296 straight flops. Considering it is slightly easier to hit a flush draw than a straight draw certainly makes it “feel” correct that it should be tougher to flop straight over straight than flush over flush, even if a straight is an easier hand to make than a flush, considered ab initio.
Over the years of playing poker, I've developed a few terms that have stuck with me and my friends when I talk about poker. So, to avoid any failures to communicate, here are a few terms I'll be using in my blog (many more after the jump):
Canoe—A small full house (i.e., a small boat). Generally something like 5s full of 3s.
Catamaran—A full house made with unpaired hole cards, e.g., 87 in the hole, 8-8-7-x-x on board. So named because catamarans are boats with twin hulls.
ET—An uber-calling station, incapable of folding bottom pair or better. Origin—"ET phone home!" Usage ex.—"Santa Claus is a gray-haired, Zima-drinking, sorghum-swilling ET." Fat Stripper hands—Hands that make you limp, and you won't pay $20 to see more or play further. Good examples of Fat Stripper hands are JT, pocket ducks, and 86s.
Hilarity ensues OR #hilarityensues—Not my original phrase, it has been used in pop culture for some time. Its origins are in TV sitcom synopses where some weird circumstances align, and the viewer is promised a rollicking good time which is rarely delivered (e.g., "Bubba accidentally gives moonshine to Baby Jessica before her first day of kindergarten. Hilarity ensues."). I've adopted the phrase as my ironic Twitter hashtag to denote situations where I snap off someone's big hand with something rather improbable, causing the loser to go on tilt and maybe even berate or assault me. Usage ex.--"Just snapped AA with 53s. Flopped the wheel. Dodging chips. #hilarityensues".
#mybad—Another ironic Twitter hashtag, used when I am berated by some player for winning a pot after making what they consider to be a bad play. Me, I'm results-oriented.
Pot Limit Gamboool / PLG — My name for Pot Limit Omaha (PLO). 'Nuff said.
Statistical Variance Box / SVB—The proper term for a player known coloquially as a "luckbox". As far too many poker "experts" have pontificated, there is no such thing as "luck"; rather, mathematically speaking, there is only "statistical variance" (or "variance" for short). "SVB" is an easy to use acronym to throw out at the table, and is also a little more discrete if you want to insult someone but not have them understand what you mean. Usage ex.—"Ironman Barbie is the world's biggest SVB ... and a d-bag."
Spousal Variance—That portion of a poker bankroll that is spent, directly or indirectly, by or for a spouse or significant other in order to play poker (i.e., to get a "spouse pass"). Examples include: spa sessions, shopping sessions, gifts, home renovations, and straight cash payments. Spousal variance also includes the extra cost of a joint Vegas trip vs. a solo trip--better lodging, better meals, etc. Spousal variance is always -EV (when was the last time your spouse gave you money to play poker?).
Yaks—Pocket Jacks. Viewing this hand causes headache, nausea, vomiting (yakking), cold sweats, nervous tremors, night terrors, and occasional syncope, paralysis, and/or nervous breakdown; truly this is the hand designed by Cthulhu himself. The gates of Hades are no longer guarded by Cerberus, the three-headed dog with a mane of live serpents and the tail of a dragon. No, the entrance to Hell is now guarded by two fire-breathing agents of doom—a pair of Yaks. Yak exposure can have a cumulative effect over time; for poker players with numerous past encounters with Yaks, even gazing on Yaks can lead to instantaneous insanity. Usage ex.—"Yaks suck Donkey balls."
