I returned from a recent overnight trip that involved an intermediary
stop at another casino to primarily cash coupons. At the first stop I
put in a minimal amount of play on a triple play NSUD machine (with
0.25% CB) that is basically a break even play for me, but helps generate
comps and bounce back. I hit a Royal in about 680 throws (or 2040
actual hands). Odds of this event in this time period are about 4.5%.
Obviously a good start to the trip, but not the main purpose of the
outing.
I continue to the primary destination where I intend to play single line
Super Aces with a 10X multiplier that makes this game much more
advantageous than the one I just came from. I make the mistake of
calling the wife en rout and mentioned the earlier Royal (you can see
where this is heading).
I've endured some painful, but statistically relatively insignificant
droughts before. Most noticeably on the triple play NSUD game where
I've had 26,000 hand droughts on deuces (1 in 125 type odds) and as an
extension of that drought one set of deuces in 46,000 hands (1 in 550
type odds). This recent trip though while not a huge financial hit
thanks to the earlier Royal, really strained my belief in the integrity
of the game I was playing.
Final results consisted of roughly 5700 hands of single line Super Aces.
I had no Royals (86% chance of this happening), no quad Aces (25%
likelihood), no quad 2-4's (5% chance) and exactly ONE 5-K type quad (an
occurrence of less than 1 in 1000). The lone quad came holding a pair.
In summary a quad of any type is about a 1 in 417 hand occurrence for
this game. I received one quad in about 13.5 quad cycles. I calculate
the probability of such an occurrence (1 or less quads in 5700 hands) at
almost 1 in 60,000.
I'm sure many have experienced such devastating droughts, but from the
probability of occurrence this 1 quad in 5700 hands was a new low for
me. Fortunately I've had 5 sets of Aces in 12,000 hands playing this
game on previous trips, so I'm still well in the black despite being way
behind now on other quads.
While calculating the odds of this occurrence for a set number of hands
is relatively straight forward using Poisson, I'm still uncertain as to
how unlikely this trip event is given that this is a small subset of the
overall continuum of trips. Assuming I take a trip like this every week
for a year and thus play 296,400 hands (52 weeks * 5700 hands), what are
the odds of experiencing at least one streak of only one quad in 5700
hands over the duration? I suspect the odds will still be very
unlikely, but I'm trying to rationalize that a 1/60,000 type event is
not totally unexpected in this game. For now I'm still a bit numb.
Thanks!
SB
PS Reminder to self to never report early positive fluctuation trip
results to wife. I'm still taking heat for explaining how a trip with a
Royal turned into a net loss.