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Post by Dubber on Sept 9, 2007 15:50:50 GMT -5
This question seems to warrant its own thread: Shortly after I started playing, Yaron put the question to me -- still a new player -- isn't there always an optimal move? Is there really a place for psychology and style in warlocks? Initially, I argued for free will and Yaron for determinism. My further exploration of that question ultimately turned into the article on strategy that gave birth to the Refuge. Clarifying question: when you (here and elsewhere) talk about 'playing psychologically' do you essentially mean trying to predict what your opponent is going to do, and responding to that with an assumption of correctness, rather than responding to an analytical array of possibilities? "Playing psychologically," to me, is less about trying to correctly predict my opponent and more about trying to cause my opponent to incorrectly deduce what I'm doing -- thereby gifting me with additional incentive. The trick, of course, is to not damage (or not allow damage to) myself while sending my opponent down a path of suboptimal initiative.
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Post by toyotami on Sept 9, 2007 23:57:09 GMT -5
Basically, in my case it means not fearing to make sub-optimal plays because of my faith that either 1. my opponent expects me to make the better play 2. I stand a chance of getting back into the game with an equally dicey gamble.
Psychological may be bad semantics - my idea for this style of play sprung up back when Exdeath was caught off-guard several times by sub-optimal plays (i was to later lose that game). When playing against the true analysers, i think a good pair of gonads to take a couple of risks is the only way to come away with a victory. Most imprtantly, knowing when to take that risk is a 'feeling' i get...i do not analyse probability nor assess risk deeply, i just get this feeling "you know what, i bet he is going to do that..." which can sometimes end up being a bit Vizzinish but i honestly believe, having played a warlock a number of times, you can feel what he is going to do (which is a reason why i occasionally lose to players i haven't played much eg.Awall)
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taliesin
Ronin Warlock
Grand Master
Posts: 156
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Post by taliesin on Sept 10, 2007 8:07:16 GMT -5
Psychological may be bad semantics - my idea for this style of play sprung up back when Exdeath was caught off-guard several times by sub-optimal plays (i was to later lose that game). You do realise that a lot of what he said that game (58247) was trash talk, and not to be taken too seriously? For instance, when he laid into you on turn 38, it was to suggest that if he'd embarked on a course of action that would, had you played correctly, been suicidal you'd have been "screwed", an assertion that was broadly incorrect. The risks he faced from playing as he'd suggested far outweighed any gains he might get, and his actual play would have been weak, even game-losing, if you'd remained aggressive and continued with the Lightning Bolt (that was your real suboptimal move, retreating to DFPW and handing back initiative). The same was true of his suggestion that he could have ducked the charm on turn 33, and when he did duck your charm on 36, an unacceptably high-risk move, you could have won from it. You're too quick to heed others' claims of superior analysis without paying attention to their veracity - it was not ExDeath who was playing the low-risk game there, and were you more inclined to re-examine what he'd said, you might have deduced this and discounted his analysis. Had ExDeath made one of those incredibly dangerous moves, he might have stolen the game earlier on; but people who frequently make these moves lose and lose big, because the risks they take for small gains usually catch up with them in the same game. You happen to have adopted a play style that is fairly safe, fairly tight, fairly similar to well-analysed play. Your strength is not and has never been taking risks. You at times assume your opponent isn't going to do something stupid and game-losing, but all good players do that. To have you speaking up in favour of high-risk play is an absurdity - it meshes so ill with what you do. When playing against the true analysers, i think a good pair of gonads to take a couple of risks is the only way to come away with a victory. There are actually two ways: analyse better than they do, or take just a tiny bit more risk, not enough to be brutalised as the pure gamblers are but enough to give you the game-winning edge. However, Slarty and I over a period crept up in the level of risk we were taking against one another while the honours were fairly even until I forswore it almost altogether and started playing a very tight game again, which Slarty struggled to readjust quickly to. I had a spate of wins from this. A little risk is good, but too much is readily exploitable.
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Post by Slartucker on Sept 10, 2007 8:52:19 GMT -5
I think that last bit is a good analysis of what happened during that period. In a way it's an interesting reversal of the period when Prioli toppled you, Taliesin, by introducing just enough risk to undo you. Also interestingly, both occasions resulted in you retiring regardless of which end of the stick you got
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taliesin
Ronin Warlock
Grand Master
Posts: 156
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Post by taliesin on Sept 10, 2007 9:35:28 GMT -5
Pfft, retiring is serious business. You shouldn't even consider attempting it unless you've had some practice first.
