RedDuke wrote: Sun Feb 16, 2020 2:41 am
There is a 50% the dealer only has the AH and a ~42% chance he has either the JH or KH in addition to the AH, 6.5% chance he has both.
Where are those numbers coming from?
Here are the exact numbers:
Probability the dealer only has the
(2C0 x 16C5)/18C5 = 4368/8568 =
50.98%
Probability the dealer has either the JH or the KH in addition to the AH:
(2C1 x 16C4)/18C5 = 3640/8568 =
42.48%
Probability the dealer has both the JH and the KH:
(2C2 x 16C3)/18C5 = 560/8568 =
6.54%
Given that IW wasn't aiming for exact precision, we can say he was right.
Note: Those numbers are based on a random distribution, but since we've already had action in this hand (3 people passed), the distribution isn't actually random. This issue only shows up with S2's range as S2 has hands in his passing range that should not be there whereas S3 does not. For example there are 560 combos of R+1 in S2's passing range that he would've called with assuming he's a good player. There are also 11 combos of non-euchre hand R+0+3 off ace hands S2 may call with, and I personally would call with R+0+2 off aces if I don't block 2 out of 3 second round suits, which is around 165 combos. Depending how aggressive S2 is, his range will be distorted between 6.53% to 8.59%. This means that S4's range will be slightly stronger than those numbers indicate. So the probability of S4 having just the AH will in reality be slightly lower than 50.98%, and the probability S4 has 1 more trump or both trump will be slightly higher. Nevertheless those numbers are still good approximations.