Suppose that an investor has had a bet on a yet-to-be-contested event, and that the utility can now be improved; such that his confronting task is to bet on the complement of the earlier-backed outcome; to such an extent so as to maximize utility. Let the potential profit, ( as a proportion of capital, ) from the early bet, be symbolized " E ". Let the updated success probability of the late bet, be symbolized " P ". Let the available decimal dividend about the late bet, be symbolized " D ". Let the proportion of capital on the early bet, be symbolized " xi ". Let the proportion of capital to go on the late bet be symbolized " xii " ( - using the same capital figure as for xi & E. ) xii = P*( E + 1 ) - ( 1 - P )*( 1 - xi )/( D - 1 ). If xi + xii > 1, and credit is unavailable, set xii = 1 - xi.
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Yes, the complement to the bet over the line, is the same team/player under the line. Of course, such betting would get tricky, if the line is subject to movement. Betting exchanges, like Betfair, are a good medium for lay-off betting, especially with racing. And we are typing about half-pointed lines, but if the line is 0, and tie betting is available, the tie bet can be dutched ( - slight deviation from Kelly, ) with the early or late bet. An early dutch may seem contrived/convenient, but realise that if a punter expects the early bet to be a firmer, but still perceives it as negative value, it is apropriate to back it; ( x ~ P ), with the intention of backing the complement later. By reading my other recent posts, one would notice that I believe that this sort of investment is productive.Comment -
For live in-game wagering this is exactly what I do and is very productive. I typically have one-side before the game and then "close" it out by taking the other side during the game. At the point that I "close" I don't try to determine EV for either side. I have an excel worksheet that I "programmed" to give me the amount to bet on the other side dependent upon the current odds that will give me an equal profit (or loss) regardless of which side wins. I am sure that this can be improved upon but I don't think the "improvement would be significant and/or worth the effort. This works for me without getting too complicated.
Joe.Comment -
Neil, you might find the following vaguely relevant:
http://forum.sbrforum.com/handicappe...tml#post230201-and-Comment -
I am curious as to the reason that this works for you, because, if the reason is that you are finding significant value with your pre-game bets, I suspect that you would significantly improve profit by dropping off in-game action. Or have you become aware of an under-rated trend, relating to teams that stomp onto the field with steam coming from their ears, only to run out of puff in the second half? Or, if you want to spook me, type about exploitation of some kind of random walk - different " experts " have told me that heaps of money has been made from this, but I don't get it.Comment -
The value is not in the pre-game wager. The pre-game lines are "predicting" how the game will end, not how it gets there.
Very close. If you "know" that a team consistently sprints from the gate, it really doesn't matter if the pre-game wager (which is based on the end of the game) is +EV or not. After the "sprint", the line will change significantly and you can "close" out at a profit. You just need to make sure that your team is consistent enough to make enough profits to compensate for the losses when they don't "sprint".
It's more like random walk with a trend if that makes sense and yes a lot of money has and can be made from this. In fact, it is the same methodology that I used for my stock options trading. There too, options are priced based on the expectation at expiration, not the path it takes to get to expiration.
Joe.Comment -
Confirmation of add-on-bet results.
Thanks, Ganchrow - yes - relevent, useful ( particularly when I get my computer organised ) and entertaining - I expect nothing less than exhaustive disscussion from fanatical purists. Mind you, this analysis stuff can be addictive. I hope that I find time to get my bets on. I am inspired to study more math. However, there are a couple of things that someone here might help me with: " Edge " features in much dicussion - what is the precise definition? I am quite uneasy with the concept of " fractional-Kelly " - I gather that there is a sophisticated form of it - what is it supposed to do? With respect to the extra-bets-on-the-same-outcome conundrum, the economic perspective is good mental excercise. In case it makes some posters feel more relaxed with the results, I have derived the add-on Kelly formula myself; using very basic calculus that I found in a high-school math book - it gives the same results that you get. As it is smallish, here it is now: x' = [ ( p + D + ( 1 - D )*x )*P - p -1 ]/( D -1 ). ( p: potential profit from earlier bets ), ( x': Kelly answer we are chasing ), ( D: latest available decimal dividend ), ( x: total investment on earlier bets ), ( P: probability of win ), ( p, x & x' all expressed as proportions of ( capital before the betting started ) ). With respect to line shifts after bets, I had derived an add-place-bet-to-win-bet formula, which is much more cumbersome; and it is not as comprehensive as your spread-sheet, as it does not cover push scenarios or constricting line movements. I suppose that this is enough for one post. N.Comment -
I can see now that there is a close analogy between our approaches, in that we are both expecting something to occur which changes the odds. However, although I sometimes close out at a pre-result profit, such has nothing to do with why I sometimes make a negative-expectation bet - my motivation is purely about utility maximization. How do you calculate the size of your pre-game bet? Neil.Comment -
My pre-game wager is 10% of my bankroll. My edge is 10% risking 2 units to win 1 unit. Full-Kelly would be 20%, Half-Kelly is 10%. I actually used 20% several years ago but I did not like the larger fluctuations of my bankroll and it became a bigger problem if I had more than 1 wager "working" at a time. I am very comfortable with the 10% pre-game wager as my edge has stayed relatively consistent. Very rarely is the entire 10% at risk as I usually "close" the wager well before I would lose 10%. In addition, I very rarely have more than 2 wagers "working" at a time.
I do not claim this to be anywhere near mathematically perfect. It is what I do and it works very well for me.
Joe.Comment -
Keep up the good work, Joe. Neil.Comment
