Midlife Crisis? What Midlife Crisis?

Nice. Let's see whether your poker intuition is better than mine.

Here's the game. Three players - John, Tom and Manu (obviously). Each gets a number between 0 and 1, 0 being the best hand. John and Manu are forced to check. Tom can either check behind or bet. John can then call or fold. Manu acts next and can overcall if John calls, call if John folds, or fold.

Strategies are Tom value bets hands better than tv, bluffs hands worse than tb. John calls with hands better than jc, Manu overcalls with hands better than mc2, and calls if John folds with hands better than mc1.

I think it's clear that 0<tv<tb<1 and that mc2<jc. In other words, Tom value bets his best hands and bluffs with his worst hands and Manu overcalls with hands that are ahead of John's calling range. However, what's the ordering of the other ranges? In other words, does John call wider than Tom's value range to catch bluffs? Does Manu? Is John's calling range wider than Manu's or narrower?

I haven't mentioned pot or bet sizes, since they don't appear to matter except that the bet size is fixed.

My intuition was completely wrong, fml.

yeah...

My guess.

Analysed the game for two players and it has the interesting result that the calling player calls exactly with the valuebet range of the betting player (and relative pot/betsize do not matter here either).

I'm gonna guess John calls tighter than Tom's value range in the 3-player one, because he still has Manu behind him and thus has to have a tighter range than HU.

Making a gamble, I think Manu's calling range might actually be equal to Tom's value range here as well.

Manu's mc1 calling range should be wider than John's, because John has the risk of an overcall from a tighter range.

That would be my intuiton as well though, so...

Originally posted by DukeFreedom
Analysed the game for two players and it has the interesting result that the calling player calls exactly with the valuebet range of the betting player (and relative pot/betsize do not matter here either).

I analysed the two player game in the book (it's in The Maths of Poker too), and the calling player has to call wider than Tom's value range because he needs some bluff catchers, so I'm not quite sure where you get that two player result from.

The answer is that John calls slightly tighter than Tom's value range, and Manu calls much wider than Tom's value range. In other words, John leaves the bluffcatching to Manu. John is squeezed between Tom and Manu, and has the worst position initially, and also relative position after Tom bets. Letting Manu do all the bluff catching also means that Tom wins the most, with Manu and John losing almost the same amount, although Manu does a little bit better than John.

My student called the players John, Tom and Stephen (god knows why), so the lablels have 's' not 'm', but you get the idea. P is the potsize, and the bet is 1. These results were generated numerically using fictitious play, but I think that, now I know the order of the ranges, we should be able to get the equilibrium ranges analytically.

Last night I had a look at the various possible ways that the players might collude against each other, and also how this is affected by whether the victim does or doesn't know that the other two are colluding, and whether the colluders know that he knows and whether he knows they know he knows and......you get the idea. There are some interesting results there too, but it's work in progress.

Yeah it was late yesterday, I think I already know where I made mistake and then it also makes sense that the calling player would call wider as well as Manu here. Still interesting that John cannot bluff catch, but now I can't help but wondering how the dynamics would be with even more players? I guess one would expect the first player after the betting player to never bluff catch then, but later players (before the last one) maybe?

it becomes a lot more complex and interesting if John can raise rather than just call or fold

Originally posted by thazar
it becomes a lot more complex and interesting if John can raise rather than just call or fold

Well ofc. There's a bit about the two player game with check raising (bluff and value) in the book, and in TMOP, but I'm taking this one step at a time. What I really want to find is a similar game with multiple equilibria to wave at the GTO fetishists amongst us. I don't have any evidence for that in the game we're looking at, but there's still plenty to think about.

Originally posted by DukeFreedom
Still interesting that John cannot bluff catch, but now I can't help but wondering how the dynamics would be with even more players? I guess one would expect the first player after the betting player to never bluff catch then, but later players (before the last one) maybe?

Seems reasonable. I could try the four player version. So many games, so little time.

What I really need is someone to collaborate with.........

I think John always has the worse range.

It does not matter if the other players are tom, dick, harry or Stephen.

We don't need upside down graphs for that.

Maybe in the next game we can let some cows play.
♦

Originally posted by mineriva
Maybe in the next game we can let some cows play.
♦

Interesting idea. How do you want to model the cows? Let's collaborate!

I've just come back from the School Easter Egg Hunt with my daughter and, for various reasons, feel the urge to blog. I don't know what it is about parents and school events, but I find it almost impossible to be all friendly with the other parents, and struggle with the whole small talk thing in a way that I rarely do in any other social situation. Maybe getting FUCK and OFF! tattooed across my knuckles when I was teenager, Night of The Hunter style, wasn't the fantastic idea that I thought it was. I may have to try turning the O into a smiley face or the ! into a ?

