We analyze a 19-night photometric search for transiting extrasolar planets in the open cluster NGC 1245 .
An automated transit search algorithm with quantitative selection criteria finds six transit candidates ; none are bona fide planetary transits .
We characterize the survey detection probability via Monte Carlo injection and recovery of realistic limb-darkened transits .
We use this to derive upper limits on the fraction of cluster members with close-in Jupiter-radii , R _ { J } , companions .
The survey sample contains \sim 870 cluster members , and we calculate 95 % confidence upper limits on the fraction of these stars with planets by assuming the planets have an even logarithmic distribution in semimajor axis over the Hot Jupiter ( HJ - 3.0 < P / day < 9.0 ) , Very Hot Jupiter ( VHJ - 1.0 < P / day < 3.0 ) , and an as of yet undetected Extremely Hot Jupiter ( EHJ - P _ { Roche } < P < 1.0 day ) period ranges .
For 1.5 R _ { J } companions we limit the fraction of cluster members with companions to < 1.5 % , < 6.4 % , and < 52 % for EHJ , VHJ , and HJ companions , respectively .
For 1.0 R _ { J } companions , we find < 2.3 % and < 15 % have EHJ and VHJ companions , respectively .
We do not reach the sensitivity to place any meaningful constraints on 1.0 R _ { J } HJ .
From a careful analysis of the random and systematic errors of the calculation , we show that the derived upper limits contain a \pm ^ { 13 \% } _ { 7 \% } relative error .
For similar photometric noise and weather properties as this survey , observing NGC 1245 twice as long results in a tighter constraint on HJ companions than observing an additional cluster of similar richness as NGC 1245 for the same length of time as this survey .
If 1 % of stars have 1.5 R _ { J } HJ companions , we expect to detect one planet for every 5000 dwarf stars observed for a month .
To reach a \sim 2 % upper limit on the fraction of stars with 1.5 R _ { J } companions in the 3.0 < P / day < 9.0 range , we conclude a total sample size of \sim 7400 dwarf stars observed for at least a month will be needed .
Results for 1.0 R _ { J } companions , without substantial improvement in the photometric precision , will require a small factor larger sample size .