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Post by freesoul on Sept 10, 2007 17:31:16 GMT -5
(quoted from a different thread) Slartucker has commented on the past on how badly certain players with relatively high ELO usually fare against high-ELO opposition, when from their rank you would expect a much greater percentage of wins. Hah, I think this applies to me in many cases. I think one of my mistakes, is that I let their higher rank get to my head, and I try to out-risk my oppenent instead of trying to outplay them. I remember when I first started playing, I put a high value on being unpredictable. I wanted people to think that I would be capable of making or the crazy big gain/high risk move, which would hopefully put them on the defensive weave. "Most imprtantly, knowing when to take that risk is a 'feeling' i get...i do not analyse probability nor assess risk deeply, i just get this feeling "you know what, i bet he is going to do that..." which can sometimes end up being a bit Vizzinish but i honestly believe, having played a warlock a number of times, you can feel what he is going to do..." ~Toyotami I think there is some merit to the "go with your intuition/gut" way of predicting your openent's play, and make your moves based on that assumption. However, I definately play with that in mind, and do what i can to not follow a pattern, or use my pattern of play against my oppenent... This probably amounts to half of my "suboptimal" plays. The other half is simply not paying attention or evaluating my oponent's moves thouroughly enough.
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Post by Rycchus on Sept 10, 2007 18:39:26 GMT -5
I do the opposite, it's the lower- or same- ranked players I lose to
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Post by calicojack on Sept 12, 2007 10:00:08 GMT -5
I've been caught out by VERY low ranked players very recently. They just pulled ... I wasn't expecting. I ended up winning all but one of them anyway, though, so the benefit is relative.
I think there are two interesting observations to make here:
1) A little risk is excellent. A lot of risk is at times even nicer because a win with balls is very satisfactory. However, you should definitely avoid falling into the continuous gutsy move trap. You keep doing the risky thing and keep getting more and more frustrated as you get slammed to pieces. When making a risky move, make sure you aren't just kneejerking to your frustrations.
2) There is never a best move. There are always a multitude of moves, each of which has its own merits, but (usually) only one of which is more likely to be the right move. Given attainable perfect information (you know the exact mood and playstyle of your opponent), you may for example derive that doing D/P on the next turn will be 80% likely to be the right play, and S/P only 20% likely.
Your correct play in that situation is *NOT* to submit D/P. The nash equilibrium play that should net you the best game results in the long run, is to toss a 10-sided die, and submit D/P if it reads 1-8, and S/P if it reads 9 or 10.
So, even in the hypothetical situation that everyone is playing for maximum gain, there's a random factor involved if you're playing right. Being less random makes your consistency exploitable.
In practice, it's really hard to connect behaviour to a name without a face. I have a read on the general playstyle of maybe only 4 players on the circuit. For everyone else I have a general look at their performance in the current game and wing it. For very high stakes I might dig around in their play history but mostly I assume they play intelligently and go from there.
I would assume that almost everyone else does the same thing.
Thus, trying to get the reputation of being a total psycho is probably going to cost you far more games in order to establish rep than it will gain you in fakeouts.
If you must, there are typical rememberable plays I'd focus on.
Example:
When you have a biggish creature, and your opponent has PSD, and you have a random enchantment spell ready, you should always protect your monster. Yes, 90%+ likelyhood your opponent will just charm you and conveniently let you take care of stumbling up your monster, but even in that worst case scenario, you haven't really lost anything. You're down on initiative but you'll gain it right back with your monster. However, I actually do the random roll thing and from time to time I will protect myself - even if I could potentially lose a giant.
I'm still not convinced this is actually the right play to make. If any of you pros are willing to release some tactical information: Do you remember me being relatively careless with my monsters? I'm personally betting at most 1 or 2 players are even vaguely aware of this fact, which means the whole point of the exercise - trying to get them to go for the monster more often, is probably lost.
