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Tag: Poker

Imagine my delight when I heard that there would be a Poker Tournament at Dartmouth! I really used to enjoy playing poker back in the day, before it was cool. For a while, during my senior year at UCBoulder, my friend Matt and I were both writing software to study Texas Hold’em and regularly going to the casinos in the few mountain towns in Colorado were they’re legal. It was a lot of fun.

After graduating and moving abroad, though, I just didn’t have any chances to play for several years. In fact, the only game I can remember playing in my entire time in Taiwan was the “penny” game I set up a couple of weeks ago. It wasn’t a huge priority to find a poker game or anything, but I was definitely stoked about hearing of a tournament.

The Setup

It was a zero dollar buy in, with only gift certificates as prizes– a fun tournament. Potato chips and random junk food were at every table. After checking with Sonia to make sure I was allowed to play, I eagerly headed over to the basement room in which it was being held. I showed up about 10 minutes early, and sat down at the one table that already had a few guys seated around it. They seemed oddly tense for being at a fun game, but they were all pretty friendly. Soon, more and more people came streaming into the room, until eventually about dozen tables were full, with eight to ten people seated at each.

It was a no-limit Hold ’em tournament. We started with a “dollar” (i.e. white chip) small blind, and a four dollar big blind. According to the organizers, the blind would double every 20 minutes, so we couldn’t dawdle too much. That wasn’t a problem at my table.

The First Table

On the very first hand, four people at my table went all-in. I couldn’t believe it. Either they had all gotten some remarkably lucky hands, or I was at a table full of maniacs. I sat the madness out, knowing I wasn’t throwing my chips away on a sub-par hand, but also knowing that nearly half my table’s chips would soon be in the hands of whoever won that hand. And so they were. After he had all the chips, he just leaned on the rest of us, threatening to put someone all-in on nearly every hand, bullying us out of the blind bids.

After the deal had gone around four more times, I was down to two-thirds of my initial number of chips. I was starting to think it would be worth it to bluff, which would have been credible at that point, when I got a great pair of hole-cards, AQ suited. I bet 10, and called a raise of 30 to see the flop. There was an ace, a jack and a three. With the high pair, I bet again, and one of my opponents called, and the one with all the money put me all-in. In the end my pair of aces beat his pair of jacks, my pile of chips was about the size of his, and the other guy was knocked out of the game. At this point, only three of us were left at my table. Not even a single person from any of the other tables in the room had been eliminated yet.

In the next hand, I had garbage, and the opponent without many chips went all in and lost. Then the game organizers announced to us that the blinds would be doubled to 2 and 4. Seeing as my entire table’s chips were divided between me and one other guy, this struck me as funny, but we kept going. Within 5 more hands, I had about 80% of the chips. Then Sonia and her friend showed up and said hi to me. I think the were a little surprised to my table mostly empty, and most of the chips in front of me.

The Second Table

About that time, the organizers noticed we were down to two people, and a couple of the other tables had eliminated players, so they sent us to those tables to take their places! It wasn’t even fair. I showed up at the new with about the vast majority of the entire table I’d come from. They were weaker players than my previous opponents, too. They were betting on inside draws. Some of them were trying to bluff on every other hand. They weren’t raising when they had winners. It took me 15 minutes to wipe out the entire table. By that time, more people were getting eliminate around the room, and people were getting consolidated to fewer and fewer tables.

The Final Table

To make a long story short, the competition was weak. Extremely weak. I knocked out a dozen more people and moved on to the final table with dozens of times more chips than we’d each started with. Unfortunately, that wasn’t quite the right impression to make. As soon as I sat down, one guy at the table said, “Woah, this guy must be a pro!”

I said I wasn’t a pro. Nobody believed me. Somehow, they figured that a professional gambler would come to their campus for their zero dollar buy in poker gave, load up on free soda and Doritos, and try to win a small gift certificate instead of going to a casino, getting comped steaks and cocktails, and winning real money.

“What year are you?” asked another.

I answered honestly that I wasn’t a student at all, and that I was playing in place of my girlfriend I was vising. That didn’t go over very well.

“This is a student tournament!”

“You can’t just invade it and take advantage of it!”

They were really competitive about this game. Admittedly, I’ve never been to a tournament before, and some of them might not have realized that this one was open to non-students. Still, I’ve been in casino games with hundreds of dollars on the table and I’ve never seen people get so worked up like this before. It was really eye-opening. If Sonia had been there, I’m sure she could have smoothed things over, especially being a UGA. As it was, though, it just wasn’t worth ticking everyone off to win. I couldn’t really walk away, either. They’d still feel like I’d wreaked the game.

So, I started doing randomized bluffs, but far too loosely. I continued to bet and play good hands, but I also played every single hand with a diamond of 7 or less. Amazingly, people became more and more talkative as my pile of chips dwindled, and soon they were asking me all about living in Taiwan, and what I thought of their school. Within 15 minutes, I had eliminated myself in what I hope looked like a completely natural performance. Then, without the gift certificate, but in a great mood, I headed over to the animation lab to find Sonia, Adelle and Dawn.

