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Dominion General Discussion / Re: Grand Market vs Platinum
« on: October 23, 2012, 01:35:44 pm »I did a quick expected $ return similar to yours. Except it breaks down each case (so odds of $21 would be 24.72% and so forth) and multiplied it by the dollars it was supposed to give you.The odds of 4 Col/Plat are pretty low (.05%). This has virtually no impact on expected utility.Yeah, a simple case is 4 Colonies and 9 GMs.QuoteActually, the value of drawing another card drops heavily when you draw your entire deck
Only when you can overdraw your deck with spare drawing capacity.
If you add a Platinum, you might end up with 4 Colonies and Plat in hand next turn.
If you add a GM, you are guaranteed $20.
The odds of hitting $23 with Plat are 35.7% (No Gm on the bottom of the deck).
Odds of hitting $21 or more coin are 60.4% (odds of there not being two Gm on the bottom of the deck).
Odds of hitting $19 or more coin (break point for Col + Prov being 18) are 77%.
Ironically, (I'm not totally sure why this is...) the expected return comes out as $20 (I double checked and my total probabilities added is equal to 1).
Now given these two options. I'm pretty sure GM is better here (as you are guaranteed $20). Also in general, I would agree with DonDon that cantrip money is usually better than treasure money, as long as you aren't extremely over-drawing your deck CONSISTENTLY (ie. a crossroads deck, would not be consistent imo).
For math purposes, I did 5/14*9/13*8/12*7/11*6/10 for each succession by adding another n/n+4 on top. Read Jomini's for more understanding.
There may be a flaw in my math, so please feel free to yell at me