You asked for it (longish answer)
CVCX has three major parts. The sim viewer and 150,000 canned sims. The simulator for custom sims. And the Calculators. The Sim Viewer can be used to examine canned sims or your own sims and calculates optimal bets, win rates, risk, standard deviation, EV, DI, SCORE, N0, CE and a bunch of other standard sim statistics. There is no Calculate button, You change the bankroll, penetration by the card, spread, rules, desired risk, back-counting, etc and the numbers instantly change. This function was use to create the Chapter Ten tables in Blackjack Attack 3rd edition.
The calculators use the results of the sims and apply formulae in Blackjack Attack to answer many questions. Below is a list of the calculators along with page references to BJA 3e:
Risk
- Risk given no goal and no time constraint - This is the Simple Risk of Ruin formula on BJA page 112. The result is the risk of ruin with no limit on the number of hands and no quit point. Simply set the bankroll. The Win Rate and Standard Deviation are automatically set to the values for the CVCX generated bets. Click Calculate to get the Risk of going Bankrupt.
- Risk given no goal but a time constraint - This is the trip ruin formula in BJA page 132. Risk is still calculated, but for a specified number of hands. The risk is lower than with the above calculator since you have a quit point.
- Risk given a goal and time constraint - This is called a double barrier formula and is found on BJA page 137. We are calculating the risk of bankruptcy before hitting a goal or playing a number of hands. Here, you set a point at which you will stop playing. The risk is lower than the above calculator since you will stop playing if you hit one of two quit points: Time or Goal.
- Risk given a goal and no time constraint - This is a modification of the above with the number of hands removed. It can be found on BJA page 139. Here you quit if you hit a goal, but there is no limit on number of hands.
Goal
- Probability of reaching a goal before going bankrupt given a time constraint - This formula is found on BJA page 136. Here you specify the maximum number of hands you will play, a bankroll and a goal. The result is the probability of reaching that goal before going bankrupt or hitting the specified number of hands. When this calculator is selected, you also have the ability to create the top seven charts in the Charts button on the tool bar.
- Probability of reaching a goal before going bankrupt with no time constraint - This formula is found on BJA page 138. This is the same as the above calculator except that there can be an unlimited number of hands. Therefore, the probability of reaching the goal is a little higher.
Results
Range of Probable Results - Here, you specify the number of hands you will play and a probability and the range of your results is calculated. For example, if you specify 95%, and the answer is -664 to 1346, then 95% of the time your winnings will be somewhere between -664 and 1,346 units. The higher the percent that you specify, the wider the range. For the statistically minded, click on the Chart button. A chart will be generated that shows the standard normal curve and the area under the curve that reflects the probable range of your winnings.
- What results can I expect given time and probability of reaching goal without ruin - This is the formula on page 137 solved for goal. Your probable results are calculated. You must give a probability. For example, if you specify 98%, you will hit the calculated goal 98% of the time without going bankrupt within the specified number of hands.
Actual
Probability of your actual results - Here you can enter the actual casino results from a trip to see how far you were from the expected results. Set the number of hands played and how much you won or lost. If the answer is 50%, you won the amount that you should expect. If you won more than you expected, the answer will be the percentage of times that you should expect at least that result. You can also chart your results against the standard normal curve by clicking on Chart. If the chart is half red and half green, you won the expected amount. If you won more than you expected, the green area shows the time where you would expect at least the amount won. This is what is known as being on the good side of the curve.
Bankroll
- What is the required bankroll given a goal and time constraint - How much do you need to avoid bankruptcy? This is the formula on page 137 solved for bankroll. Here, you enter the number of hands you will play on a trip, your goal and the desired probability of reaching that goal. The required bankroll is calculated.
- What is the required bankroll given a goal and no time constraint - How much do you need to avoid bankruptcy? This is the formula on page 139 solved for bankroll. This is the same as the above calculator, except there is no limit on the number of hands played.
Time
- Hands required given risk of ruin and time- This is the formula on page 137 solved for time. Here, you calculate the needed number of hands.
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