There's also a thing Slartucker once mentioned:
If your opponent is going to come out net positive with a given play, no matter what you do, that's the move that's gonna happen. No amount of 'risk taking' is justified by thinking anything else will happen. In other words, being ballsy and going for a big win on the assumption that your opponent will also be ballsy is only smart if your opponent has something to lose and feels the need for a ballsy play to regain initiative. A player in the lead is going to go with the safe move, 20 times out of 21.
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Post by Slartucker on Sept 12, 2007 11:14:49 GMT -5
It's worth pointing out that many situations cannot be analyzed so precisely. The 80%/20% model Surial mentions is useful in closed situations such as FOD defenses, PSD and moreo SPFPSD junctures, disease dioramas, and so on. However, most turns out the game, the outcome is not so blatantly turned one way or the other, yet what gestures you enter are just as relevant. There are just too many tiny decision points stacked up before somebody gets a reward to be able to slap numbers on things. And in these cases -- unless your opponent has state spaced it into the ground, and you also know how, a state of affairs I've only ever experienced with Taliesin in one of two very particular situations -- there's just no point in playing a move you think is suboptimal. Because without that meeting of the minds with your opponent, you're not taking a risk, you're just taking a stumble.
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Post by Rycchus on Sept 13, 2007 18:52:47 GMT -5
There is never a best move. There are always a multitude of moves, each of which has its own merits, but (usually) only one of which is more likely to be the right move. Given attainable perfect information (you know the exact mood and playstyle of your opponent), you may for example derive that doing D/P on the next turn will be 80% likely to be the right play, and S/P only 20% likely. Your correct play in that situation is *NOT* to submit D/P. The nash equilibrium play that should net you the best game results in the long run, is to toss a 10-sided die, and submit D/P if it reads 1-8, and S/P if it reads 9 or 10. That's bollocks. If you submit D/P then you're 80% likely to be right. If you submit D/P 80% of the time and S/P 20%, you're only 68% likely to be right. Calculation: You being right = (Doing D/P AND D/P right) + (Doing S/P AND S/P right) = (0.8x0.8)+(0.2x0.2) = 0.68Hence, for a game where you know your opponent's mind and on a per-move basis (as in, not one of the standard weaves where predictability might be an issue) the correct play is D/P.
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Post by calicojack on Sept 14, 2007 8:20:05 GMT -5
Rycchus, you forgot that we're all working with attainable perfect information. I think I should clarify that term first: I don't mean 'attainable' in the sense that you could ever actually have it in real life. I mean attainable in theory. KNOWING your opponent's move is not attainable info (if you would know the game is over completely). Knowing their mood, the exact chances of their moves, and all that, is. In theory. Nawglan's archive makes it even very very slightly practical sometimes.
So, given that the other player ALSO works on attainable info, if I know you don't believe in nash equilibrium, I know you will never EVER take a risk. EVER. You always go for the obvious move. Which means I can always counter the obvious move*. And all of a sudden you are forced to take the not so obvious move just from time to time to make sure that I can't exploit your consistency. Of course, you shouldn't go for the worse move very often because it's, well, the worse move.
The nash equilibrium explains exactly how often you should 'fake out' so that your opponent can't exploit your consistency without overdoing it on the fakeouts. In this case it was easy to calculate because I magically sucked some numbers out of my thumb.
Example: Let's say you ALWAYS, *ALWAYS* charm me when I have a monster and a mind enchantment. It's usually the right play (as I'll obviously be protecting the creature), but if you are consistent like a swiss watch, I can win games very very quickly by not protecting my lumbering giant, but myself instead. But, once I start doing that, you'll start charming the giant from time to time, which forces me back to usually protecting it because on the whole I'd much rather get charmed than lose a giant. If we keep playing each other over and over, the # of times you charm the monster v. the number of times I protect it will balance out over time. That would be the nash equilibrium. The exact equilibrium depends on our individual ratings between the events. But there would be an equilibrium, and to avoid any sort of tells, you might as well use a random number generator to make your decision once you've found your equilibrium point. If I were to go: Screw it, I'd rather just know what I'm getting into, I'll just always protect the giant, that's just safer, the tables turn and YOU can exploit MY consistency. Less thoroughly, but on the whole, if you have a giant, and you keep repeating the 'opponent has charm, you have mind enchantment, you protect monster, he charms you' thing over and over, the game doesn't really progress. It's just waiting for one of the two to screw up. So that's no good for me either. I'll need to protect self and risk the giant every so often just like you need to go for the giant every so often.
