Wordy

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StonedPetitioners

   

the_origin_story

"I'm thinking about running 20 Persistent Petitioners in my EDH deck with Thrumming Stone..."
"That's definitely not enough."
"How many would you run?"
"I don't know? All of them?"              

"I don't know" is possibly one of my favorite phrases to hear. It's an open invitation for discussion and exploration. But this case of IDK stuck with me pretty hard, even after the conversation drifted elsewhere. I had to know exactly how many Petitioners I should run to ensure a brutal and efficient mill kill. I had to. Maybe it had to do with the fact that I'm cheap and I didn't want to spend $50+ dollars for a stack of commons. Maybe it has to do with my hatred of dead draws in commander. Regardless, my mission had started...

the_obvious

The answer for how many petitioners to run in EDH is obvious if you are trying to one-shot a player, it's 32. If you ripple out 32 advisors with Thrumming Stone, you can pay for their effect 8 times, which results in 96 cards being milled. Since every player starts with a hand of 7, and a commander or two in the command zone, milling 96 ensures one player is dead. The more interesting thing for me as a semi-competitive filthy-casual was this: How often will rippling out 32 petitioners happen with the first one we play? Since your deck is randomized,  you're not always guaranteed to hit all 32 with ripple*--- I wanted to know exactly how often I could expect to succeed.

the_experiment

Simulating Thrumming Stone's success rate with Persistent Petitioner/Rat Colony effects isn't too difficult--- you just create a random list of zeros and ones, where zeros are not petitioners and ones are, then simulate the ripple 4 effect over that stack. The hard part is deciding the arbitrary conditions to seed my experiment with. Since I just wanted to see results and make cool graphs, I jumped in with the following:

• Commander: Any Blue Commander
• Your starting hand: 
• 2x Islands
• 1x Sol Ring
• 1x Mana Vault
• 1x Thrumming Stone
• 1x Persistent Petitioner
• 1x Anything-Else
• Turn 1:
• Draw 1
• Island -> Sol Ring -> Mana Vault
• Turn 2:
• Draw 1
• Island -> Thrumming Stone -> Persistent Petitioner

Assuming this start, the deck has 90 cards left by the time we cast our first petitioner with a Thrumming Stone on the field: 7 for your starting hard, 1 for your first turn, 1 for your second turn, and 1 for your commander, for a total of 10 cards. Since one petitioner is assumed to be in our hand there will be 31 petitioners left in our deck of 90 cards.

the_results

I simulated rippling on turn 2 a total of 10,000 times, and generated the following histogram showing the probability for the number of petitioners we can expect on the board:

The result? If we ripple with one petitioner on turn 2, there is a 65% chance we get all 32 petitioners out of our deck and a 35% chance we get less than 10. Not terrible but not inspiring. What if we add more petitioners?! What if we had less?! Wonder no more and watch the pretty gif:

We can see from the gif that once you put about 30 petitioners in your deck you have about a 50% chance at getting the one-shot kill. And the odds just keep getting better from there. To make things easier, if you want to know how successful you'll be at one-shotting people with X petitioners in your deck, consult this table:

.		Petitioners in Deck	Probability of Getting All Petitioners in One-Shot
		4	<0.01%
		5	<0.01%
		6	<0.01%
		7	<0.01%
		8	<0.01%
		9	<0.01%
		10	<0.01%
		11	<0.01%
		12	<0.01%
		13	<0.01%
		14	<0.01%
		15	<0.01%
		16	0.03%
		17	0.03%
		18	0.11%
		19	0.19%
		20	0.47%
		21	0.97%
		22	2.52%
		23	7.36%
		24	18.4%
		25	26.35%
		26	34.37%
		27	41.26%
		28	47.62%
		29	52.42%
		30	57.5%
		31	61.98%
		32	65.33%
		33	68.78%
		34	72.27%
		35	75.38%
		36	77.63%
		37	79.57%
		38	81.52%
		39	83.49%
		40	85.87%
		41	86.39%
		42	88.94%
		43	88.94%
		44	90.08%
		45	91.85%
		46	92.24%
		47	93.26%
		48	94.02%
		49	94.66%
		50	95.3%
		51	95.59%
		52	96.06%
		53	96.72%
		54	96.74%
		55	97.28%
		56	97.54%
		57	97.94%
		58	98.18%
		59	98.62%
		60	98.71%

So how many petitioners should you run? Hell if I know. If you want to one-shot people 98% of the time, put 58 in. If you're ok with one-shotting people 75% of the time, play 35. I can only hope the table above helps someone, or else what the hell have I been doing with my time. 

Till next time, cheers. 

-AJ



*Every time I go to thrum, it's expected that my petitioners will always be at the bottom of my deck. Until, of course, I lend the deck to a friend, in which case all of the petitioners are guaranteed to be at the top of the deck.