Optimizing Poker Decisions using ICM

by: Jason Waddell

Poker is a hard game. Tournaments payouts add a layer of complexity to the process. Chips won do not directly correlate to dollars earned. Let’s take a relatively simple hand.

icm1

 

We are in the top 3 of a tournament with the following payout structure:

  • 1st: $30.15
  • 2nd: $18.10
  • 3rd: $12.05

The player on the button folds, and we are left with a rather binary decision: push or fold. Although our hand is terrible, the cards are live, and letting the small stack double-up for free by taking the blinds isn’t a terribly attracting. How can this hand play out? Discretely there are 4 possibilities:

  • We raise, are called and win.
  • We raise, are called and lose.
  • We raise and our opponent folds.
  • We fold.

How do we make that decision? Enter the Independent Chip Model (ICM), a model which translates the players’ tournament holdings to their expected tournament winnings in dollars (or any other currency). Basically, plug in the payout structure and each player’s stack size, and ICM gives you each player’s expected winnings.

The above four outcomes result in the following stack sizes at end of hand:

Starting Stacks:
1682 (Button)
1790 (Hero)
1028 (BB)

Stacks if we raise, are called and we win:
1652
2848
0

Stacks if we raise, are called and we lose:
1652
762
2086

Stacks if we raise and villain folds:
1652
2150
698

Stacks if we fold:
1652
1610
1238

In terms of ICM for the hero (that’s us!), we have:

ICM pre-hand: 21.4

  • ICM if called and we win: 25.6 (+4.2)
  • ICM if called and we lose: 16.6 (-4.8)
  • ICM if raise and villain folds: 22.90 (+1.5)
  • ICM if we fold: 20.6 (-0.8)

Broken down like this, the decision is purely mathematical, as a function of two quantities:

  • The probability villain folds to our shove
  • The probability that we win, given a call.

This is a simple expected value calculation, bread and butter for any statistics student. Villain’s cards are unknown, and using simulation we know that the probability our hand (57 offsuit) beats a random hand is 40.5%. This is a bit of a simplification, as villain’s probability of calling could change as a function of his hole cards, but in this situation it should be fairly representative.

What is the probability villain folds? Well that’s a true unknown, and one we have to guess at. But first, let’s see what our expected ICM looks like as a function of villain’s probability of folding. The weighted expected value calculation is:

icm2

 

Next, we visualize this formula by examining expected ICM as a function of our villain’s probability of folding (p_fold).

icm3

 

If we fold, we know our expected ICM: it’s fixed at $20.6. Thus, we want to pick the option that maximizes our ICM. Here, we can calculate where the black and blue lines cross. Solving for p_fold, we get a value of 0.134, or 13.4%. So the question is, do we expect villain to fold more than 13.4% of the time?

Let’s step into his shoes for a moment. His remaining chip stack is 698. If we shove, he faces calling his stack to win a pot of 300 + 300 + 90 + 698, or 1388. This is giving him odds of almost exactly 2:1 to call, which means he is properly priced to call with basically any two cards.

Thus I expect villain to fold less than 13.4% of the time, and we go ahead and fold our cards.

 

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Notes from the Road: Switzerland

By: James Stevenson

Back in March I was filling in my “Reason to go Switzerland” list, as one does, and it was looking pretty good:

1) I have dear friends there I haven’t seen in a while.

2) It’s not London.

3) It’s my birthday soon, and after I waste lots of money on birthday presents for myself it would be a good idea to miss some work and blow more money on a short trip.

4) I need to hitchhike so I can blog about it and my friends can tell me what a great writer I am.

These were all good reasons but the real reason was number 5:

5) My friend Andrew wants to give me his record collection and he lives there.

I collect records so that I can look cool. I’ve got a bookshelf filled up with records and second hand books so that when people come visit me they’re impressed with my intelligence and material wealth. “A man that devoted to archaic media must be a manly man indeed,” they think. I bought some expensive looking music equipment to complete the effect, and I even bought lights for the room to make it clear that I do actually read.

Sometimes, though, I notice people don’t even glance at my amazing possessions, and that really annoys me. The solution is obviously that I need more records, so when Andrew very generously offered me his collection I gleefully accepted.

My first thought was to hitchhike to England with them, after all, the cheapest way to move stuff between countries is definitely to get other people to pay for gas. I’d never hitchhiked with that much baggage before, though. Would anybody give me a lift? I wasn’t sure until I heard about this:

As the story goes, Tony Hawks, the author, accepted a drunken bet to hitchhike around Ireland with a refrigerator. He started in Dublin and made it all the way around the coast, up through Northern Ireland and back down anti-clockwise. If he could do that then I could do my trip with a couple bags of records. Easy.

