2 April 2001 I should've posted these thoughts on April 1, in honor of the day, but considering I didn't =have= these thoughts until this morning, I =suppose= I won't lie by backdating this entry.... though I do backdate my checks (which, I know, has no effect on late fees. It's a totally pointless lie.) In any case, I wanted to talk about truth and lies. First of all, I want to concur with Keats that "Beauty is Truth, Truth Beauty -- that is all Ye know on Earth, and all ye need to know." That is not to say that lies are necessarily ugly, as many lies are very pretty indeed (who really cares for an ugly lie? Well, postmodernists, but that's a different issue. Still, believing in an ugly lie is one of the more futile things I have ever heard of.) I'll get back to that sentiment, but I want to revisit something I wrote in January 1998 - about lying techniques. Both involved telling the truth, but the first involved telling =both= the truth and the exact opposite alternatively (this works for yes/no questions), and the other involved taking all questions literally (this is the "it depends on the meaning of the word 'is'" kind of lie). Basically, one of the more effective ways to lie is to tell the truth in a way that noone believes you. Examples of this: a) Tell somebody your big secret/confession/surprise on April Fools' Day. This has limited usefulness as one can use it only one day of the year, and you need to have as your victim someone who is on guard against April Fools' Day stories. b) Tell the truth in a sarcastic tone. Again, you have to pick someone who has sense enough to recognize sarcasm. A sneer on one's face is also helpful. Actually, that second technique of sneering, and voice tone, can come in real handy for many people in telling lies. If one can lie nonverbally, one has got it made. That is really the only reason I can lie so well (again, to remind some people - I don't lie often - as to why, you shall see below). However, some reactions are hard to control, and so some people prefer to damp all nonverbal cues when telling lies, though this technique is simply the best way to convey no information, as opposed to telling a lie (this is why good poker players have a "poker face". I've found non-poker faces work only against newbies, who can easily be suckered into believing one is bluffing (or not) by one's facial expressions.) Most of the time, one is not really wanting to lie but to conceal information. First of all, if you can make sure noone knows you =have= info to conceal, you're best off this way. For example, I got to go to Wendy's with my Ma or Dad after my math class on Saturday mornings when I was in middle school. I don't think Amy & Carey never caught on to this, as I was careful to make sure all evidence was gone by the time we got home. They never even knew there was something to ask about. I'd still be able to lie about it, but the issue never came up because they didn't know I had information that they would want to know. This is a secret-keeping technique: don't let other people know you have secrets! Back to frequency of lying -- something many children do not understand, though it seems many catch on by adulthood -- if you lie alot, noone will believe anything that comes out of your mouth (if you're really slick, you'll use this to your advantage by telling the truth, which you know noone will believe). If you lie too much, the power of your lies diminishes. However, if you never lie, you never get some of the benefits of lying (such as avoidance of punishment, or impressing strangers). How to balance this? In real life, this is a sticky problem, because the payoffs don't necessarily have a numerical value, and some people are more likely to believe or disbelieve a lie, depending on what it costs them to be skeptical (so a tired parent may believe a lie about cleaning your room, but one who has got a neat streak may check the room right away). Still, let me consider a model problem where we can see the benefits directly. We're going to play a super-simplified "poker" game: From shuffled deck of four cards (jack, queen, king, and ace), the first player pulls out a card and looks at it. Then the first player lays down a bet of one dollar (or not). Then the second player decides whether or not to call the bet. If the second player does not call the bet, the second player gives the first player a dollar. If the second player calls the bet, and it turns out the first player had drawn an ace, then the second player pays the first player 3 dollars. If the first player had =not= drawn an ace, the first player has to pay the second player 2 dollars. This is a game in which the first player has complete information and when deciding to bluff =knows= they are bluffing (this is a problem in real poker, because some people consider themselves bluffing even when they hold a strong hand... they simply do not know the probabilities of the game. For example, in five card stud, two pair, even low, is a great hand.) So, the question is, how often should the first player bluff? Well, let's consider the worst-case scenario: the second player =always= calls a bet. That means every time the first player bluffs, they lose 2 dollars, and everytime they don't bluff, they win 3 dollars if they got an ace and nothing if they didn't. So if p is the frequency at which the first player bluffs, then the expected winnings of the first player is: 3/4*p*(-2) + 1/4*3 = 3/4 - 3/2*p. Obviously, if the second player =always= calls the bet, the first