Is a postal entry competition worth the £0.54p stamp? I enter a the ITV 'Loose 'Women' competition every week by postal entry as the £0.54p stamp is cheaper than the £2.00 text entry.
However. The TV channel only picks out one person's postal entry to be entered into the main draw along with all the text entries.
My question is, if there are 1 million text votes and 5000 postal votes, what are my odds of winning by text and postal entry? 
Hopefully then I can decide if it's worth the extra £1.46 to enter by text!
This is a matter of great importance! There are designer handbags to be won!
 A: If all 5000 postal entries are converted into a single text entry, then the postal entries should cost $\frac{1}{5000}$ as much as a text, in order to be equally expensive.  However, the postal entries cost approximately $\frac{1}{4}$ of a text.  Hence the postal entries are a poor value compared to texts, regardless of the worth of the handbags or other prizes.
Another way to think about it, the 5000 postal customers are paying 2700 pounds between them, for a single entry. (not to mention the cost of all those envelopes and paper).  They could instead get together, chip in for a text entry, and have 2698 pounds left over.
Hence the first takeaway is "don't bother entering by postal entry".
The second takeaway is "don't bother entering by text entry".  All contests, including this one, are designed for one purpose only: to make money for the contest organizers.  You would be better off saving your 2 pounds each week.  At the end of the year you'll have over 100 to spend, and you can get quite a nice bag for that sum.
A: The premise of this question seems to be incorrect:
ITV's terms and conditions 4.1 suggest the winner is drawn randomly from all entries.  Ofcom monitored the competition in 2011  and received clarification that "each entry has the same chance of
being selected, irrespective of the method of entry".
The specific T&C of "Loose Women" state that if you enter twice by phone or text, you do get a third entry for free (still cheaper to enter by post), but as any entry has negative expectancy (loses money) the optimal strategy for this game is not to play.
If the dream of winning is worth more than the price of a stamp, then the best method of entry is to send a postcard.
