The sum total of all the low probability trades and high probability trades equals one. It makes no difference if you buy the one delta call 100 times or buy the 99 delta call 100 times.
There might be a million reasons why someone wants to buy an option. He might have a view on the direction, on the terminal distribution, on realized volatility, on implied volatility etc. I am pretty sure an option buyer understands that he has much lower probability of payout, but when that payout comes (assuming he is buying an option because he has that view/informational advantage of some sort) it's going to be a large win.
I should not have used the term adjustment. I was not refering to making an adjustment on a deteriorating trade. i was actually refering to the initial choice of probability vs potential. That being, selecting a strike more otm to begin with vs less otm, creates a higher probability trade. That we can adjust our chances for success, but not actually have an edge, when the trade is initiated.... other than a perceived one. I suppose there is the rare split second timing when a trader may get lucky to spot something before others do, and thus have a edge. But I'm not refering to the rare exceptions.
No, you are till not there. Maybe your language skills are poor but your "total" probability does not change based on how far OTM you are. Think about it this way. Every strike price is a probability for a given stock. Each of those strikes has their own probability with a corresponding payoff that is equal to it's expected value. The sum of all those strikes prices equals a probability distribution. The sum of all the strikes is equal to a probability of one. So as you go further out in strikes, you lower your probability of that particular strike but increase the payoff. The seller of that sames strike has the inverse bet as you. They have a high probability of a lower payoff. But the sum of all the possible trades from all the possible strikes has to add up to one. There is no way around this math.
I agree. But isn't it also true that each current trade is independent of the previous trade and the next trade? Thus, the issue is, what is the consequence of being wrong on a particular trade, and the probability of being wrong on that particular trade.
Each trade carries it's own probability. But that "one" probability is part of the total probability distribution which equals one. So it doesn't matter which trade you make. You could make one of them or all of them. There is no way to "manipulate" the probability distribution.
'it's either a slow bleed or a bullet to the head' So we can't win??? What if the probability of winning $.25 is 4 times the probability of losing $1. Would you take the trade?? E = 4(.25) - 1($1) = 0 Why bother?? Then what if the probability of winning $.25 is 5 times the probability of Losing $1: E = 5(.25) - 1($1) = .25 It doesn't mean you'll win every time but if you take a large number of trades with positive expectations you should win in the long run even if a downdraft occurs. Why is that? Aren't options priced so that you can't win?? i.e. aren't options priced to a negative expectation?? Well... people who own stock buy puts to protect themselves from a disasterous downdraft. PM and I sell them the puts... I try to sell them puts with a positive expectation on my side. When the downdraft occurs maybe we go broke and the put buyers survive. I try to hedge by using spreads instead of naked puts. If you do the math the spreads usually have a higher expectation because they hedge against the real big decline while the naked put takes the full hit. Of course the naked put seller has a somewhat bigger cushion because he didn't pay for the hedge... but the far OTM put that closes the spread is usually cheap relative to risk. If the hit is small naked puts are better, if the hit is large spreads are better. It's just a matter of when the downdraft occurs relative to how many nickels we have collected, and can we see it comming or not. If we see it comming we can cancel the insurance policy and maybe miss the knife. SO I look for situations that SEEM to have a high price on the put I am selling and a low price on the put I am buying. (This is what produces a positive expectation). We both look for situations where the price of the put we sell SEEMS high relative to the risk of loss... which again produces a positive expectation. BTW: If we are desperate for trades and sell puts for cheap prices (i.e. a negative expectation) we are doomed. If things look dicey I try to get out before I take the whole downside hit. If you are playing positive expectation and truncate your losses you can (maybe) win in the long run.
I agree with the math, but I'm not sure of it's relevance in the actual world of trading. I'm not talking about manipulating the probabilities. I'm talking about selecting one and managing the "consequences" of that decision. For example, I could have a losing trade at expiration, whether it be on a high or a low probability trade. But that "unit of cash" does not necessaily disappear, just because I lost that probability bet. It would if it were invested in a spread that dropped below both strikes. But it would not if I bought the stock and it later recovered. So I'm not sure I understand the "relevance" of understanding the probability math, as it relates to option trading in ones actual account. What's relevant, is the "consequence" of being on the wrong side of a probability trade. The issue is about selecting a probability outcome, that you have a chance to "manage" if/when you are wrong.