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The fundamental theorem of video poker

As so often happens at the Palms, I’d ended up sitting next to a professional video poker player.  You can always spot them by that slapping action on the buttons, which is something that only comes with hours of training.

I’ve tried it, and it makes me look great for a few minutes but my arms get tired really quickly.  I’m such a noob.

Thanks to the slot card reader, I knew this particular chap was called Rick and that he had over 100,000 points on his card.  I’ve seen many players with more than that, but even so he has probably achieved the the lofty status of never having to pay to eat again.

Once you achieve the "MVP" tier of the Palms’ slot club (50,000 points earned in 90 days) you get half off at the buffet when you redeem points to eat, and if you make the "Hall of Famer" level (200,000 points in 90 days) you get a 75% discount.  So not only do you have gazillions of points to redeem, you just can’t spend them fast enough.

You can only eat so many $4.25 champagne brunches.

You apparently get other shit like movie passes and free car washes at those levels too.  Obviously, it’s part of my summer plan to achieve this status.  Who doesn’t love a free car wash?

Anyway, Rick was having a bad day on Deuces Wild.  He told anyone who cared to listen that he needed to take a break as he just made three mistakes in a row.

As he got up and wandered off, I glanced across at his screen and saw: 8h 7h 4h 5c 4s.  He’d held the first four cards, with the last 4 making a worthless low pair after the draw.

I know this one now without looking it up.  When you have a four card straight draw with a gap but three of those cards are the same suit, you should always hold for the long shot straight flush above the gutshot straight.  This holds true even if there are two gaps in the straight flush draw (as in this case: 8 7 4).

He’d done it wrong, but at least he’d realised and taking a break was a smart move.

Perhaps he could have taken a longer break than four minutes, but I guess it doesn’t take long to go to the ATM and fetch a coffee, and any break much longer than that is really going to eat into your hourly rate.

He sat back at the same machine and the woman next to him asked if he liked that one in particular.  He explained, "I usually play on the other side, but it’s not been hitting so I came this side today".

Well, game selection is important.

He continued, "This week it’s been full of tourists so it’s hard for the regulars to get a read on it".

"Tourists" are clearly the "internet players" of the professional video poker circuit.

He went on to boast how he can usually tell when – as well as at which machine – the jackpot is going to pay out.  "It should go early today, not like $1300 or $1400" (in reference to the progressive jackpot, which resets to $1000 when a royal flush is hit, then increases with each game played until the next one).

I’m quite surprised he wasn’t wearing shades so the machines couldn’t soulscan him right back.

It wasn’t long before I was dealt a hand I needed to think about: three aces with a three card royal flush draw and no wild cards.  With a pair and a three-to-the-royal option, you always go for glory (in deuces wild, any pair has to improve to three-of-a-kind or better for a payout).  With trips already on screen, I wasn’t quite so sure what to do.

My strategy card said to hold the aces, but I still hesitated because of the progressive jackpot.  At that time it was set to pay $1122 for a royal flush instead of the usual $1000.  I just couldn’t work out if it was enough to make a difference.

Rick saw me scrunching my face up at the screen, then my cheat sheets, then starting to type the hand into my phone so I could check it later after I finally made a decision, and he jumped to my rescue.

"You have to go for it", he offered.  "Three to the royal beats pretty much everything".

Well, he’s not far off.  The only hands you would normally hold over a three card royal are a made straight, a made flush or an open-ended four card straight flush draw.  Oh yes, and three of a kind.

But after he said that, how could I not draw to the royal flush?  You just know that it’s going to draw the two cards you’d have needed (or at the very least one of them and a wild card) if you hold the aces and nothing would have put me on tilt for the rest of the trip more than seeing his "I told you so face".

I was never so glad to see rags: a meaningless 7 and 3 was about as emphatically not a jackpot as you can get, nor would it have improved my three aces to a bigger win.

This hand was actually not as close as I thought it would be.  I plugged the numbers into some video poker software and it calculated the ER of the three aces as 10.09 (that’s an expected return of just over ten coins for a five coin bet) and the royal flush draw came in at 6.54, if you disregard the progressive.  So, in normal circumstances, holding the three of a kind is worth over 50% more!

Pumping the jackpot up to $1122 in the simulation didn’t make any difference to the strategy.  The value of trips doesn’t change (because there’s no way to redraw to a royal flush) but the three card royal draw’s ER rose to 7.05.  It’s extra free money when you hit it, but it’s still nowhere near enough to throw away trips for.