So it was settled. I got up early and headed to the spot, an intersection in Sidcup. As far as I know, Sidcup is a pretty nowhere place in south London, but it’s quite dear to me.

I first discovered Sidcup back in 2012, when I was hitchhiking for the first time. It was after a long day of bad luck. I’d been stuck in a gas station in Belgium that morning, trying to get a lift for 5 hours and getting a horrendous sunburn instead. When I ended up on the ferry to England that night I was exhausted and red like a lobster. It was late and dark and I didn’t really have any idea what I was going to do when I got to Dover.

On the ship I met a group of English guys and they offered me a lift. They were five or six rough looking London guys, dressed in leather or whatnot, and they had names like Jacko, Panache, Rizzo and Moses. This one guy Joey was constantly joking around and laughing and the whole scene made me nervous. I honestly thought they were gunna rob me. “What the hell,” I thought, “at least it’ll make a good story”.

As it turned out, they were 1.5 bands (The Vex and The Supernovas) travelling back to England after playing some gigs together in Europe. We piled into their van, and the guys were all holding amps or guitars on their laps just to make room for me on the last seat. They were all super nice, but I was still scared. Once we got on our way they started blasting Chas & Dave, some ridiculous old English comedy music. They were all singing along at the top of their lungs and laughing as we sped down the motorway. I started to laugh too, long and loud and deep, and all my fear just went out of me completely. These were excellent people.

We ended up pulling into Sidcup some time after midnight to drop Jacko off. They asked me if I’d ever heard of Sidcup and laughed when I said I didn’t. I got the impression that nobody has ever heard of Sidcup. A couple days later I was on my way out of London again, and the spot for getting a ride to Dover turned out to be in Sidcup. I was overjoyed.

And so once again I found myself waiting there this March, holding my sign for Dover and watching cars blow past me in the morning air. I nibbled some stroopwafels and waited, enjoying the warmth of the sun on my back. A mass of cyclists drove past me and cheered. Later someone drove by and threw a rock at me. After a couple hours, around 11 o’clock, someone pulled over and offered to take me to train station and buy me a ticket to Dover. I turned him down, assuring him I’d get a lift.

By then the traffic was starting to thin a little and I really wasn’t sure I would get a lift, but just as he pulled away a lady pulled over and offered me a ride. She gave me a cup of tea and we sped happily away. My driver was in her early 60s, on her way to a new home outside the city. She’d lived in London her whole life, including a year or more homeless. She’d lived in a building full of squatters, whole families raising children and whatnot. It sounded very communal and friendly; she said the kids were all kind of raised together by the whole group.

She let me out at a service station very close to Dover, and I started asking everyone if they were driving to Dover. One man got out of his car and started walking towards the shop, moving in a bit of hurry. I figured I had nothing to lose and asked him if he was heading to Dover. He said he was.

“Any chance you could give me a lift?” I asked.

He laughed to himself, as if he’d wished he said something different but hadn’t thought fast enough.

“All right. Wait here and I’ll be out in a moment.” He hurried away into the shop, with a funny little smile on his face.

This turned out to be one of the most interesting rides I’ve had. My driver was a doctor on a way to a meeting in Dover. He was in charge of a region of hospitals in the south of England, and he struck me as a very smart man. He often had that little smile, as if the world amused him in many little ways.

We were somewhere in the meat of our conversation when we got to talking about suicide.

“You know, doctors have the highest suicide rate in the country,” he said.

“Oh really? I guess it’s pretty stressful, right?” I asked.

“Well it is, but it’s not really that. I think when a doctor decides to kill himself he knows how to do it. You almost never get a doctor that tried to kill themselves and failed.”

“Do you know what you would do?” I asked after a pause.

“I know exactly how I’d do it,” he replied. “I’d inject myself with morphine and insulin.”

“How does that work?” I asked.

“First morphine to take away all the pain,” he told me. “Then I’d inject myself with insulin and my blood sugar would start to drop. I would drift off and my heart would stop. It would be very peaceful and easy.”

We didn’t speak for a short minute.

I told him about how the Celts used to throw themselves off cliffs when they got old and decided they’d become burdens on their families. (Come to think of it, I have no idea if this is true.) They also used to go into battle almost completely naked, wearing nothing but a golden torc. I said I had this crazy idea to get up on a building, get naked, put on a torc, and jump off when I was old and thought it was time. He was afraid of heights and didn’t like the idea.

We agreed that there’s never really a point in your life when you think it’s time to die. The desire to live is buried so deep in us that it is very hard to reject. That said, there is a beautiful French phrase: “L’appel du vide”, or “the call of the void”. It’s the temptation some people feel in high places, on top of a building or a cliff, the temptation to just take that plunge. I’ve had that feeling before. It’s terrifying.

