what are the chances of winning?

Quite simple, your chance of winning any giveaway is 1 divided by the number of total entries, including your own.

(EDIT: In other words your chance of winning is equal to everyone elses, although other restrictions may prevent you from entering some giveaways)

https://www.steamgifts.com/discussion/IRi4K/analysis-of-winning-probability
a more in-depth answer

50/50.

Either you win, or you don't.

You'll increase your chances by joining group and invite only giveaways (as these usually have lower amount of entrants). You should also make your own giveaways here, this will increase your steamgifts level which will give you access to giveaways that are level restricted.

Am here almost 9 years - won 27 games... Last game won 1 year ago, other game 2 years ago..
Here are ppl who have account for 3 years and won 560 games...
Consider urself

According to steamgifts ( https://www.steamgifts.com/stats/community/giveaways ), there in general 600 entries for public giveaway (so 0,167 % of win) / 88 Entries for Invite only (so 1,13 % of win) / 55 for Group (1,82 %) / 68 for Whitelist (1,47 %)
So two simply advice for you :

• Check sometimes discussions for some invite giveaway.
• Check description, because you can found some secret giveaway in it sometimes (like this one for HotShot Racing ( https://www.steamgifts.com/giveaway/KO1N2/hotshot-racing ) i have create a couple of week ago / 500+ entries for the public / only 15 and 8 entries for the invite giveaway hidden in the description)

Your total chance to win stacks with every giveaway you enter. The less people, the more likely to win. But that doesnt mean you have to enter everything you can.