On average, if I do not get wiped out, I should gain $125. Number of Trades (Flips): I am going to play the flipping game 250 times. The “Stop Trading” Equity: If during the simulation, my Risk Capital falls below this amount, I am “ruined.” I have lost the game and cannot place any more bets. The simulator will choose different amounts, and for this case I am going to analyze with Risk Capital from $1 to $500. To help out in this analysis, I use a modified version of my Monte Carlo simulator spreadsheet for Excel, which you can freely download right here: (There is a more advanced simulator available at my Calculators page.) To run the analysis, I need a few numbers: The Starting Equity: this is the amount I will have before I start playing the game. Since eventually we will progress to evaluating complicated trading strategies, I prefer to use Monte Carlo simulation to get the risk of ruin results we desire. For a simple coin flip like this, you could derive an answer directly using mathematical equations and probability principles. You can guess, of course, but most people would rather know up front the required amount of capital to safely play this game without risk of ruin. What about the middle? What if you had $2, or $5 or $10? Are you likely to get ruined if you start with any of those amounts? Without doing some calculations and analysis, you just do not know. Those are 2 extremes – very little capital, versus a great deal of capital. Your risk of ruin (getting wiped out) is really, really small. With this much capital, the chances of enough tails coming up to wipe you out is infinitesimally small (not zero, though). In other words, you are ruined! Game Over! Alternatively, let’s say you start with $1,000,000. Whoops, you lose your $1, and since that is all the money you have, you have no money to bet on the next flip. The question is “how much capital should you start with to play this game?” Let’s say you start with $1 and the first flip is tails. Let E 1, E 2 and E 3 be the events of getting 2 tails, 1 tail and 0 tail respectively.At this point, you know you have a long run profitable game (or trading strategy). If two coins are tossed at random, what is the Two coins are tossed randomly 120 times and it is found that two tailsĪppeared 48 times and no tail appeared 12 times. (iv) P(getting zero head) Number of times zero head appearedĪre tossed randomly, the only possible outcomesģ. (iii) P(getting one head) Number of times one head appeared (ii) P(getting two heads) Number of times two heads appeared P(getting three heads) Number of times three heads appeared Let E 1, E 2, E 3 and E 4 be the events of getting three heads, two heads, one head and zero head respectively. Number of times three heads appeared = 21. (i) three heads, (ii) two heads, (iii) one head, (iv) 0 head. So, by definition, P(F) = \(\frac\).Ģ. If three fair coins are tossed randomly 175 times and it is found that three heads appeared 21 times, two heads appeared 56 times, one head appeared 63 times and zero head appeared 35 times. = 3 (as HH, HT, TH are having at least one head). = Number of outcomes having at least one head (i) Number of favourable outcomes for event E The possible outcomes are HH, HT, TH, TT. = P(T) = total number of possible outcomesġ. Therefore, P(getting a tail) Number of favorable outcomes (ii) If the favourable outcome is tail (T). = P(H) = total number of possible outcomes Therefore, P(getting a head) Number of favorable outcomes (i) If the favourable outcome is head (H).
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