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A plat ingot ~every 4 battles with the Collector's Catalog sounds about right, yes. Statistically, you'll get a Trap every 20th battle with the Connoisseur's Catalog.
After you've gained enough stats to comfortably drop accessories like Sorceror's Marks or Warrior's Wristbands, I'd add the Collector's Catalog first. Add the Connoisseur's Catalog second as soon as you feel you can get away with it.
You'll get a lot of platinum ingots during turtle farming either way.
But if you use the one to get rare item, you might get the rare item in which case you won't get the bonus rates from the normal one (there's still a 1% RNG but you lose tons of drops in the end). There was a post on another forum about it.
Using only the normal catalog allow you to get both the rare & normal drop.
When checking for drops, the game checks rare first; if you get the rare drop the game doesn't even check the common drop. Therefore equipping the Connoisseur Catalog results in a small drop in the chance to get a common drop. In specifically the case of Adamantoise, with no catalogs and a 5-star battle rating, you have a 5% chance to get a Trapezohedron and a 23.75% chance at a Platinum Ingot (overall 28.75% at a drop). With Collector Catalog only the Platinum Ingot chance increases to 35.625% (overall 40.625% chance at a drop). With both catalogs the chances are 5.5% for Trapezohedron and 35.4375% for Platinum Ingot (overall 40.9375% chance at a drop).
If you have no need for Trapezohedrons whatsoever and only care about gil, it's better to only wear the Collector Catalog. In most cases, if you have room for both Catalogs you should equip both.
Each Trapezohedron costs 2 million gil, and Platinum Ingots sell for 150,000 gil each. Therefore, you need to farm 13.333 Ingots (rounded up to 14) to buy a Trapezohedron. With a drop rate of 93.75%, you'll need to fight about 15 battles on average to obtain 14 Platinum Ingots, so on average, you'll need 15 battles to obtain a Trapezohedron. Meanwhile, if you play on Normal Mode using Connoisseur Catalogs, you'll need 18.18 battles on average to obtain one Trapezohedron, so the farming will likely take longer. With Easy Mode, the enemies also have reduced stats, which further lowers the time spent for grinding.
I'm gonna have to try this because all I need is the Treasure Hunter achievement and it is breaking me! Gil is so hard to come by in this game.
This true but the connoisseur's catalog rolls the rare drop first and there have been several times when the toise doesn't drop anything.
Someone on this thread mentioned that statistically you'll get a trap every 20 toises with the connoisseur's catalog. The problem is the first 19 toises you're unlikely to get plat drops. So if we assume that a trap drops for every 20 toises with the connoisseur's catalog equipped that's a lot of time grinding. Assuming you're using easy mode to farm and have the collector's catalog equipped which practically guarantees plat drops I will make more gil that I can use for anything than needing a trap to make an ultimate weapon. The connoisseur method vs. the collector method means I waste IRL time using the connoisseur method to get one trap while the collector method I will make 3 million gil for 20 toises which means I've already bought the trap while you're still farming for it and halfway to buying another.