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RETURN & VARIANCE CALCULATOR INSTRUCTIONS

 


Summary

After selecting the calc inputs, click "Calculate." The calc inputs and outputs are described below. Click here to return to the return & variance calculator.

 

Required Inputs

Game -- To select a game click on the game group in the top menu, then select the bubble in the left menu that corresponds to the desired game. For blackjack games, there is a software pulldown. After selecting a software in the pulldown, available blackjack games with that software are listed in the left menu.

Bonus -- Bonus is the size of the bonus. To check variance and expected return for play without bonuses, leave the bonus input at 0. The calculator only supports cashable bonuses (both pre-wager and post-wager). For sticky bonuses, see the two-tier betting simulator.

Wagering -- Wagering can be expressed as either a total wagering requirement or in terms of the bonus. For example, a casino might offer a $100 bonus with 40xB wagering on blackjack. Enter either a bonus of "100" and wagering of "40", selecting "xB"; or enter a bonus of "100" and wagering of 40x100="4000", selecting "Total."

Bet Size -- Bet size is the bet size per hand. The calculator assumes a fixed bet size across the full wagering. In video poker, bet size is not the coin size. It is the coin size * coins per hand. See the example, in the multiple hands section for more detail. For ultimate texas hold'em, bet size is the ante bet alone, not the sum of the ante + blinds. For 3-card 2nd chance, bet size is the sum of the ante bet and side bet.

 

Optional Inputs

Bankroll -- "Standard" bankroll results assume no influence from bankroll limitations, so EV remains the same for all bet sizes. "Limited" bankroll results assume bankroll limitations influence results, so EV increases as chance of busting early on in the wagering increases.

Deposit -- Deposit is the size of the player deposit. The Deposit input is only visible when the bankroll input is set to "Limited". It is not visible and does not influence results when the bankroll is set to "Standard".

Multiple Hands -- Multiple hands relates to simultaneously playing several blackjack or video poker hands against a single dealer hand. If you are playing 100-play video poker with a total bet of $5, the bet size per hand would be .05 . Set bet size to .05 and "multiple hands" to 100. If you are playing one hand at a time, use the default "multiple hands" value of 1.

Player Hands & Dealer Hands -- When video blackjack is selected, the multiple hands input is replaced with two new inputs -- "player hands" and "dealer hands." These correspond to the number of player and dealer hands in your video blackjack game. Bet size is the bet size on each hand, not the sum of bets among all hands. Again if you are playing one hand at a time, use the default value of 1.

Corr. Between Hands -- Correlation between hands refers to the correlation between payouts of each hand in video poker. A correlation of 0 indicates that each hand is fully independent from one another. A correlation of 1 indicates that the payout is the same for each hand. Most video poker variations have a correlation of 0.10 to 0.15. The correlation between hands input is only visible when a video poker game is selected.

House Edge -- House edge is the house edge of the selected game. For fine tuning to a specific rule set or paytable, you can modify the house edge value from the defaults. Adjust the "Expressed" input selection to change whether house edge is expressed per hand (standard) or per unit wagered.

Standard Deviation -- Standard deviation is the standard deviation of the selected game. For fine tuning to a specific rule set or paytable, you can modify the standard deviation value from the defaults. Standard deviation is expressed in terms of a single hand, so standard deviation remains the same for single-hand and multi-hand video poker. Adjust the "Expressed" input selection to change whether standard deviation is expressed per hand (standard) or per unit wagered.

Final Bet : Initial Bet Ratio -- "Final Bet : Initial Bet Ratio" is the ratio between the average final bet and initial bet. It only influences results in games with possible bet raises, like blackjack and war. The final bet : initial bet ratio input is only visible when playing a game with possible bet raises, and the "Expressed" input is set to per hand.

Expressed -- The expressed input relates to whether the house edge and standard deviation are expressed per hand (standard) or per wager (more relevant for playing a bonus). House edge is defined in terms of initial bet. A more useful figure for bonus play is what I call the house edge per unit wagered. This value corresponds to the average loss on each unit wagered. Select "per hand" to use standard house edge and standard deviation values, which are expressed per initial bet. Select "per wager" to use house edge per unit wagered and standard deviation per wagered.

Load Into Sim -- When the "Load Into Sim" button is clicked, a pop-up window opens with a Java simulator programmed to the calc inputs. You can use option this to confirm and compare calc outputs with simulation results.

 

Outputs

Expected Return -- The expected return is the average gain with the programmed inputs. Positive values indicate a gain. Negative values indicate a loss. Expected Return is expressed in the same units as the bonus and deposit inputs.*

Chance of Bust -- The chance of bust output corresponds to the chance of losing both the deposit and bonus before completing the wagering requirement. This value is only visible (and meaningful) when the bankroll input is set to limited.*

Chance of Gain -- The chance of gain output corresponds to the chance of making a net gain, after completing the wagering requirement. This value is only visible when the bankroll input is set to standard.*

# Standard Deviation Range -- Assuming a normal distribution, 68% of results should fall within the 1 standard deviation range, and 95% of results should fall within 2 standard deviation range.

 

*The limited bankroll EV calculation is based on an original formula, which I have not yet finished. Nevertheless, in its current form, it is usually quite accurate. The limited bankroll chance of bust calculation is based on formulas in Don Schlesigner's book Blackjack Attack (with some minor additions). Neither formula accounts for the distribution of results being non-continuous, the non-normal distribution of games with rare high payouts, and the increased house edge in some games when unable to make a maximum bet. For example, blackjack EV is accurate for smaller bets, but not for larger bets when large full-bankroll bets are likely, increasing house edge above the programmed value. The standard bankroll chance of gain approximates return as a normal distribution. This is a good approximation for blackjack and other games without rare high payouts. However, the distribution of video poker return does not appear like a true normal curve until reaching enough hands to hit several royal flushes. You can use the return & variance simulator to confirm results. I recommend using the simulator, instead of the calc for the games video poker, hold'em high, let it ride, and ultimate texas hold'em. See this list for the minimum number of hands required for accurate results on other games.

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