This is not exactly about trading but I encountered this on P. 43- 44 of "Option Volatility and Pricing Strategies" The question under consideration is simply what is the value of a dollar bet on a roulette wheel that has numbers 1-36 plus zero and double zero and pays off 35-1 if you pick the right number. In other words it pays 35-1 on a 37-1 shot. He concludes that a dollar bet is worth about 92 cents and arrives at this figure by multiplying the 35 dollar return by the chance of winning which is 1/38 thus (35) (1/38)= a little more then .92 So he gets a dollar bet being worth 92 cents or put differently an %8 disadvantage to the player. This number seemed higher then what I had always read so I considered the problem myself. Over 38 trials we win 35 bucks once and loose one dollar 37 times so we are minus 2 dollars after every 38 spins. 2 dollars / 38 = 5.26 cents or so. So I have the player loosing 5.26 cents for every spin or a 5.26 % disadvantage for the player. So he thinks the fare price for the dollar bet is a little more then 92 cents and I think its a little less then 95 cents. who is right? If it turns out that I am retarded I would like to apologize in advance for this. If I am right should I still read the rest of the book?
My money's with Natenburg. He's looking at expected value. Natenburg's book is a must read for option traders. In your example, what happened to the $1 that you had to put up to earn $35?
You can look at it 3 ways: 1. Positive Utility: Although the financial expectancy is negative, the utility expectancy is positive. The value of "winning $35" is more than 38 times the value of "losing a measly $1." One could look at casinos/lotteries as a dream-selling service -- the player is paying a few cents/$ to indulge their dreams of winning and living the good life. (These non-financial rewards for participation are another reason why the markets will never be financially efficient) 2. Delusions of Luck: People either don't understand probability or delude themselves about their true chances. The majority of people think they are "above average." Others look at it terms of luck - if they are on a hot streak, then they think that they have a high probability of winning or if they are on a losing streak, then they think they are "due" for a win. (Some traders add the delusion that they are "in control") 3. Loss Aversion: People are evolutionarily programmed to take greater risks if they are in bad situation. As Andrew Lo put it, if you are faced with a Saber Toothed Tiger, you are willing to jump off a cliff to get out of the situation. Likewise, if you are in financial trouble, you might take your last dollar and buy a lottery ticket. (This is especially nasty for traders because it leads to doubling down, overleverage, etc.) Trade carefully, trade well Traden4Alpha
It's probably a typo. I have the 1994 revised edition with the roulette example on pp 36-37. The correct house edge of 5.26 cents per spin is listed.
Probably the same part of their brains that makes them pay interest on credit card charges for things they don't even want, but "need and deserve".
Colonel Blood: "The Casino's edge in a double 00 wheel is 5.26%, so your calculations on this front are correct" def: "In your example, what happened to the $1 that you had to put up to earn $35?" The problem is Natenberg calculated the payoff as 35-1, when the actual payoff is 36. You get your own dollar back with the other $35 on your winning spin. If you don't get your own dollar back on your winning spin, then the loss would be 38 dollars vs. $35 payoff = -$3 per 38 tries, and Natenberg's figure would be correct.