![]() ![]() The odds are exactly the same for the Tall bet. The following is the probability any given total has NOT been rolled at least once within x units of time: This will not matter for purposes of adjudicating the bet, because events still happen one at a time. In other words, the time between events follows an exponetial distribution with a mean of 1. Assume the time between events has a memory-less property, with an average time between events of one unit of time. ![]() Imagine that instead of significant events being determined by the roll of dice, one at a time, consider them as an instant in time. Integral Calculus - This method is surprisginly easy with the use of an integral calculator.For the Small and Tall it would require a 6圆 transition matrix and for the All a 12x12. Markov Chain - This method is tedious and time consuming. ![]() However, for mathematical purists like me, simulations are always so intellectually unsatisfying.
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