In Dover I made my way to the ferry terminal and tried to get a lift with someone. I never have much success here, as most people already have their tickets booked and just drive straight to the ship. I didn’t waste too much time and bought a ticket pretty quickly.

On the ship I asked every person I could find, and all but one kind man turned me down. He was driving south to Paris, and could take me about one hundred kilometres before we’d have to part ways.

We got on the road and settled in for a long ride. Brian, my driver, lived on a houseboat in Paris and was a pilot for EasyJet. He must have been sixty or more. Years ago, he’d studied aeronautical engineering, and he was telling me all kinds of things about the degree he did. He loved to tell me stories about the things he’d studied, since I knew a little about the mathematics he’d done. He told me about proving little mathematical things during his degree, and I got the feeling he rarely talked to anyone that he could tell these stories to. Now that I think about it, he strikes me as a little lonely.

He told me he was hitchhiking once and had been picked up by a one-eyed man in a Jaguar. One-Eye was on his way to a date, and he was pretty nervous, so he brought Brian along with him. They went to a pub and had a few drinks, and when the girl arrived she turned out to be stunningly beautiful. One-Eye was still a little nervous, and they invited Brian along with them. Brian could tell it was going to work out and left them to it.

He told me later that he wanted to get a motorbike when he retired, and ride around like Arnold Schwarzenegger in Terminator 2.

“When I leave the plane after a flight I always say to the crew ‘I’ll be back!’, but they never get it.”

Brian ended up going out of his way and taking me another 80km to a gas station near St. Quentin. He let me out and we said a warm goodbye. After a good ride the goodbye is always a little strange. You’ve been friends for a few hours and now you both know you’ll never see each other again. You both feel like saying “Hey well I’ll see you again soon, right?” but you don’t, and there’s kind of a hole in your words where this sentence is supposed to go.

Brian drove away and I went into the shop. I idly watched the TV, where Daniel Radcliffe was doing a dubbed sex scene in French. It was pretty late; not many cars were coming through and the truckers were all bunking down for the night.

Eventually the place closed up and the staff kicked me out of the café. There was still one little hallway open in the back of the building, so I found a corner where I could hide and curled up to read a book and get some sleep. I wasn’t sure I was allowed to sleep there, so I didn’t get my sleeping bag out or anything. I lay down under my sweater and shivered nervously all night, wondering if the door next to me would open up and some janitor would step through, see me, and kick me out into the cold. It wasn’t until around 4am that I realised how dumb I was being. I got out my sleeping bag and got comfy, but before long a group of truckers started hanging around the coffee machines, chatting loudly. I couldn’t get any sleep, so as soon as the café opened I went back inside and got a cup of coffee.

The early morning traffic was coming in and I asking around for a lift. I wanted to head south to Reims, then cut east towards Alsace. Last summer I’d been on this route. I’d actually been picked up by the police because I was standing on the edge of the motorway trying to thumb a lift. They’d taken me to a big service station and there’d been loads of drivers heading to Switzerland, so I wanted to head that way again.

Around 7am I met a young Dutch couple on their way to Geneva. Their car was jammed full of baggage, and they told me they didn’t have any space. They were pretty friendly, though, so I was disappointed. I went back inside the café. Later I saw the man, Jeffrey, again and struck up a conversation. We were just chatting about travelling and whatnot when his wife, Rosmili, came by and joined us.

“We were talking before about maybe moving some of our stuff over and getting a seat for you,” Jeffrey told me.

“But we need to know that you’re not going to murder us,” Rosmili said.

I laughed and promised not to kill them. I guess they were satisfied, so we went to their car and looked at our maps. Geneva was not where I wanted to go at all, but I liked them so much I decided to go with them. They didn’t seem to mind. We piled in and sped away!

“I just want to apologise, in advance,” I said, “but I didn’t really get any sleep last night. If I fall asleep please don’t think I’m rude.”

In the end we rode together for five hours or more, and we talked the entire time. They were absolutely excellent people, interesting and friendly and smart. We bullshitted about all the things I love to bullshit about: films and books and music, travelling, people, and of course the standard intellectual conversation things like religion and death and happiness and whatnot. They’d been married twelve years, but they seemed to me still very much in love, and very happy. They told me they’d decided not to have kids. They were perfectly happy enjoying the world together as the two of them. They were very refreshing; I wish there were more people like them.

When we reached Geneva the goodbye felt very wrong. That hole where one of us should have said “Hey, we should keep in touch” was gaping and obvious, but we both resisted. We hugged and they pulled away. “Be safe!” Rosmili shouted.

