Thanks Nitty, I really appreciate the compliments!

I absolutely agree with So_Nitty's comment every word. It is amazing what a interesting dynamic this video developed with almost no showdowns and cards at all. Outstanding job Tyler.

I really like that idea. My wife and I were talking over dinner last night about how I could better show the strategies.

My wife and I were talking over dinner last night about how I could better show the strategies.

Ha ha, this made me laugh. Mustn't it be great to be in a relationship with a poker player? :)

PIO +1

Thanks Kostanzhoglo, appreciate the comment!

Awesome, glad you are enjoyed the video!

haha, I love being compared to mad genius. I'm thankful that I have managed to keep both my ears so far. :)

"Can I beat the games?" will always be a question, since I live in the U.S. and most of the best players in the world play on PokerStars.

Essentially as a U.S. citizen to play on PokerStars, I need to either live in a 2nd or 3rd world country far from home, obtain citizenship in a 1st world country that allows gambling, or travel year round.

1. I have a family, so traveling year round isn't an option.

2. For me personally, it seems slightly silly to move to a 2nd world country to make more money.

3. I'm willing to pay (or make less money) to live in a country that is closer culturally to the U.S..

This leaves Canada. My wife and I seriously considered becoming Canadian citizens, but the hassle and expense seems to outweigh the benefits of the move. Becoming a Canadian citizen requires either starting a business in Canada or going to a Canadian university and then obtaining a Canadian work permit. Both methods require (rightfully) a multi-year commitment to Canada. Given the instability of poker, this commitment seemed to be -EV. In the last 3 years, PokerStars has continued to make changes that are detrimental to pros. I expect this trend to continue. I'd be making a multi-year commitment for a job that I think PokerStars prefers didn't exist. That is a tenuous proposition.

The downside of my decision is that I will always leave myself open to a criticism that I can't beat the games. I can't assure you that I can, because it's unknowable. What I can tell you is that I played on PokerStars for over 10 years (2005-2015) and amassed a little over $2,000,000 dollars of winnings at 2/4 through 5/10. I was the biggest winner at 2/4 in 2010 and 2011, the second biggest winner at mid-stakes in 2011, and the second biggest winner at 2/4 in 2009 according to PokerTableRatings (PTR), and the 5th biggest winner at mid-stakes in 2014 according to Russian PTR. I still work on my game regularly and spend the majority of my study time on equilibrium strategies. However, you can still make the somewhat farcical argument that one of the best players at mid-stakes over the last decade who still studies regularly is now a losing regular and I can't disprove it.

The next obvious criticism is "What bro, you know so much about high stakes, why aren't you playing it?" Surprisingly, the simple fact is that I don't want to play high-stakes. I don't like 10 $40K pots a year deciding my income. I've invested my money well and don't have much pressure to maximize my income. You, of course, can argue that you can't differentiate me from a losing high stakes player and this is true as well. However, I would note that, for obvious reasons, a winning high stakes player will not give you this level of analysis , which makes analysis from a player in my position the best you are going to get.

P.S. I don't think your post is intended this way but it comes across as "What bro, can't beat the games?". My suggestion for future posts is to not ask the coaches if they are losing players, you'll get better responses.

Thanks TBE! I appreciate the kind words :)

Thanks Kaytor, I appreciate the love!

Sweet, glad you liked it. Happy to have you on the team!

Would love for you to use the same format ! :)

Thanks Ben! Your comment made my day :)

Heh, as I was watching I was involuntarily thinking "I should copy this," which seems like one of the least fakeable sorts of compliment :)

Hi Zach,

Great point, I just checked my sims are you absolutely right. I have the Kh7s4sTd at 75% bet-size, in position player folds 33%. If this was a minimum defense spot, the player would fold 42%, so the extra equity is very important in the change of the calling frequency.

Apologies if this is incorrect and I find it interesting that the reasoning led to the right conclusion, but I am not sure that using semi bluff equity to change the 1-a frequency is the correct approach. In general I am not sure we should be aiming to make the semi bluffs 0 EV to bet. Consider a situation where someone is betting pot size with 65% nuts and 35% air. we have an always call situation. If we now make the 35% semibluffs with 20% equity we move to an always fold situation. So moving this variable on its own # semi bluffs vs # pure bluffs should probably make us less likely to call as all else being equal it increases the range advantage that the bettor has.

Excellent point. Holonomy, I agree.

Awesome biznitch, stoked you liked it!

Thanks Phil, really stoked you liked it!

I did the naive frequency (bet/(bet+pot)). It indeed can be more complicated. This spot however is generally close to this frequency.

I've noticed this effect as well on occasion. I think what's happening here is that the strategy space on the flop is very robust regarding betsize. To expand- we could build a strategy with most of the betting volume going to a variety of possible sizes without much EV penalty. I believe the algorithm can sometimes "struggle" to find the best possible size (because some combination of all the sizes is so close in EV), and it can take a very large number of iterations before the algo settles on the best size. It also might be the case that the algo settles on a strategy using multiple sizes that is very slightly worse than the best possible size, and it will never get to the best strat (for instance I've seen some cool stuff where if we nodelock a given situation then release the nodelock, the algo can't find its way back to GTO; to me this suggests the algo's ability to find GTO isn't perfect). If this is true, on occasion we can "see where the algo is going," and nodelock the best looking size and actually exceed Pio's EV by a very small amount (though again, I expect this might go away or be duplicated with a sufficiently large number of iterations).

PIO implements a form of gradient descent to calculate the Nash equilibriums. The method works like this.

Imagine we are standing on a hill-side covered in trees and we need to get to the nearest town. Towns are generally in a valley and near water. When we no longer can see our surroundings, one of the easy ways to get to the nearest town is to walk downhill. By walking down hill, we will eventually find the lowest point on our hillside and the stream babbling merrily down the hill. We can follow the stream, which flows downhill, until eventually we find a town. This method generally works, but sometimes we end walking down the wrong side of the mountain and the water either flows underground or into a freshwater lake with no exits. We would usually turn around and walk back up the hill. However gradient descent can only move downhill, so we become algorithmically stuck at this poor location.

Gradient descent is a process of walking downhill toward a local optimum (the town). However, sometimes we walk down the wrong side of the mountain and end up at suboptimal location that we can never get out because we can only walk downhill.

On your particular problem, it's more likely that you walked into the town from the left-side in your first sim and from the right-side of the town in your second. Remember that we never actually get to the exact center of town (Nash), we only get within the city limits.

Thanks Diego!

Awesome! Binge-away!

Thanks nogamble!

I was actually referring to Linus's calling range. ATs is near the cutoff for bet/calling here. :)

I'll see what I can do. It might not be possible, because I'm in the U.S., but I think it'd be super interesting/valuable.

We looked hard at it, but decided we wanted to raise our children closer to our parents.