The Mathematics Involved in a Betting System

The betting criteria most based on mathematical considerations in gambling are the Kelly betting criteria, The Kelly criteria are well known in gambling theory and are a formula used to determine the optimal size of a sequence of bets. Simply put, the Kelly bet amount is the optimal amount used to maximize the expected growth of funds while minimizing risk. The goal of a Kelly betting scheme is to double the funds used in a very short time. The full Kelly betting criterion requires 222 units. Most players further divide the Kelly units into ½ or ⅓. This corresponds to 445 or 667 units. The latter, i.e. the ⅓-Kelly unit, gives a 98 percent chance of doubling the funds used and represents a 2% probability of bankruptcy to go – that is, to lose all of your money.
The Kelly equation works in such a way that the betting unit is measured according to the size of the total funds used. If a player originally had $ 35,000, the wager is $ 50 (for convenience, rounded up to 700 units). If a player has a run and makes $ 5000 profit, the original unit at $ 50 is no longer optimal because the player is underpaying too much money per bet given the increased funds available. Similarly, the $ 50 is no longer considered optimal if the player gets a real shot in a session and loses $ 5000. In this case the bet amount would be too high. In both cases, the Kelly betting approach would be logistically impossible to apply due to its dynamics. The player would have to recalculate his betting unit after each win and loss. As a way out of this logistical dilemma, most players apply the principle of resizing the betting unit when the total funds have reached a predetermined value that they have set. A change of 25% or 30% up or down justifies the adjustment of the unit.

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