5 months when I was asked what I want, 7 more for the bag to arrive. Hermes isn't a game to me though, I wasn't after a bag at all and I didn't spend strategically though I did get my bag right after I bought a very expensive pair of boots but now I think that was just a coincidence since another store "stole" the commission on them during the transfer.
I'm very enthusiastic about the Maison, I love their commitment to craft and teaching young people to build things by hand. I love the artists they support with their scarves and the techniques they employ to make their products last a lifetime. I never thought I would spend the money I do with the brand but it's the only house I buy from at that level. I'm a casual person, their products work for my lifestyle whereas Chanel is just too "fancy" for me. I buy beat up old vintage H and new from my local boutique, my store staff knows I LOVE the leather, the production techniques and that I still own all the items I've purchased. They love my enthusiasm more than they love my spending and I get great offers because they know I appreciate the things I buy. My SA/SM offered me a very rare Barenia bag because they know that I will cherish it and also that I'm not afraid of the leather
I agree with everyone, don't buy things you don't want and don't buy things just to get a bag offer. If you want to be offered the exact bag you want in a reasonable timeframe, it's way way cheaper to buy from a reseller. There are zero guarantees with H. If you're not in a rush, I'm still not sure you'll get a favorable outcome if you're measuring your shopping against a bag.
We've covered a lot of this in the past, it's probably worth going back a year on this thread and reading. I've written about the way offers work and also what I know about when/if a SA can offer a bag.