Poker coming to Monmouth?

Yeah, I hear my buddy Scott LaFountaine is opening up a poker club here in Monmouth. It should be good. I know he'll have stakes at least as low as $0.50/$1.00, and it will be pay by the hour to play, plus some initial fee. I think he can scrape by with $3 at the door, $1 per hour, and since there is no rake or whatever, I think he should offer stakes as low as $0.01/$0.02, or even play money chips. It won't affect his hourly rate, and it will encourage more casual players, which is where the profit is for everyone.

What do you think, Scott? . . . Now I'll have to get him to read this somehow . . . *poke*

Yeah, Math & Poker

They really don't have that much to do with each other. Well, not arithmetic anyways. Game theory, yes, but most people think of that as something else. Psychology really can give you the same results that game theory does. They both use a lot of statistics, and attempt to predict behavior. Psychology more so than most mathematics.

I read Caro's Most Profitable Hold'Em Advice. All about psychology. Very little about odds, etc. Mostly about image, business, and psychology. You really want to entertain your table mates, so they pay you to entertain them. Like a tip, "oh, your funny and I like you, so here, take a pot."

Also, if you are friendly, and seem to not take the game seriously, and seem to be lucky, they won't be inspired to play particularly strong against you, they will just play easy and friendly and let you take their money. So always stay friendly. Never let anyone know you play seriously, and don't ever criticize anyone's play. The last thing you want to do is let them know you are analyzing and scrutinizing their play. If they think you pay attention to how they play, then they might pay attention to how they play. And you don't want that. :p

So, what did I learn? Math & poker are like . . . well, they're just not that related, necessarily. Sure, there might be some "optimal strategy" according to game theory, but you can do much better than that if you just play tight, and convince everyone else your just splashing around like the rest of them. Or even if you don't convince them, as long as they keep doing it, and you all have fun, you'll kick their butts. ;)

So good luck, and have fun out there. And why not, win a bunch of money too.

Rounder => Moneymaker => Poker Boom

I saw Rounders after Chris Moneymaker won the 2003 World Series of Poker, but I just heard it announced durring the 2009 World Series of Poker (the Ante Up for Africa tournament) that Chris Moneymaker got into poker because of the movie Rounders.

Good job Matt Damon.

I loved that movie btw.

I'm a hee haw.

Here is part of a conversation Meli about my poker play last night (from Skype).

[11:32:29 AM] Michael Rivers says: I'm a hee haw baby.

[11:33:25 AM] Michael Rivers says: I lost a big pot, like $20. But I only lost about $7. But I should have only lost about $2.

[11:34:07 AM] Melissa Greco says: you are random

[11:34:39 AM] Michael Rivers says: Jim had a trash hand like K2, I had AQ, flop came 722, with two hearts, and I bet $2 (I had a flush draw, Ah, Qh, 7h, 2h).

[11:35:03 AM] Michael Rivers says: Darren called (he had KK). Jim went all in for ~$7.

[11:36:29 AM] Michael Rivers says: I went all in for like $20 to make Darren fold. It worked, but it was still a stupid play. I should have just folded. Someone could have had 77 and I would have been drawing dead (<1%>

[11:37:39 AM] Michael Rivers says: Plus, I was just on a draw, I was in trouble if he had anything, and I could have been drawing dead. As it was, Jim made a full house, and I would have lost even if I did hit a flush, but that's when I decided to cash out with the $20 I still had.
I had around $30, but I think I was too tired to play anymore.

[11:37:44 AM] Michael Rivers says: Live & learn, right babe?

The thing is, Jim has such a tight image, I thought he couldn't have a 2. But he could have easily had 77. And I don't remember clearly, he may have been in the big blind, so if my raise was only 3x, he can call with pretty much trash. Then if he has just a 7, when I make a flush, he still makes a full house >8% of the time.

I think I still had positive equity in this case, but in general I don't think I'll be doing that in the future. Like I said in the message, when someone makes a huge bet (and they're known as a rock), and you could be drawing dead, folding is ok. I'll even go a step further and say, "just fold!"

So yeah, I'm a hee haw.

Blackjack Time

I've got the bug. I'm learning to play blackjack. And I'm doing the mathematician's way. Logically. I'm determining the optimal strategy myself, instead of just trusting the widely accepted basic strategy. I'm determining the optimal strategy for every situation as in basic strategy, but based on the count. My guess is basic strategy assumes the count is 0. By varying your strategy based on the count, you may be able to get an edge in blackjack based purely on strategy change, and without even varying your bet.

Figuring if this is true or not should require some advanced statistical analysis. So I'm busting out the old Hogg & Tanis. Anyways, you can read more about my endeavor at AI Fun, my other blog.

Enjoy ;)

Casino

I don't have a big enough bankroll to play at the casino yet. In other words, if I lose my $200-$600 buy in playing no-limit Texas Hold'Em, I won't be able to pay my credit card bills or rent or buy groceries. So I played bingo for less than $20, and played exactly three hands of blackjack costing me $20. (I only played blackjack because Melissa was egging me on. She contributed $5 of the amount lost.)

So at home I decided to practice counting cards. On one episode of "Breaking Vegas" I heard a professional blackjack player say, "if we could count down a deck in less than 30 seconds, then we knew we were ready." I've practiced counting cards before, and its hard. I'm not sure if its that I think high cards should be +1 and low cards should be -1 instead of the opposite, or what. But I practiced, and I got a little better. Still, when I timed myself, I never broke a minute. In other words, I'm way too slow to count cards like a pro.