I was finally in Switzerland, and I was starving. I bought a gigantic Easter bunny and a loaf of zopf, which is this amazing Swiss bread made with some inordinate amount of butter. I made my way lazily toward the train station, eating happily. My weariness started to set in, and I began to feel terrible. I kept eating.

I thought about hitchhiking to Zurich, but when I reached the train station I got jumped by a bunch of ticket machines. They beat me up and emptied my wallet. They threw a ticket to Zurich at me and said if they ever saw me around there again there’d be trouble. I got on a train, stuffed my mouth with butter bread and chocolate, wondered why I felt even worse than before, and fell asleep.

Four days later I was back on the road with fifteen kilos of vinyl that I could barely carry. I managed to get home to London in one day: 19 hours and five lifts door to door. Not much of this trip stands out in my memory, except this rich Swiss hippie telling me about his expensive music equipment and how he preferred LSD and DMT parties to cocaine parties. I remember one of my drivers telling me to go to Laos and rent a motorbike. I also remember taking the train home from Dover with this random dude I met on the ferry. We didn’t have much to talk about except this other little kid who walked passed and said “You’re a couple of cunts, aren’t ya,” then disappeared down the train.

Now it’s midnight two months later and I’m in a café watching old guys play chess. I’m trying to work out what my closing thoughts are. There’s something hypocritical about a guy with a top mathematics degree sticking his thumb out and asking for help, getting total strangers to carry his Grateful Dead and Pink Floyd albums six hundred miles across Europe. There’s also something strange about meeting amazing people and deciding never to see them again. There’s something wonderful about that funny little smile my second driver wore. I don’t know what it all means, I’m just going to keep hitchhiking until I work it out.

ChannelFireball: Signets and Faydens

by: Jason Waddell

So it turns out I’m not terribly consistent with the rate at which I write articles, so here’s a third in two weeks. It takes inspiration from our “Debate Topics” forum thread. Let me know if you like the format, there’s plenty more to cover!

 

ChannelFireball: Journey to Nyx Cube Review

by: Jason Waddell

It’s that time again. The quarterly review, where I evaluate cards I’ve never ever played with. You should read it.

Ode to Tinder: Part 1

Ode to Tinder

“It’s a Match!
-Send Message
-Keep Playing”

I always keep playing. Welcome to Tinder, the interactive “Hot or Not” game where acceptably attractive locals occasionally interrupt your day with mundane conversation. Tinder: train your stereotyping in minutes a day. Tinder: where something better is surely out there.

For the unacquainted, Tinder is a multiplayer filtering exercise wherein one attempts to eliminate from contention potential matches in the dating pool as ruthlessly and efficiently as possible.

Phase 1: The Photo

Your goal here is to train your mental algorithm to reject candidates mechanically and without error. You’re the motherfucking Henry Ford of the dating: the more optimized your assembly line, the higher your profits. Humans are a commodity, act accordingly. Here are some tips to jumpstart your own algorithm.

Rule 1: Isolate or bye-solate

Screenshot_2013-11-22-20-08-00 (1)

Have they chosen a photo that leaves them with an ambiguous identity? Is your match not competent enough to recognize the function of a dating site photo? Chances are, they don’t legally possess the mental faculty to grant consent, even while sober. Avoiding sexual assault allegations starts with you, and it starts by swiping left.

Rule 2: Bot recognition

Screenshot_2014-01-03-17-03-25

Does their pic seem too good to be true? Can you count the bumps on her areola? Is there a URL in the photo? Courting a robot only ends in heartbreak. There are other (living) fish in the sea.

Rule 3: It’s me or the dog

Screenshot_2014-04-25-21-19-43

Rule 4: The Duckface

Screenshot_2014-01-11-13-34-30 (1)

I downloaded the wrong picture from my phone, so you get this instead.

Rule 5: Gender-Bender

Screenshot_2014-03-01-12-43-34 (1)

Occasionally a user will register as the wrong gender. If they can’t properly navigate a registration form, chances are they can’t hold their own while you attempt to verbally navigate the intricacies of financial reform. I’m not saying you shouldn’t swipe right, but should you do so, you’ll find that Hector can only service you as a physical, not intellectual, sparring partner.

Rule 6: What’s in a name?

Screenshot_2014-04-29-18-48-39

Okay, this was a little misleading. I love the name. This was actually a test for you all. Take a second. Have you figured it out?

Here we stand in clear violation of Rule 1. I don’t actually know which one the account holder is. I’m looking for a date with Doritos, not with Chris Hansen.

 

 

Join us next week, when we discuss Phase 2: Texting, Breeding Between the Lines