In fact, the jackpot has to reach a massive $2000 before you would consider breaking the three aces (ER=10.09) for a three-card royal flush draw that contains an ace (ER=10.11), and even then it would be an extremely volatile play for a tiny edge.

With the jackpot that high the overall return of the machine becomes a whopping 102.70% (compared to 100.76% with no progressive) although I’m sure there must be other strategy adjustments you need to make to take full advantage of the monster jackpot.

In fact, Rick did tell me that when the meter gets to $1350, that’s when you throw away the wild card if you’re dealt a royal flush with one wild deuce.  That’s correct, although he’s probably not accounting for the fact that any jackpot of $1200 or more will trigger tax paperwork.

A $2000 progressive would happen only very rarely the Palms because the meter rises very slowly.  When it does, you can be sure that the bank of machines will be perma-occupied by pros until it hits, and then they’ll all go home.

And it was thinking about that kind of mass exodus - which you really do see after a brief moment of fake, bitter congratulations when a substantial progressive is hit – that got me thinking.  Rick’s bad advice not only cost me a little EV, but it also cost himself – and every other player sitting at that bank of machines!

When I make the correct play and hold the three aces, I will hit a royal flush on the draw exactly 0% of the time.  However, when I hold the three card royal draw, it is a possibility.  It’s a very slim possibility (the odds are 1080-1 against) but nevertheless it still happens more often than never.

The key thing is that when I do get lucky, not only do I win the jackpot but the progressive meter resets to $1000.

Let’s pretend I did hit it.  A few seconds ago, Rick was playing a game with a $1122 jackpot which had an expected return of 100.97%.  Now it suddenly became a standard 100.76% game.

A couple of tenths of one percent doesn’t sound like much, but even with that modest progressive his hourly win rate (before comps) was 28% bigger before the jackpot got hit.

If the progressive had crept up to about $1400, that would have been a 101.5% game until my jackpot just went and ruined it by cutting the player’s edge in half!

It’s easy to think that it’s completely irrelevant how well or how poorly the guy next to you plays at video poker because it’s a solo game.  In fact, when a progressive jackpot is involved, your edge can be affected directly by the decisions that those around you make.

Therefore a sharp video poker player would have absolutely encouraged me to hold the three-of-a-kind.  It makes no difference to him whether I’m making the optimal play on this hand, but it would make a difference if I made a donkey play that reset a jackpot which he still had a shot at winning.

And so, in anticipation of my inevitable 2+2 book deal, I proudly present the Fundamental Theorem of Video Poker.  You may call it the FTOVP if you wish.

"Whenever a player incorrectly holds a royal flush draw, they lose and everyone else playing that game also loses.  However, whenever a player incorrectly fails to hold a royal flush draw, they lose but everybody else gains".

OK, I admit it should really be called "an occasionally relevant theorem of multi-player progressive jackpot video poker", but it’s not quite as catchy is it?

The view, revisited

A few more pictures of the spectacular view I had from my suite at the Rio, now I’ve had chance to sort through them a little bit.

Panning the entire view from right to left we see: Imperial Palace, Harrah’s and Venetian, with parts of Caesars in the foreground (the Colosseum is far right).

Then Mirage, Palazzo, Wynn, Treasure Island and Encore…

… condos, condos, condos and construction of the Fontainebleau project.

Trump and Stratosphere, with the Circus Circus Adventuredome in the foreground.  Downtown Las Vegas is in the distance, with the Plaza far left.

 

Continuing all the way round to the left, we see the other Rio hotel tower and the pool, with the Valley stretching out towards the North.

Finally, a wide shot of the Strip at sunrise, from Stratosphere (far left) to Imperial Palace (far right).  If it wasn’t for the funny glare in parts of the picture I think this would be my favourite photo ever.  I guess I’ll just have to learn how to use Photoshop…

Unlucky numbers

So, just how unlucky was I in my poker tournaments on this trip?  I can certainly fudge some figures together to show a pretty unlucky number.

In the three main tournaments I played, I got my entire stack in and called exactly three times.  I lost them all.

If it had been just three coinflips, I’d be losing them all roughly once in every 8 times that this sequence of events cropped up.  I’d still be cursing my luck.

However, because I was a massive favourite in one hand the actual number is more like 1 time in 80.  The other 79 times, I’m winning at least one of the all-ins and going a little bit deeper in at least one of the tournaments.

There’s no guarantee of converting that into winning money, of course, but if you constantly fail to get past your first all-in situation there’s absolutely no hope.

In my key hand at the Golden Nugget (it didn’t quite bust me, but left me so short stacked everything afterwards became irrelevant) I was a 95% favourite when the money went in.

