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Limitations Of Kelly Criterion Bankroll Mangement System 170 views

Background

The Kelly Criterion was developed by engineer for Bell Telephone, John Kelly in the 1950s just after Senator Estes Kefauver had conducted hearings on organized crime's involvement in sports wagering.


Kelly was faced with the task of explaining a complex set of circumstances regarding power loss in electrical transmission lines to non-engineer top executives so Kelly came up with an analogy to make a complex task easier to explain


Those who remember the Paul Newman/Robert Redford/Robert Shaw movie, "The Sting" will recall how the con artists set up what was called in their argot, "a wire" where "past-posting" of horse racing wagers occurred.

Kelly's analysis (I believe) consisted of utilizing information that occurred as the thoroughbreds rounded the first turn.

Kelly then stated that information would be possessed of "value" if wagers could somehow be executed at that discrete point in time.


While Kelly's analysis did explain the problem in simpler terms, stock market analysts and gamblers realized the analogy was mathematically "valid" to their areas of expertise.


The Kelly Criterion

The issue is when one does indeed enjoy a positive expectation, how does one properly "size: wagers as a percentage of total bankroll to maximize profit.

The weighted, unfair coin of 4 heads for every 3 tails (57% heads) at 11/10 would dictate a wager size of [57 - (43/0.91)] = 9.75% wager on "heads" for every flip of the coin to maximize profit (tangent point at apex of parabola and tangent line at apex parallel to the x-axis abscissa in a 2-dimensional cartesian graph)


The Problem

Sports wagering is both "fluid" & "dynamic" where as the unfair coin is "hard" & "static"

One most often does not know how to quantify one's edge so Kelly wagering becomes "guesswork"

Kelly also is volatile which would cause aggravation & stomach upset even in the unfair coin folk where an absolute certainty of an edge is known


The Most Significant Benefit of Kelly

It comes from looking at that parabola at it's tangent point parallel to the abscissa

At the apex of maximized profit the tangent line touches just one point on the graph

At any parallel line moving south towards the x-axis, the once" tangent" line now becomes a "secant" line intersecting the parabola at two points (the left side point of intersection is "underbetting" by a discrete percentage of bankroll relative to an enjoyed positive edge ; the right side point of intersection is "overbetting")

Kelly's main value shows that the phrase, "got a hunch; bet a bunch" is reckless since the secant line represents the same profitability yet underbetting carries no risk of bankroll ruin

Kelly thus demonstrated mathematically his mastery of the obvious by stating that if one enjoys an unquantified positive edge that one must make sure to underbet in order to figuratively keep himself in the game

Edited 4/12/19 at 12:50AM by AdvantageTipste - No reason listed.

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