Mrsjb's been away in London since Wednesday, learning how to counsel people with eating disorders. I'm hoping she doesn't decide to practice on me, especially since School events always bring out my inner comfort eater. Mrsjb's absence has meant I've been juggling work and childcare for four days now, and it's pretty shitty I can tell you. Fortunately the two youngest claimed illness on Friday, which I used as an excuse to stay at home. I did my PhD supervisions by Skype, and spent the rest of the day sorting out the three player [0,1] game. I'm going to write it up soon, although I have to wait for my student to submit his dissertation first, but it's pretty interesting stuff in my opinion. As expected, John and Tom can completely shaft Manu by Tom bluffing super wide and John always calling. However, all the money ends up with John in this case, so it could only happen by explicit collusion, which isn't that interesting. John and Manu can never beat Tom by colluding - it's a complete waste of time. However, the remaining alternative - Manu and Tom colluding against John - is much more interesting because there's a nonobvious (to me anyway) opportunity for them to collude implicitly in such a way that they divide up their extra winnings at the table, not away from it.

The last thing I'm trying to sort out is a metagame, where Tom can either play his equilibrium strategy or his colluding strategy, Manu the same, whilst poor old John can choose between equilibrium and an anti-collusion strategy. I'm still sorting out the details of this, but I'm really pleased that there's a surprising amount of nontrivial insight to be gained from this simplest of three player games. ♠_biggrin:

I've also been playing a bit more recently. I decided I should stop fannying about and just four table Zoom. However, I'm being a bankroll nit and playing NL25, even though I'm rolled for NL50. I've decided I don't care about my graph, just my balance, so I don't look at it any more, but I seem to have about as much as I started the month with, and I've not felt like I'm running particularly well or playing particularly badly, so that'll do for me. The main thing is that I'm rather enjoying it. My style has been influenced by my week of free access to PokerSnowie (haven't bought it yet), and I will carry on Zooming for now.

I think I might actually go to this

http://www.pokerstrategy.com/news/content/180-man-SNG-course-with-TomSom87-starting-tonight-at-22:00-CET_82582/

I do like my 180 mans, and it actually starts at about the only time I can actually manage.

Originally posted by jbpatzer
I think I might actually go to this

http://www.pokerstrategy.com/news/content/180-man-SNG-course-with-TomSom87-starting-tonight-at-22:00-CET_82582/

I do like my 180 mans, and it actually starts at about the only time I can actually manage.

Lol. And it's gone! Wtf was that all about?? Was I hallucinating?

I saw it as well ...

Originally posted by EmanuelC16

I can't help wondering how you communicate in real life nowadays. Have you abandoned the spoken word too?

Originally posted by jbpatzer

Originally posted by EmanuelC16

I can't help wondering how you communicate in real life nowadays. Have you abandoned the spoken word too?

Originally posted by EmanuelC16

Originally posted by jbpatzer

Originally posted by EmanuelC16

I can't help wondering how you communicate in real life nowadays. Have you abandoned the spoken word too?

Originally posted by jbpatzer
I've just come back from the School Easter Egg Hunt with my daughter and, for various reasons, feel the urge to blog. I don't know what it is about parents and school events, but I find it almost impossible to be all friendly with the other parents, and struggle with the whole small talk thing in a way that I rarely do in any other social situation. Maybe getting FUCK and OFF! tattooed across my knuckles when I was teenager, Night of The Hunter style, wasn't the fantastic idea that I thought it was. I may have to try turning the O into a smiley face or the ! into a ?
.

Perhaps, instead of the tattoos, you could have gone for these rings?. Just slip them on for that special occasion

Originally posted by Hamishk

Originally posted by jbpatzer
I've just come back from the School Easter Egg Hunt with my daughter and, for various reasons, feel the urge to blog. I don't know what it is about parents and school events, but I find it almost impossible to be all friendly with the other parents, and struggle with the whole small talk thing in a way that I rarely do in any other social situation. Maybe getting FUCK and OFF! tattooed across my knuckles when I was teenager, Night of The Hunter style, wasn't the fantastic idea that I thought it was. I may have to try turning the O into a smiley face or the ! into a ?
.

Perhaps, instead of the tattoos, you could have gone for these rings?. Just slip them on for that special occasion

Those are OK, but you really need them as a mirror image so that they still say FUCK OFF when they've been embedded in someone's face at high speed.

Originally posted by EmanuelC16

Aaaand it's back.

Coaching: So you want to grind 180 mans?