The entire premise of that was theoretical, it has hardly any practical value (except as a basic explanation that faking out every once in a blue moon against players you'll be seeing a lot more of soon can have some limited value, though I've also already said that all this hinges on people remembering your playstyle which is not likely) - but this thread is at least partly about the idea that given super experts, that warlocks loses all randomness. I was saying that given super experts, warlocks definitely will not lose all randomness. In effect it'll become more random if both players are chess-grandmaster-level crazy about this game and dedicate their entire life to it.
Read up on game theory if this is all gobbledygook to you.
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Post by calicojack on Sept 14, 2007 8:22:12 GMT -5
*) If there's a reasonable counter. As I've said before, if you got a good move that can't really be turned against you, no matter what your opponent does, go for it.
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Post by Slartucker on Sept 14, 2007 8:30:02 GMT -5
Rycchus actually wrote the article and did the graph on that kind of equilibrium (up on the next refuge update). I think the sheer quantity of words you have used has confused your message, Surial. I know it confused me.
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Post by Rycchus on Sept 14, 2007 8:52:13 GMT -5
Yes, and in that kind of repeatable situation it is applicable to roll dice or toss coins, including the example you gave on charms, surial.
This is not what you were talking about before. You were talking about a per-turn calculation. Predictability doesn't come into this.
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taliesin
Ronin Warlock
Grand Master
Posts: 156
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Post by taliesin on Sept 14, 2007 9:50:35 GMT -5
The entire premise of that was theoretical, it has hardly any practical value Au contraire. There are certain end-game positions where this is very useful, the obvious one being the pure 50-50 where coin-tossing ensures you do not lose anything from being predictable (though nor do you gain anything either). Calculations can similarly be made for multiple 50-50s, or some of the Disease positions where there exist various dummying possibilities. And yes, your initial claim was flat-out wrong: "Your correct play in that situation is *NOT* to submit D/P. The nash equilibrium play that should net you the best game results in the long run, is to toss a 10-sided die, and submit D/P if it reads 1-8, and S/P if it reads 9 or 10." This is completely incorrect. If you know perfectly the probability of what move your opponent will submit (i.e. the possibility of you being predicted is not being factored into the calculation) you ought always to submit the move with the highest probability of success. I'll demonstrate this for the 2-possibility case: p1 = probability of outcome to first option favouring you p2 = probability of outcome to second option favouring you
c1 = probability your choice is the first option c2 = probability your choice is the second option
p1 > p2, 0 <= p1, p2, c1, c2 <= 1, p1 + p2 = 1, c1 + c2 = 1 and hence p2 < 0.5
p = (p1 * c1) + (p2 * c2) (as is obvious, the second option coming up when the choice is the first, and the first option coming up when the choice is the second are losses and hence do not factor in)
// Substitute in c2 = 1 - c1 p = (p1 * c1) + (p2 * (1 - c1)) p = (p1 * c1) + p2 - (p2 * c1) p = (p1 - p2) * c1 + p2
// now substitute in p1 = 1 - p2 p = (1 - 2 * p2) * c1 + p2 p = c1 + p2 - (2 * p2 * c1)
Now we have our probability calculation, we can show that p1 is in fact the highest possible probability with a proof by contradiction.
Assume there exists some choice of c1 which yields a probability more favourable than p1: p1 < c1 + p2 - (2 * p2 * c1) (1 - p2) < c1 + p2 - (2 * p2 * c1) 1 < c1 + 2 * p2 - (2 * p2 * c1) 1 < c1 + (2 * p2) (1 - c1) 1 - c1 < (2 * p2) (1 - c1)
divide through by (1 - c1) to get
1 < (2 * p2) BUT p2 < 0.5 and contradiction.Now, the calculations you were trying to do are suited to minimising predictability when you do not know what move your opponent will make, and different moves lead to different probabilities of victory on the subsequent turn. They are not suited to maximising the expected gain when you do know what probability attaches to each move your opponent is likely to choose. Is this clear? Rycchus has a more rigorous mathematical background than my own, and is probably the last person here who needs to be told to "read up on game theory".
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