player should never bluff. However, every game, the second player has the expectation of -3/4, which =can't= be optimal for the second player. Likewise, if the second player =never= calls the bet, they are guaranteed to lose 1 dollar on every round. So we need to optimize for =both= the first and the second players. Let p=frequency of first-player bluffing, and q = frequency of 2nd player calling a bet. Then the payoff function for the first player (this is a zero-sum game, so the second player's payoff is simply the negative of the first player's) is calculated thusly: bit from 1st player getting ace, 2nd player call bet: (1/4*q)*3 bit from 1st player getting ace, 2nd player =not= call bet: (1/4*(1-q))*1 bit from 1st player =not= getting ace, bluffs, 2nd player calls bet: (3/4*p*q)*(-2) bit from 1st player =not= getting ace, bluffs, 2nd player not call bet: (3/4*p*(1-q))*1 If one expands the whole thing, you get the expected value for the first player: 1/2q + 1/4 - 9/4pq +3/4p For each given propensity of the second player to call (q), there is a p which will maximize this amount (and such p will be either 0 or 1, for this equation is linear in p) -- so the max value will be either: 1/2q + 1/4 or 1 - 7/4 q. The only q for which there is no disparity in these two values is q=1/3. Likewise, for any given bluffing propensity p, there is a q which =minimizes= the value (because the second player wishes to minimize the first player's take). Again, q will be either 0 or 1 for this minimum value: 1/4 + 3/4p or 3/4 - 3/2 p. The only p for which these two values have no difference is p = 2/9. So the minimax point is achieved when the first player bluffs with a frequency of 2/9, and the second player calls the bet with a frequency of 1/3. This results in a return of 5/12 for the first player (yes, this is an unfair game, stacked against the second player). But, as we saw above, there =are= situations in which the first player can win more, or the second can lose less. The point is that things are in balance at the point which we found. If the first player bluffs more often than 2/9 of the time, then the second player =always= calls the bet, and the second player ends up losing less money (and, in a few cases, will =win= money). If the first player bluffs less, the first player doesn't make as much money. If the second player calls the bet more often than 1/3, the first player can stop bluffing entirely and win more money in the long run. And so on, and so forth. The solution we found above was a minimax solution: the first player should think of the situation in which the second player plays with an optimal strategy (minimizing the return), and try to maximize their return under this situation. The second player, likewise, must consider that the first player will bluff an optimal amount whatever strategy they (the 2nd player chooses), and must try to minimize the return under this situation. Simply put, this is the result which one can expect if both players are completely rational beings, able to react immediately to the way others play. However, luckily for many of us who are =not= totally skillful poker players (or liars), people aren't completely rational, and often one finds that one is far from a minimax solution. For example, there's this really mean 7 card stud variant I like to play called Baseball. It has =8= wild cards, and people have the opportunity to "buy" more cards. This game splits the pot between the high hand, and the high spade in the hole (there are three face-down cards (aka cards in the hole)). If one is not holding =at least= a full house, one is not in a good situation. This game has 8! 8! wild cards! That screws with probabilities like nobody's business. Well, people new to the game of poker have just learned the order of the hands, and, if one is even sneakier, one has shown them what the probabilities for the hands are in regular 7-card stud. So, for example, one newbie may be getting all excited over having a flush (with two wild cards). They decide to stay in it all the way. I, on the other hand, have four-of-a-kind (also with two wild cards). One does =not= bluff in a game like Baseball, esp. with newbies, because they think they have fabulous hands and will stay in til the end. This is the case of where a player =always= calls a bet (you can be sure =someone= will stick with you to the end, because they think their "high" hand is still really high with that many wild cards in the game), so one should never bluff. On the other end, we have five card stud, no wild cards, high hand only. Play with the same newbies, =without= them knowing the probabilities of hands, and they're almost guaranteed to fold. This is a case where one should always bluff, for the probability of getting =at least= a pair is less than half. If one has one pair, stay in; heck, if you've got a decent high card, stay in. You can even do this if a newbie has a pair showing (real stud has 4 up cards -- so only one card is hidden), esp. if it's a low pair. Many people won't stay in even that long. Still, I wouldn't play 5-card stud, because people tend to find it boring. One can find similar games, which are more interesting, and just as likely to scare off newbies. The problem is, of course, when one runs into a skilled poker player. That's the time to cash in one's chips, and watch them at work. In any case, I think this is long enough for an entry, so I'll have to talk about truth some other time.

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