Target Betting

[ReplayRandall]

Romankoz, Horseplayers and gamblers have been using systematic betting approaches for eons. Take the time to read this 13 year old thread, as I'm thinking you may a lot in common with the posters from this site:

http://www.majorwager.com/forums/han...anagement.html

[traynor]

Originally Posted by thaskalos

Hope remains in the heart...even when all else is lost. It's a self-preservation mechanism, I think. We need some sort of "hope" in order to keep going during the tough times. But hope isn't the same as self-delusion, IMO. The losing horseplayer who is expecting things to improve in his financial life is being "normal", as I see it...while the habitual loser who truly considers himself a "winner" is exhibiting the sort of behavior which allows psychiatrists to drive around in Rolls Royces.

The question would then be, is "hope" based on illusion or reality? One can always "hope" to find some whatever, and never even come close to such. One could say the "hope" drives the search.

However, a high-degree of self-efficacy does not include "hope" (as the word is normally understood) as motivation. Rather than searching for solutions elsewhere, one tends to create one's own solutions. It is a different conceptual paradigm--one still searches, but for different things, and for different motives.

Think of Liam Neeson's decision after beseeching for a sign of heavenly intervention (perhaps filled with "hope" that such would come just in the nick of time) in The Grey. That is not a case of "all hope being gone." It is a case of "If it is going to get done, I am the only one who is going to do it."

[traynor]

Originally Posted by Robert Fischer

If you are the rare elite player who somehow has a positive ROI, there's really no sense in using a due column or parlay. Even positive-expectation-Win-Betting is no guarantee free from peaks and valleys that come with natural results.

If you are like myself and don't have a positive ROI, it's probably not a good idea either.


If you have a good understanding of what such money-management systems actually leverage (and at what expense), and you make a conscious decision to "gamble", and you are perfectly fine with that, -then you can play along and try to get lucky with a hyper-aggressive type of strategy.

I think you make my point quite eloquently in your statement above.

[thaskalos]

Originally Posted by traynor

The question would then be, is "hope" based on illusion or reality? One can always "hope" to find some whatever, and never even come close to such. One could say the "hope" drives the search.

However, a high-degree of self-efficacy does not include "hope" (as the word is normally understood) as motivation. Rather than searching for solutions elsewhere, one tends to create one's own solutions. It is a different conceptual paradigm--one still searches, but for different things, and for different motives.

Think of Liam Neeson's decision after beseeching for a sign of heavenly intervention (perhaps filled with "hope" that such would come just in the nick of time) in The Grey. That is not a case of "all hope being gone." It is a case of "If it is going to get done, I am the only one who is going to do it."

Hope is always at least partially based on illusion...IMO. If it were based on "reality", then we wouldn't call it "hoping". We'd call it PLANNING.

I tend to lean toward the PESSIMISTIC side, myself...with a healthy dose of paranoia mixed in, for good measure. It may not make me the "life of the party"...but I think it's served me pretty well in my gambling voyage. Daydreaming doesn't seem to be a serviceable attribute for a gambler...in my opinion anyway.

[Robert Fischer]

Originally Posted by traynor

I think you make my point quite eloquently in your statement above.

Humor aside, we seem to be far apart on some of the more fundamental aspects of bet sizing.

[Magister Ludi]

Prerequisite: high school algebra

The following is proof of the fallacy of a progression in an unfair game with an even payoff. It can be easily adapted to the case of an uneven payoff.