I seriously need to learn the basic strategy, and then how the strategy changes with the count, if I'm going to play at the casino. Even if it is just $5 a hand, like I said before, I don't have a big bankroll. I only played 3 hands because I split on two 8s, at the dealer's advice. Which was weird, because she had just said earlier, "I'm not allowed to give advice. I can't tell player's what to do." Then she proceeded to tell me to split 8s against her ace. Nice job dealer. I didn't get her name, even though she was wearing it on her shirt like a good casino employee.

Together there were six of us that went to the casino. I considered it a favor to Carly for her birthday next week. I've never played bingo with them before, and they love to play bingo. Out of the six of us, I think we spent close to $160, and not one of us won a thing. Oh well, that's poker. Err, um life. ;)

After getting some promising results I decided to start recording some. Obviously I can’t wait until I see some results and then record them – That skews the statistics (or something like that).



This does not necessarily correlate with the optimal strategy provided by Cassidy. But I was excited to see P1 value betting roughly twice as much as they were bluffing, which is part of the optimal strategy given for bet size 1 bluff size 1.

All of these results will be based on bet size 1 with ante size 1 and 1000 hands per game.

This first test (after I got curious) is not as specific. If I had displayed the “field of players” that the AIs were up against we may be able to see why their strategies are what they are. An even more refined (maybe binomial cubed?) mutate method may be used to force the field to stay closer to the “breeders” listed. Lets look at some more results. I’ll show 5 more with the same parameters.

In generation 6 above we have the first appearance of a winning P2 strategy that value bets less than a winning P1 strategy. Next gen. the strategy was way different.

Okay, this time I accidentally chose 20 generations to run instead of 10. (Was thinking 20 since there are 20 AI of each P1 and P2 for each generation. Oh well.

Player 2 bluffs between 4% and 30% (usually around 10%) while Player 1 seems to oscillate between almost 0% and about 50%.



Here somehow P2 won in gen. 1 by simply betting almost all the time. That wasn’t the best though. This one gives close to the suggested optimal strategy for P2 of value betting 1/3 of hands while bluffing 1/6 of hands. Would look like (.33, c, .83).

Interestingly P1 seems to do well almost never bluffing at times.

Okay, we’ll run one more…

Here P2 did well bluffing between 5% and 15% while player 1 again jumped from over 50% to nearly never bluffing. Again, Player 1 almost always (except in the last generation) value bets less often than P2.

This tendency for P1 to value bet and to bluff less often than P2 is stated to be part of an optimal strategy for this situation by Jack Cassidy in The Last Round of Betting in Poker where he gives an optimal strategy for this game as

(1/6, ½, 1/12) for P1 ,

and (1/3, ½, 1/6) for P2.

I think it may be valuable to check by how much these winners are winning and what their opponents strategies are. (These are settings in the program that can be easily set, but I should output to a file instead of the command prompt to adequately store the data.)

Everyone hates Math!

I mean real math. People don't mind doing calculations, or using formulas. But when I try to get someone to verify some logic, I stun people. Just asking, "does this make sense?" seems to offend people.

My math senior project is to review, explain, and extend an article from a math journal. I'm doing The Last Round of Betting in Poker by Jack Cassidy from The American Mathematical Monthly. It seems like even Cassidy doesn't want to do any of what I've come to know as real math. He doesn't give explicit definitions. He doesn't clearly state his assumptions. He doesn't support many claims.

One problem I have with it is that it uses the [0,1] game, which is beautiful and elegant when representing a uniform distribution of hands (0 being the best hand, 1 being the worst). That way, the probability of a random hand y in [0,1] being greater than or equal to a fixed hand x can be expressed as

P(x≤y) = y.

But, in Cassidy's article, he states he is using the [0,1] game, but the only thing he seems to use it for is the notation of ≤ to mean better than or equal to. And then, instead of referring to the [0,1] game he claims to be using, in examples he translates directly from probability (which he writes as F(y)) to a hand in the game for which the probability for having a hand equal to or better than that is equal to F(y).

So, I don't really have time to do it right now, but I would really love to examine if his results really are optimal solutions (neither opponent can adjust to improve their overall expectation), see if this pair of optimal solutions is unique - in other words, see if more than one pair of optimal solutions exists (maybe they will all satisfy the equations given in his article).

Anyways, the strategy seems brittle. He gives results that when translated to the common [0,1] game (not exactly what he uses) with bet size equal to pot size, and uniform distributions, we get the strategies (1/6, 1/2, 1/12) for P1 and (1/3, 1/2, 1/6) for P2. This means P1 should bet the best 1/6 of hands, and bluff the best 1/12 of hands, and call with hands better than or equal to 1/2 (1/3 of starting hands if opponent bets). Similarly for P2. But I wonder, can either player improve their expectation? If so, they are not an optimal pair. I know that if P1 or P2 decided not to bluff at all, it then becomes wrong for P2 to call so much. As it is, it does not matter where the call values are (1/2 seems almost arbitrary). But if 1/2 is the right value, then value betting more or less hands should reduce the expectation, and bluffing more or less hands should do the same.

I have to finish my senior project now though, so I won't worry about these details now.

Let me know if you know anything about this.