Thanks for the responses Tony and Tuffty. I'm afraid I have little original or useful to add; in fact all I've managed is to confuse myself.
But to get back to your example (shamelessly lifted from Scripho) which I read a number of times - are you saying that with a large enough run of coin tosses they will approximate very closely to 50/50, but not necessarily exactly (in fact, probably never...)?
Yes. The more tosses, the closer the proportion of heads to tails will draw to 50:50. There is no requirement for the numbers to be exactly equal at any point in the series, and the likelyhood that they will be decreases as the series increases.
And, at a time in that sequence, especially in the beginning of the series, there could well be a significant imbalance which might not 'rectify' until relatively late in the series?
Yes, sort of, but beware of exactly what you mean by "rectify". While the proportion will slowly rectify toward 50:50 (though not in strictly linear fashion), the absolute difference between the number of individual heads and tails need not, indeed almost certainly will not, gravitate toward 0.
Although what happens at infinity? You could either assume the difference in throws would be 0 as the percentages would be infinitely close to 50:50 or that because the number of throws is infinitely large, the infinitely small difference in percentage that necessarily exists between them would still be enough to give a wildly different number of throws. I go with the latter. Does anyone know the answer? Ta.
To restate in the real world, even more patronisingly
Say heads take a surprising early lead of 20 after 50 throws (i.e. 35 heads to 15 tails) it is tempting to think tails are due a run ("the corrective") because you know the series tends as a whole towards a 50:50 distribution. But after another couple of million throws, though the proportion will now be much closer to 50:50, the number of total throws will be so big that the difference between heads and tails thrown will probably now be in the hundreds, e.g 999,900:1000100 =1:1.02 = 49.5%:50.5%
Thus backing one side after the other has enjoyed a long run is no better a strategy than backing that side at any point in the series. This was, at least to me, rather counterintuitive, though I wholly accept it as truth.
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My notional trading strategy is not quite a Martingale because I am not proposing to double the stake with every loser to eventually win my initial stake back (you are right about the infinites required to do this with certainty of success), I am proposing to add to a stake after a selected number of losers, for a selected number of trades, then reduce to original size. The stake is "dynamic",if you like, depending on previous market action, and the idea is to encapsulate an unusually juicy trend in the occasional raised stake period.
Why will this be likely? Because not only have we been consolidating for bl**dy ages but also the stakes will be raised incrementally until there is either a big winner and/or the average pip per trade within the raised stake period exceeds the system average.
The stake increase is designed to happen rarely, pehaps only each time the number of max consecutive losers exceeds the number as derived from mathematical formula, or perhaps the dreaded backtests. This may of course never happen.
Of course if the winner is 4 pips and it occurs after two 30 pip losses I look stupid :cheesy:
Increasing the stake at this point might be a good strategy because, unlike the coin, which knows nothing of its past performance, the chance of a win soon WILL be larger than usual. It will be larger than the average 35% success rate whereas a coin will always be 50%. A consolidation is about to burst, and the win is likely to be bigger than usual too, a factor unconsidered in the coin example.
Sorry. The rest of me is shouting "Well if the system wins 35% on average then even after 10 losers there is still only a 35% chance of the next trade being a winner, and the next one, and the....etc. you idiot! Nobody gives a toss if it's a coin or a dartboard, it wins 35% of the time, full stop, and you have just contradicted yourself most ignominiously!"
And as I must certainly concede to you that it is by no means impossible for the expected max losing string of losses to double in practice, albeit a carpaccio-rare "black swan" event, I will not be implementing any form of this stake meddling strategy. Well, perhaps I'll add 1% to my stake after 10 losers until a winner crops up again
for fun.
For now, a positive expectancy is more than enough to elicit my gratitude.
And in relation to the instruments you trade Frugi, do you have an analysis of the %-age trading to non-trading periods over the last X months? And is there any pattern? I tend to use recent market action to help me decide if I'm more likely to have a trend day in any given instrument than by using range techniques. (Damn! There's Trend-O-Find accidentally let out of the bag
Do you mean "%-age trading to non-trading" or "%-age trending to non-trending"? If it is the latter there is no pattern I can truly discern, despite the best attempts of my brain to find them lurking in the noise. Trends, as a factor of time, probably last about as long as the frequency with which my system wins and that is all I can tell you. What patterns there are tell me weakly when a trend has started and how likely it is to continue, but not when this may happen. I used to think I could predict the timing of moves based on past action - indeed I probably could 50% of the time - but now I don't bother to try.
That is not to say that if I see ES has consolidated in a 3 point range for 74 straight hours that I won't try and buy an explosive upside breakout, but it is to say that since I don't know when or if this will happen until it happens, there is no point in trying to tweak my mechanical systems to take account of it. To do so one must be discretionary at the moment of birth and I don't believe a mechanical system can do this with logic alone.
Anyway Bramble my brain is now all a-scramble and the cats are idly circling, just like my thoughts, so I'd best leave these notions to someone with a better grip on stats and stop trying to tinker with a perfectly adequate brace of systems!
PS I remember that calculation for max expected losses. In fact I think I robbed a formula off poor old Scripophilist again - it enjoyed a similar result to yours and I still use it!
