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Message: [QUOTE="IADaveMark, post: 6426430, member: 490208"] Sorry I'm just now seeing this. I was out of town earlier in the week and not sitting at my computer (which is odd for me). But since I have "math, statistics, game theory, and psychology" listed in my signature line as what I do for a living (and, in fact, have lectured on all of the above around the world), I figured I would chime in. Incidentally, one of the reasons that I have been drawn to poker more and more over the years was because of my love of, and subsequent study of all of the above. For those of you who are into [URL='https://en.wikipedia.org/wiki/Complexity_class']mathematical complexity classes[/URL], poker is one of the best [URL='https://en.wikipedia.org/wiki/NP_(complexity)']NP-hard[/URL] games around. Ever. This also means that it can't be "solved" by a computer until the heat death of the universe. However NP-hard problems are great fun for people because we don't need to "solve" it perfectly. We need to get as close as we can. And the exploration in that wide open state space is not only what makes it challenging but what makes it fun. Anyway, for starters, one of the things that is missing in the question that the OP presented is the concept of [URL='https://en.wikipedia.org/wiki/Strategy_(game_theory)']Game Theory[/URL]. Interestingly, game theory is often where math and psychology collide. Game Theory covers a number of different aspects that are easily recognizable in poker. One of the most obvious is the concept of a [URL='https://en.wikipedia.org/wiki/Strategy_(game_theory)#Mixed_strategy']mixed strategy[/URL]. For example, if we were playing rock paper scissors and I was constantly throwing rock, what would your reaction be? The answer to this is pretty easy of course. You would start throwing paper so that you could always beat me. While it might take a few more rounds to sort out, the same thing would happen if I was rotating through playing rock, paper, and scissors on every single game in that order. You would figure out my pattern and know that you needed to counter it by playing a similar cycle but matching them so that they would always beat my play. The same can be said for a lot of other games and situations. If you are perfectly predictable, then you are exploitable. People can know in advance what it is you're going to be doing and react accordingly. The obvious solution is to change things up, even to the point of randomness. There's a couple of problems with this, however. If both players are playing completely randomly, it isn't really much of a game, is it? The other problem is that using rock paper scissors as an example is a problem in that it is a completely balanced game. No one item is better than the others. Each of them can lose to 1 and beat one. Poker, of course, isn't like that. You can't just play randomly regardless of the cards that you are dealt. However, each of the given situations of the cards that you have and what's on the board can be thought of as its own little decision game. We use a mixed strategy when we play the exact same situation in a number of different ways just to throw people off. Continuing the example that I said above, if I were to always go all in when I had top pair or better, bet half pot when I had middle pair, and check on all of my missed flops, it wouldn't be very long until people could figure out that it's probably not a good idea to call when I go all-in. That's why we do stuff like checking when we flop top set sometimes but betting it at other times. And that's where part of the psychology kicks in. But sorting out what's good, what's bad, what's a potential opportunity and what's a situation where we are very likely completely locked out is all math. Math and statistics are the most important part of the game simply because things such as hand rankings can be reduced down to “X > Y”. Going beyond that, we end up with more complicated things such as "what are the odds of me getting X which would be greater than Y?” Obviously that's where we get stuff like pot odds in order to size our bets, determine what bets we will call, etc. That's just pure math. So what if we were to rewrite rock paper scissors so that it wasn't completely balanced? Taking a game such as the classic [URL='https://en.wikipedia.org/wiki/Stratego']Stratego[/URL], it was pretty obvious which pieces beat what other pieces based entirely on their number rank. With some exceptions. For those that aren't familiar, the lowest number beat a higher number. So a 8 would beat a 9, a 7 would beat an 8 [I]and [/I]a 9, a 6 would beat a 7, 8, and a 9, etc. Well then, since a 1 would beat 2s through 9s, why didn’t people just take their 1s and mow through the opposition? Well, because there were bombs… and bombs blew up anything that attack them. But they couldn’t move! So just take your 1 and attack things that move, right? Well, there was another piece—a spy. The spy could move, and everything else could beat it… [I]except [/I]for a 1. The spy was the only moveable thing that could kill a 1. So how do you do this? How do you use your spy effectively to kill the marauding 1? If you start moving [I]towards [/I]the 1, the other player might get suspicious. OTOH, you could do that with any other piece… say, a 6. Boldly move towards the 1 and chase it even though you know you would lose if you caught it. And this, my friends, was a proper bluff in my childhood. Same thing with placing bombs. Many people would place bombs around their flag to keep it from being captured. Only 8s could defuse bombs safely. So a player would find a bomb, find another bomb next to it, and figure that the flag was nestled safely behind them. Nope… we would SOMETIMES put a flag way far away from the bombs just to get the other player to waste time and units pursuing in the wrong direction. In the meantime, we would be doing our own exploring in the hopes of doing damage or finding the enemy’s flag before they figured out our ruse. Another bluff—although one that was a larger setup ahead of time that took longer to play out. Notice now how the rules of the game involve math—specifically the hierarchy—and other things such as how many of each type of piece you started with, that 9s could move much faster than the other pieces, etc. However, we could use that math and the unknown surrounding the situation to our advantage. Make the other player fear or at least be wary of something. Make the other player believe something that wasn’t true. Lure the other player into traps. All of that is the psychology of the game. And this is poker. You can play it without the psychology and all of the tricks, certainly. However, you then start edging towards predictable and, therefore, exploitable. And remember the fact that the other player might be doing psychological manipulation of you! It takes knowledge and awareness to prevent that from happening. So whether you are actively using psychology and game theory in a situation or game, you need to know how it works in order to keep yourself from being tricked and beaten. Incidentally, you will hear people talk about GTO play in poker. That is "game theory optimal". GTO is the play that means that you can't do [I]worse [/I]regardless of what the other player does. In game theory, there is a similar idea called [URL='https://en.wikipedia.org/wiki/Pareto_efficiency']Pareto Optimality[/URL] where you can't make one player better without making the other(s) worse off. This is great if we are seeing the best outcome for everyone involved... find that optimal solution and we're good. But that's not what we are trying to do in poker. That's why GTO is preferred. We want to have the "safest" situation. Oddly, GTO play requires the use of a mixed strategy so that we aren't exploitable... it just helps to tell us what that mixed strategy should entail and how much we should use each of the options. It's... well... it's... [I]complicated[/I]. And yes, it is a combination of math and psychology. So there you have it. Learn the math first, then understand the game theory, and tap into psychology to utilize it to your advantage. [/QUOTE]

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