Blinds were 50/100 and I’d raised one limper to 600 with my KK.  I got an immediate call from my left who then also called my flop bet and my turn push for about 6000 chips in total.  The board was J424, he had QJ and revealed "I thought you had pocket tens".  Obviously.  The river brought another jack, one of the two remaining cards in the deck he could win with.

You’d think that one would have hurt more, but actually I felt pretty good about it.  A coinflip is a coinflip and there are times you just have to push and hope.  You usually don’t want to get called because half the time you’ll be going home.  This time know I played the hand just fine.

Being a 95% favourite is an absolute luxury.  You’re four times less likely to go broke on the hand than with pocket aces against pocket kings all in pre-flop.  There’s no shame in betting the ranch when you’re in such a commanding position.

Whereas with 50/50s, well… you can always ask yourself "did I really have to do that?".  The answer is usually "yes", but there’s always room for debate.

So, sorry to all my backers that I couldn’t manage to bring back a fat wad of cash for you, and unfortunately I can’t pay you in Sklansky Bucks.  Next time I’ll try to be luckier.

Live updates: Golden Nugget Grand Poker Series ($225)

Begins at noon (8pm UK time)

Half a pencil

I can’t think of a hotel I’ve stayed at that didn’t put a notepad and pen in the room.

After all, I usually nab the pen. I have a pot full of them on my desk.

However, all the Imperial Palace has to offer is half a pencil.

I can’t tell if they actually make them this size, or if the maids just sharpen them each day until they get down to the lettering.

You wait 5 days then 50 come along at once

By rights, I should now have a photo like this one up on a Winners’ Wall somewhere.

Unfortunately, Harrah’s Laughlin doesn’t have anything of the sort (and if they did, they probably would have asked me to change my shirt) so I’ll have to make do with this one the dude sitting next to me took when I hit this video poker machine for TEN FREAKING GRAND!

It was looking like I’d go right through the trip without hitting a 40,000-1 royal flush at all. So instead I hit this 650,000-1 dealt royal flush on the bottom line of a 50-play machine.

At 4,000 coins per royal, times 5c per coin that’s $200 for each one. Fifty times. Just let me say it again – that’s ten grand!

This must have been by an east-facing window (views of the outside world are permitted in casinos in Laughlin) because the glare on the screen from the morning sun is horrible. I couldn’t get a very good photo at all, but at least I managed to get myself in the picture with this one.

The sign on top of this bank says "Hottest Slots of the Month". The players club actually compiles a list you can collect with the locations of which particular machines have been paying well lately. I’m assuming this one will stick around on the list for another month now.

If you played this game with a maximum $12.50 bet per spin for three hours every day, you’d see this miracle hand on average once a year, and to do so would cost over $40,000 even in this "full pay" (99.5% payback) version of the game. Most similar machines are much less generous.

I had hardly any time left before needing to leave – I had to get back to Las Vegas to check into the Imperial Palace and then get down to Binions to register for the tournament before noon – and apparently it usually takes about an hour and a half for the casino to issue a cheque.

Otherwise the whole process of winning was impressively fast. A slot attendant appeared almost immediately, the supervisor was about ten seconds behind and one started to fill in the tax paperwork while the other called up to the eye in the sky to make sure I’d shown genuine delight at winning, or something. No problem with the tax withholding, I gave them my ITIN and I got 100% of the money.

In cash. Counted out into my hand in the middle of the casino floor.

This is what ten grand in notes looks like.

And yes, they do all have Benjamin Franklin’s face on, this is not a made-for-TV brick of $1 bills with a $100 on each end.

Two hours later, it was in the bank (I’m not daft) and I still made it to Binions with ten minutes to spare – where I saw garbage for five hours, then lost a race with ace-king against a pair of tens.

So, live poker probably owes me a coinflip but I think it’s safe to say that for the time being I’m sitting somewhat ahead of expectation at video poker.

Live updates: Binion’s Poker Classic ($500)

A bit of poker-style gambling

In case the graph didn’t make it clear, I’ve made it through to the second round of the WSOP satellite. I play again at midday (8pm UK time).

Not sure if I’ll bother with a chip graph this time, it was pretty intense trying to keep up with meaningful updates and the whole thing was over in exactly one hour. It’s only because I got lucky that the graph had more than 3 points on it.

We started with 1500 chips and doubling the blinds just wasn’t fast enough. It went up every fifteen minutes: 25/50, 50/100, 100/200 then 200/500.