Let

b_k = bet value at the kth level
p_k = probability that series terminates with a win at the kth level, having been preceded by k-1 losses in a row
n - 1 = greatest number of losses in a row that can be sustained
e = player's expectation

e = + p_1b_1 + p_2(b_2 - b_1) + p_3(b_3 - b_2 - b_1) +...
+ p_n(b_n - b_(n-1) - ... - b_1)
+ (1 - p_1 - p_2-...
- p_n)(-b_n - b_(n-1) - ... - b_1)

The terms on the first line represent products of the probability that the series will terminate with a win at each successive level times the net profit at that level. The term on the third line gives the product of the probability that the series ends in failure at the nth level times the net loss.

regroup the terms:

e = 2p_1b_1 + (2p_2 + p_1)b_2 + (2p_3 + p_2 + p_1)b_3 + ...
+ (2p_n + p_(n-1) + ... + p_2 + p_1)b_n
- (b_1 + b_2 + ... + b_(n-1) + b_n)

p_k = (1 - p)^(k-1)p, where p is the probability of a win on any individual play and 1 - p is the probability of a loss.

substituting:

e = [2p]b_1 + [2p(1 - p) + p]b_2 + [2p(1 - p)^2 + p(1 - p) + p]b_3 + ...
+ [2p(1 - p)^(n-1) + p(1 - p)^(n-2) + ... + p(1 - p)^2 + p(1 - p)^1
+ p(1 - p)^0]b_n - (b_1 + b_2 + ... b_(n-1) + b_n)

factor out p so that the kth term is rewritten as:

p[(1 - p)^(k-1) + (1 - p)^(k-1) + (1 - p)^(k-2) + ... + (1 - p)^2
+ (1 - p)^1 + (1 - p)^0]b_k

use the formula for the sum of a geometric series and rewrite the kth term:

p[(1 - p)^(k-1) + (((1 - p)^k - 1)/((1 - p) - 1))]b_k
= [(2p - 1)(1 - p)^(k-1) + 1]b_k

e = sum_{k = 1}^{n} [2p - 1)(1 - p)^(k-1) + 1]b_k - sum_{k = 1}^{n} b_k
e = sum_{k = 1}^{n} [2p - 1)(1 - p)^(k-1)b_k + sum_{k = 1}^{n} b_k - sum_{k = 1}^{n} b_k

cancel the last two summations and factor out (2p - 1):

e = (2p - 1) sum_{k = 1}^{n} (1 - p)^(k-1)b_k

Since (1 - p) is positive and b_k is positive, the summation is positive. Therefore, the sign of e depends on the sign of (2p - 1). In an even-payoff unfair game, p < .5 and (2p - 1) is negative. In a fair game, p = .5 and (2p - 1) = 0.

[DeltaLover]

Originally Posted by Magister Ludi

Prerequisite: high school algebra

The following is proof of the fallacy of a progression in an unfair game with an even payoff. It can be easily adapted to the case of an uneven payoff.

Let

b_k = bet value at the kth level
p_k = probability that series terminates with a win at the kth level, having been preceded by k-1 losses in a row
n - 1 = greatest number of losses in a row that can be sustained
e = player's expectation

e = + p_1b_1 + p_2(b_2 - b_1) + p_3(b_3 - b_2 - b_1) +...
+ p_n(b_n - b_(n-1) - ... - b_1)
+ (1 - p_1 - p_2-...
- p_n)(-b_n - b_(n-1) - ... - b_1)

The terms on the first line represent products of the probability that the series will terminate with a win at each successive level times the net profit at that level. The term on the third line gives the product of the probability that the series ends in failure at the nth level times the net loss.

regroup the terms:

e = 2p_1b_1 + (2p_2 + p_1)b_2 + (2p_3 + p_2 + p_1)b_3 + ...
+ (2p_n + p_(n-1) + ... + p_2 + p_1)b_n
- (b_1 + b_2 + ... + b_(n-1) + b_n)

p_k = (1 - p)^(k-1)p, where p is the probability of a win on any individual play and 1 - p is the probability of a loss.

