A Monte Carlo simulation (110,000,000 trials) indicates the probabilities of going bust on drawing the first, second, third, etc. card. What’s perhaps a little counterintuitive here is that your chance of going bust is greatest on the very first card.

The probability of not going bust at all is indeed very low at about 0.00818, or about 1 in 122.

One possible approach to an analytical solution would be to find the probability of going bust exactly on cardCode:`Card No. P(Bust) 1 0.076893664 2 0.070856309 3 0.065324627 4 0.061534691 5 0.056613664 6 0.052106036 7 0.048971273 8 0.044997109 9 0.041377409 10 0.038879827 11 0.035692882 12 0.032733609 13 0.030703064 14 0.028123509 15 0.025783191 16 0.024155927 17 0.022094164 18 0.020206318 19 0.018910109 20 0.017293673 21 0.015778855 22 0.014740900 23 0.013469982 24 0.012283309 25 0.011463027 26 0.010425500 27 0.009485545 28 0.008849800 29 0.008035573 30 0.007307218 31 0.006802091 32 0.006170755 33 0.005588500 34 0.005224036 35 0.004708727 36 0.004263855 37 0.003956445 38 0.003580955 39 0.003235282 40 0.003005618 41 0.002701982 42 0.002444018 43 0.002256636 44 0.002036473 45 0.001834173 46 0.001695718 47 0.001522209 48 0.001369009 49 0.001257355 50 0.001127145 51 0.001015691 52 0.000934200 Never 0.008178364`

and summing these individual probabilities over 1 ≤n≤ 52. Subtracting this sum from 1 will give the probability of not going bust.n