Two players progressed from each table of eight, and I assume it will be the same format today to reduce the field to just one table of ten to play for the cash and the Main Event seat. At that final table, about 40 hands will determine who wins bottom place money ($500) and who wins the top prize ($10,000). Just like on TV, I suppose.

To say it’s all a bit random would be an understatement.

But, on the other hand, the quality of the opposition is terrible. This game had everything you could ever dream of. Players who have no idea of the value of their cards, or their chips. Even though the chips have numbers on them, in case you forget.

It was just like the scene in Ocean’s Eleven where Brad Pitt is teaching a bunch of movie stars to play poker, except nobody was famous and the dealer already knew to deal to the left.

Given more chips and enough time, I am absolutely positive I could have pissed all over my table yesterday. As it was, I was forced to get lucky in a 3-way race holding KJ against A6 and 23. Making the overcall there with the nut low wasn’t even the worst play I saw.

These players mostly weren’t here for poker, they were here in spite of it. The tournament took place in the promotions area where slot tournaments are held (the machines were all around the edge of the room) and I’m sure that really that’s what everyone else wanted to be doing. It’s much more fun to slap a button and not have to think; to have a machine tell you whether you won rather than have to try to work it out for yourself.

One player tabled QJ on the river twice, making a hesitant call each time. The first time the board showed two queens, a jack and two little cards with four hearts and his full house beat a king-high flush. (In the WSOP, that same call with the absolute nuts would get you a one round penalty for soft-playing). The next time he called on the river holding QJ on a board of 67TA2 with 3 spades. A busted gutshot straight draw has rather less showdown value.

He wasn’t alone in being married to a drawing hand with zero cards to come. When one player bet the river holding 23 and having paired the 3, she got paid off by JT because there was a king and queen on the flop.

A pre-flop raise was usually a minimum raise, although any raise was rare. A flop bet, was usually a minimum bet – usually following the question "how much can I bet".

The betting patterns were so peculiar I don’t think there was any chance of trying to play this any other way that staying out of trouble, picking a couple of spots and getting lucky when it mattered.

In fact, I even laid down AQ pre-flop when we were five handed. The first player to act moved all in and I looked round the table to see what was going on. It was the first time anyone had taken more than 5 seconds to make a decision and suddenly I’d drawn attention to myself.

The big blind, who had us both covered, had already counted out the call and was holding the chips over the line ready to release. Unable to put either of them on a geniune hand, I didn’t want to take a likely 40% shot at survival so I let them fight it out and the big blind’s K9 knocked out KQ with a straight.

It was satisfying to qualify and I’m sure it would have been frustrating to miss out. I did see one dude in a Bodog top walking out of the room on his cellphone, presumably complaining about losing a 60/40 against a hand that should have never been in the pot. At least he didn’t have sunglasses on.

I’m under absolutely no illusions that it’s an automatic win. Clearly I do have an edge over the field, but there’s really not enough time to let it have much of an effect. I like my spot, but the poker gods have to like me too.

Still, I only have to get lucky twice more to win a ten grand seat now.

EDIT: 2nd in the "semi-final".  Only one player from each table advanced though so I’m done.  There’s a cash drawing at 5pm for a last chance of some winning.

Celeb spotting at the WSOP

The WSOP is awesome. Just look at some of these famous players’ backs of their heads I got to see.

And a couple from the actual front side…

I have not a clue who the last one is, but he’s wearing a Poker Stars "Team Pro" shirt, so he must be a big deal.

Then again, 90% of the people in that room think that they are.

Live updates: Harrah’s Laughlin WSOP Satellite

Harrah’s Laughlin is sold out. You wouldn’t really know to look at it, but apparently it’s a 1600-room hotel. Tiny by Las Vegas standards but pretty big for Laughlin. And it’s sold out.

I know this because they told me when I checked in last night, and they told the couple next to me too. Then a random guy in the elevator told me the same thing.

I don’t think I’ve ever been in Laughlin on a weekend before so I don’t know if it’s normal, but it sounds like it’s pretty big news.

I was too late to register for my tournament last night so I still have no idea how it is going to work, when it will start or how many runners are in it. The hotel being full is not a good sign, as they originally told me that 400 rooms were reserved for this promotion.

I can still register at 11am, apparently. I have a suspicion that it might be a shootout format but I’ve put up a blank graph anyway in case there’s something worth reporting on. Click the graph to see the chipgraph.com page with comments, there might be something interesting to tell – you never know!

EDIT: I’m registered to play at 4pm.  At 10am there was a group about to start and my choice was 2pm or 4pm.  There’s about a dozen tables in the room, so 400 runners is a definite possibility!  The structure will be kinda fast too…