Video Poker: Balancing Bankroll Sizes and the Risk of Losing It All

Introduction

This section tackles the topic of bankroll size versus the risk of total loss in video poker. For those unfamiliar, the risk of total loss refers to the chance of depleting one's entire bankroll. The subsequent tables illustrate the number of betting units needed based on an acceptable risk level, the specific game, and included cashback. A 'betting unit' refers to five coins; for instance, for a 25-cent machine, a betting unit would equate to $1.25.

For instance, a player utilizing full play deuces wild with a 0.25% cashback would require a bankroll of 3,333 units to maintain a 5% risk of total loss. A chart provided will help clarify this figure. It's worth noting that these requirements may appear elevated compared to other sources that factor in the risk of loss before hitting certain benchmarks. The tables presented are designed for evaluating total loss risks over an extended timeframe without a definitive endpoint, except for amassing an infinite bankroll. Therefore, these resources are best suited for players interested in managing a bankroll for an open-ended gaming experience.

The table that follows pertains to 'full pay' deuces wild. This specific pay structure can be referenced in my video poker tables but is typically characterized by a payout of 5 for achieving four of a kind. The expected return on this game stands at 100.76%, with a standard deviation of 5.08.

The next table pertains to the '10/7' double bonus category. Information regarding this pay structure can be found in my video poker tables and is generally denoted by payouts of 7 for a flush and 10 for a full house. The expected return for this game is 100.17%, with a standard deviation of 5.32.

The subsequent table concerns the 'full pay' jacks or better format. Details on this payout structure can be located in my video poker tables and is commonly represented by payouts of 6 for a flush and 9 for a full house. The anticipated return on this type of game is 99.54%, accompanied by a standard deviation of 4.42.

Methodology

The creation of the aforementioned tables relied purely on mathematical principles. The underlying theory is analogous to the solution methodology presented in problem 72 on my mathematics problems site. In essence, if p symbolizes the probability of total loss with a single unit, then p' represents that probability with three units, and so forth. By leveraging known probabilities associated with every hand's outcome, a complex equation could be devised: p equals the sum over all potential outcomes of pr²is the probability of ruin with 2 units, p³which denotes the return associated with hand i. Through an iterative process, I computed the value of p. The cashback was allocated to the player for each hand played. For example, if the cashback percentage was set at 1%, then one cent would be added to each winning hand, including instances of no wins at all for each $1 wagered._i * p^r_i, where pr_iis the probability of hand i and r_iStandard Deviation calculated for n-hand video poker

is the probability of hand i and r i