Risk



Risk given no goal and no time
constraint  This is the Simple Risk of Ruin formula on
Blackjack Attack 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. 

Risk given no goal but a time
constraint  This is the trip ruin formula in Blackjack
Attack 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 Blackjack Attack 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 Blackjack Attack
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 Blackjack Attack 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. 

Probability of reaching a goal
before going bankrupt with no time constraint  This formula
is found on Blackjack Attack 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. 

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. 
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 goal and
desired probability  This is the formula on page 137 solved
for time. Here, you calculate the needed number of hands. 