Betting the ideal bet size will increase your betting account almost 3% per bet on average. So you tell us: is it worth it?
75% I got just by setting it up in excel to optimise the expected log utility (weighted log of each outcome). That should account for all the moments. 50% I did just looking at the mean and standard deviation, and using the normal formula for that. This is obviously a negative skew trade, so I'd expect the solution with all moments to have a lower bet size than 50%. But then it's a weird distribution compared to what I'm used to GAT
No, I'm not asking you to pick one of the outcomes. They all are present at all times, even though only one of them will occur for any particular bet. Think of them like the six sides of a gambling die. All six sides are always present, but only one side at a time will ever be on top. The question is, how much should you bet (as a % of your betting acct) to maximize your expected gain?
If that's so, then it's worth it, clearly. That wasn't the outcome of my quick calculation, though, I must say. It seemed to me that betting one "unit" per time would increase your betting account by only 0.0575 units per time. As I said above, I did it very quickly and may have made some gross error, in which case apologies. I'll look again in more detail when I have time.
If you had followed the links you will see the answer. You can lead a horse to water but you can't make it drink..... Ignore the links at your own peril
Those links are based on bad formulae. I've posted tons about this. Do the search. The reason I asked for a number from you was so you could see for yourself how awful those calculators are for anything more complicated than a simple casino bet. You can lead a horse to water but you can't make it drink.
A high A high post count does not equal a successful trader. I will continue using the formulas and continue enjoying being consistently profitable without fear that I am ever in a position that is too large and I risk ruin. What people fail to grasp is you can have a 90% win rate and lose money. You can have a 10 % win rate and make money. Continue doing what you are doing.
I've had more time, now, and have looked at this again. It seems that the expectancy figure in my answer above is correct, but my PF figure (which I didn't think about for long enough, or "at all", really) was sadly mistaken. Here's my reasoning, based on putting on 100 trades risking 100 units per trade. Out of those 100 trades ... The profitable trades: 35 trades each win 20 units, for a total profit of 700 units 20 trades each win 12 units, for a total profit of 240 units 4 trades each win 50 units, for a total profit of 200 units Summing these, the profits come to 1,140 units The losing trades: 25 trades each lose 15 units, for a total loss of 375 units 15 trades each lose 6 units, for a total loss of 90 units 1 trade loses 100 units, for a further loss of 100 units Summing these, the losses come to 565 units So the expectancy is 1,140 - 565 units (which is +575 units, on balance) on 10,000 units invested (for 100 trades at a risk of 100 units each), which is +0.0575 per unit, as I said. And the profit factor is clearly 1,140/565, which is 2.018, as Visaria rightly said. So it is worthwhile. (None of which actually answers the original question, but at least it acknowledges my silly mistake regarding the PF - sorry to have taken up your time with that).
No problem. You're learning, which is the most important thing. As you've probably gathered from the other posts, this is a Kelly-type problem, but given its complexity, no simple Kelly formula or Kelly calculator is going to give a satisfactory answer. If no one posts the best answer, I'll post what I got and show how much the account grows.