What's value to player when BJ always pays- even when dealer also has BJ?
cottage cheese,
The answer depends on the number of decks. I'll show how to calculate it for 6D.
We have to determine the probability of simultaneous BJ's. For 6D, we get the prob. as
P(2 BJ) = [2*24*96/(312*311)]*[2*23*95/(310*309)] = 0.0021665...
which is roughly 1 in 461.6 rounds.
Now, with normal BS this would be a push, because with BS you don't take "even money". However, with your Unique Rule, this is instead a win of 1.5 units... assuming BJ pays 3:2, of course.
Therefore, the player gains 1.5*0.0021665 = 0.003250..., or +0.325%, which is a pretty good improvement.
Hope this helps!
Dog Hand
cottage cheese,
By the way, I should indicate that this "BJ wins vs. Dealer BJ" rule is worth a lot more to a card counter than the +0.325% (for 6D BS) shown above in this thread, because both the probability of simultaneous BJ's and the counter's wagers increase with increasing count. The actual improvement in EV depends on a number of factors, chiefly the penetration and the bet schedule, and so is most easily found through simulation.
As an example, consider a 6D, H17, DAS game with 5/6 penetration played heads-up by a HiLo counter spreading 1-15 as follows:
<=+1, 1
+2, 2
+3, 4
+4, 10
>=+5, 15
This is the canned 1-15 spread in CVData.
Without the bonus, his EV is +1.120%, but with the bonus, it's +1.568%: an improvement of +0.448%.
I analyzed the CVData output and found that only 3.80% of the rounds had a TC of +5 or more, but the player received 5.22% of his BJ's in these "+5-or-better" rounds.
Hope this helps!
Dog Hand
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