substituting:

e = [2p]b_1 + [2p(1 - p) + p]b_2 + [2p(1 - p)^2 + p(1 - p) + p]b_3 + ...
+ [2p(1 - p)^(n-1) + p(1 - p)^(n-2) + ... + p(1 - p)^2 + p(1 - p)^1
+ p(1 - p)^0]b_n - (b_1 + b_2 + ... b_(n-1) + b_n)

factor out p so that the kth term is rewritten as:

p[(1 - p)^(k-1) + (1 - p)^(k-1) + (1 - p)^(k-2) + ... + (1 - p)^2
+ (1 - p)^1 + (1 - p)^0]b_k

use the formula for the sum of a geometric series and rewrite the kth term:

p[(1 - p)^(k-1) + (((1 - p)^k - 1)/((1 - p) - 1))]b_k
= [(2p - 1)(1 - p)^(k-1) + 1]b_k

e = sum_{k = 1}^{n} [2p - 1)(1 - p)^(k-1) + 1]b_k - sum_{k = 1}^{n} b_k
e = sum_{k = 1}^{n} [2p - 1)(1 - p)^(k-1)b_k + sum_{k = 1}^{n} b_k - sum_{k = 1}^{n} b_k

cancel the last two summations and factor out (2p - 1):

e = (2p - 1) sum_{k = 1}^{n} (1 - p)^(k-1)b_k

Since (1 - p) is positive and b_k is positive, the summation is positive. Therefore, the sign of e depends on the sign of (2p - 1). In an even-payoff unfair game, p < .5 and (2p - 1) is negative. In a fair game, p = .5 and (2p - 1) = 0.

Wow!

Every one in this forum should now be really impressed!

This is so impressive and original..

[traynor]

Originally Posted by thaskalos

Hope is always at least partially based on illusion...IMO. If it were based on "reality", then we wouldn't call it "hoping". We'd call it PLANNING.

I tend to lean toward the PESSIMISTIC side, myself...with a healthy dose of paranoia mixed in, for good measure. It may not make me the "life of the party"...but I think it's served me pretty well in my gambling voyage. Daydreaming doesn't seem to be a serviceable attribute for a gambler...in my opinion anyway.

Absolute agreement. I think the greatest hindrance (for most bettors) to making a profit is a self-induced delusion derived from "positive thinking." Reality is pretty neat once one understands it. Once one understands what one has to work with, finding useful solutions becomes MUCH easier.

[traynor]

Originally Posted by Robert Fischer

Humor aside, we seem to be far apart on some of the more fundamental aspects of bet sizing.

With a negative ROI, the optimal wagering strategy is "none of the above." As in, "don't bet."

[traynor]

Originally Posted by Magister Ludi

The following is proof of the fallacy of a progression in an unfair game with an even payoff. It can be easily adapted to the case of an uneven payoff.

What does that have to do with horse racing?

[traynor]

It is not that self-delusion in regard to real world ROI is "wrong." It is that pretending something is not broken does nothing to fix it. Attempts to fix it, or to even consider fixing it, are "resisted" because they threaten the maintenance of the illusion. The "positive thinking" becomes self-destructive and self-defeating.

Festinger opened it for all to see with his research in cognitive dissonance.

[Robert Fischer]

Originally Posted by traynor

With a negative ROI, the optimal wagering strategy is "none of the above." As in, "don't bet."

There seems to be some sort of 'communication barrier' at play.

It is disappointing that we could not engage in a discussion.

[ReplayRandall]

Originally Posted by Magister Ludi

The following is proof of the fallacy of a progression in an unfair game with an even payoff. It can be easily adapted to the case of an uneven payoff.

Magister Ludi, your posts have officially hit rock-bottom, all credibility...gone. It's so bad, even Trifecta Mike won't bail you out with a supportive post....

[Saratoga_Mike]

Originally Posted by ReplayRandall

Magister Ludi, your posts have officially hit rock-bottom, all credibility...gone. It's so bad, even Trifecta Mike won't bail you out with a supportive post....

...TM's just a log-in change away from the rescue

[DeltaLover]

Originally Posted by ReplayRandall

Magister Ludi, your posts have officially hit rock-bottom, all credibility...gone. It's so bad, even Trifecta Mike won't bail you out with a supportive post....

Obviously a ridiculous attempt to prove a self explained issue.

What is even worse, is the way he wrote it.. If you really want to impress by throwing around trivial math equations, you should at least have the ability to format them using latex or something similar, so they are readable without much effort..