aceside
aceside
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Joined: May 14, 2021
May 22nd, 2026 at 6:41:57 AM permalink
Subtracting the original house edge of 0.02185 from each of your calculation EV numbers, we get the list of EV changes after removing the whole rank of four cards:
= -0.003925
= -0.001571
= -0.000036
= 0.000562
= 0.00426
= -0.002556
= -0.007087
= -0.014476
= -0.048625
= -0.047436
= -0.043571
= -0.034223
= -0.024949.
So, the EV change is snake shaped.
gordonm888
Administrator
gordonm888
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Joined: Feb 18, 2015
May 22nd, 2026 at 7:25:09 AM permalink
Any starting 2-card hand in UTH for which you bet 4X is profitable for player.

Let's count the number of times that a rank appears in a (+EV) 4X opening hand. Unsuited hands, including pairs, will count as 1 and suited hands will count as 0.25.

Ace___13
King___10.75
Queen___7.5
Jack___5
Ten___5
Nine___4
Eight___4_____A8, K8, Q8, 88
Seven__3.25
Six___3.25
Five___3
Four___2.25
Three___2.25_____A2, K2s, 33
Deuce___1.25_____A2, K2s

When eliminating ranks, this is a relative frequency of profitable starting hands in UTH that are eliminated. Of course, AA is far more profitable than 33 so this is far from a complete story.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
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