Making modest goals doesn’t work. They just don’t motivate me enough to make real progress. I find that the results I get from setting several relatively easy goals are usually worse than those I get from setting none at all. Small goals aren’t exciting enough to give me the drive to actually achieve them, yet they are enough to sap my motivation when I don’t achieve them.
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Last night, I went back to Taibei to play chess with my old co-workers. It’s kinda scary, really. They’ve all been playing regularly, Martin’s been reading books on strategy, and I fully expect to get left way behind in terms of ability shortly. Mike W. was there, though and the topic turned to gambling. As many of my friends know, Matt and I got really interested in poker, especially Texas Hold ’em. Matt wrote a program to analyze the strength of various opening hands against different numbers of opponents. I wrote a Perl program to help train myself to group various opening hands in terms of strength based upon where one is sitting. For example, if you’re in a 10 person game, sitting to the dealer’s left and holding an unsuited Ace-Queen, it’s time to fold. If you’re holding the same cards and sitting to the dealers right, you’ll definitely want to pay to stay in and see the flop.

Game Theory

Then game theory and optimal bluffing came up. Sometimes, there are situations in which a consistent strategy will always fail, and yet a somewhat random strategy, or a mixed strategy will prevail. It sounds irrational, but it is true. Mike asked me to explain it, and I wasn’t able to do so very clearly. So, I’ll have another go at it here. First, there are a few important distinctions to make, though.

Optimal Strategies vs. Exploiting Strategies

There are two kinds of strategies used in poker. In optimal strategies, the opponent is assumed to be strong and adaptive. Optimal strategies are evaluated based on how well they would fare against an optimal opponent. Exploiting strategies are designed to exploit a weak opponent as fully as possible. For example, if you play against a timid opponent who never calls, you can win money from him more quickly by bluffing every time (a strategy designed to exploit his weakness) than you could by using an optimal strategy. The bluffing strategy I’m about to describe is an optimal strategy that will work even if opponents know you do it.

An Example in Which Random Betting is Optimal

Imagine that you are playing a poker game in which the first four cards are dealt out face up, and the last card is dealt face down. After each new card is dealt, each player may bet and raise once. In this game, you and your opponent have just been dealt your final cards, there are $40 in the pot and he has bet $10. The maximum bet is $10.

Opponent’s hand:3♣ 3♠ 6♦8♣
Your hand:K♠ J♠Q♦10♥

There are 8 cards on the table. Your last card, which your opponent has not seen, is one of the 44 remaining cards in the deck. Of those remaining cards, any of the Kings, Jacks, Queens or Tens would give you a bigger pair than your opponent’s threes, and any of the Aces or nines would give you a straight. In other words, of the remaining 44 cards, 20 will give you a winning hand and 24 will give you a losing hand. However, you are still in the stronger position if you use an optimal bluffing strategy. Consider these three cases:

You Never Bluff

In 24 cases out of 44, you have the weaker hand and you fold. In the other 20 cases you bet $10. Your opponent, being a strong player, recognized that you do not bluff and never calls your bet. You win the $40 pot in 20 games out of 44. Since half of the money in the pot was yours to begin with, you earn $20×20 = $400. In the 24 games in which you fold, you lose $20×24 = $480. In the long run, if you employ this strategy, you’ll lose $80 every 44 times you play this way.

You Always Bluff

In 20 cases out of 44, you have the stronger hand and bet $10. Your opponent knows you always bluff, so he calls. You win $40 from the pot, plus his $10 from calling. Since $20 of the pot is your money to begin with, you win $30×20 = $600. In the 24 games you lose, you lose your $20 in the pot, plus a $10 bet each time. That’s a $30×24 = $720 loss. In the long run, if you employ this strategy, you’ll lose $120 every 44 times you play this way.

You Use Game Theory to Bluff an Optimal Amount

It is possible to use your opponent’s pot odds to determine how often to bluff. In this case, always bet on the 20 winning cards plus four of the 24 losing cards, and you’ll have the edge. It doesn’t matter how you determine when to bluff, as long as it’s random (at least to your opponent’s perspective). You could say, I’ll bet if I draw a winning card OR a two of any suit. You could ask your friend to give you a random number and then divide it by 24 and only bet on losing cards if the remainder were under 4. Anything random will work. Bet on the 20 winning cards, plus 4 losers. Unless you give tells or your opponent can crack your “randomization” scheme, there is no strategy he can employ that will give him the edge.

Your Opponent Folds When You Bet

You bet on your 20 winners, plus 4 of the losers. Your opponent folds every time, so you win $20 from the pot 24 times for a total of $480. You fold on 20 of the 24 hands in which your last card was a loser, losing $20×20 = $400. In the long run you’ll win $80 every 44 times this situation comes up against an opponent who folds.

Your Opponent Calls You

You bet on your 20 winners, plus 4 of the losers. Your opponent calls each time. On the 20 hands in which you really do have the stronger hand, you win the $20 he put in the pot, plus the $10 call. That’s a total of $30 x $20 = $600. On the four hands in which you bluff and lose, you
lose $30 x 4 = 120. On the 20 hands you fold, you lose $20 x 20 = $400. In the long run, you’ll win $80 every 44 times this situation comes up against an opponent who calls.


Don’t underestimate math geeks! By utilizing game theory, it is possible to construct a mixed strategy that can win in some situations when any consistent strategy would fail.

Notes: I realize that I didn’t address the possibility of the opponent drawing a 3rd three or a 2nd six or eight, each of which would beat a high pair, but not a straight. I’ll leave that as an exercise for the reader. This is a simplified example. For a more realistic one, see the comments below.

The optimal bluff is calculated based on the pot odds your opponent would if you bet. Advantage is maximized when the odds that your bet is a bluff are equal to your opponent’s pot odds.