Quote:
Originally Posted by lardydardy
Are the fortune cookies in the spins equally distributed? I keep getting multiples and I'm not sure if it is one of those McDonald's monopoly type things or not where one or two cards are rarer
The cookies are equally distributed, so if you've collected 9 out of 10, the probability of getting the 10th on your next try is 1/10, and no matter how many attempts to get it you've failed already, the average number of cookies that you'll draw until you get it is exactly 10 (incl. the last, successful, draw).
See
Wikipedia: Geometric distribution for the maths; for the collection of the 10th cookie, p=1/10.
In general, if you already have n cookies, then the probability of getting a new (not duplicate) cookie on the next try is of course p=(10-n)/10, hence the avg number of tries until the number of unique cookies in your collection increases from n to n+1 is 1/p = 10 / (10-n).
Therefore, once you restart with 1 cookie (after you get the 10 BI prize, you'll automatically get 1 cookie for the next collection cycle without playing), the avg number of cookies you'll need to draw to collect 10 different ones is 10/(10-1) + ... + 10/(10-9) = 10 * (1/9 + 1/8 + ... + 1) = 10 * H_9 = 7129/252 ~ 28.2897. (H_9 denotes the ninth
harmonic number.)
Hence the rake is ~5% (~4.992%, actually). Indeed, for the $1 BI, the avg value of a cookie is $10 / 28.2897 ~ $0.35349. The 3 entrants get a $4 prize pool 42% of the time, a $8 one 8% of the time, and 3 cookies (1 per player) worth ~$1.06046 in total 50% of the time. Thus the avg prize pool is $4*0.42 + $8*0.08 + $1.06046*0.5 ~ $2.85023. Dividing it 3, we obtain the prize EV of $0.95008 per player and the rake value of $0.04992.
Last edited by coon74; 03-18-2018 at 03:40 AM.
Reason: correction of the harmonic number