"Frequent_Flyer" <frequent@somewhere.com> wrote in message news:<Ume_a.10682$mB5.727137@twister.southeast.rr.com>...
> I am answering each of your questions here and if you can figure out the
> payout compared to standard 6 deck Vegas blackjack, I would greatly
> appreciate it!
>
> 1) There are 4 decks in the shoe
> 2) You can still win/lose your original bet with the side games
> 3) The straight flush is of 3 cards not 5.
> 4) You can win the bonus on 3 of a kind even if other cards come up. You
> can split a pair of 6s and if you get another 6 on either of the split
> hands, you still win 3:1.
>
>
> FF
Ok. I can't give you a precise expectation for the game, but I think I
can get a good estimate. Actually, I am surprised by the results and
maybe a more precise analysis is in order. I am sorry I really don't
have time to do that. Also, please check my work to see if I made any
mistakes. I am assuming 4 decks, No hole, early surrender, H17, RS4,
DA2 (DOA) for this game (numbers below are in percent- so .54 means
.54 percent of 1 unit).
www.blackjackinfo.com has this game starting with an EV of +.07
percent (player favorable).
Base EV: +.07 (for S17 it's .14)
No Natural Blackjack: -2.675
3 of a kind bonus: +1.95
Straight Flush bonus: +.54
------------------
Total EV: -.115
Below I have details about how I got the 3 numbers for the special
rules. I am surprised because this is a very good game to play. I
wonder if I have made some assumptions that I shouldn't have.
You should use the BS chart from www.blackjackinfo.com when playing
this game. Put in all the rules I stated above and they will generate
a chart for you.
I don't think there will be many strategy deviations for the 3 of a
kind bonus. This is only because there are not many marginal pair
hands where you normally stand but would be ok hitting or splitting.
One possibility is splitting 9s against a dealer 7, in this game you
might want to split instead of stand.
The straight flush bonus also won't have many strategy deviations. If
you have a suited 6,7 against a dealer 2, I think you would want to
hit instead of stand. The same might apply to a suited 8,9 against a
dealer ace. These are both very marginal plays where the chance at the
bonus is worth the deviation.
If you are a card counter, then a whole lot more work needs to be
done. The lack of a 3/2 BJ has a huge effect, and I'm not really sure
if card counting would be successful with that rule. If so, the
bonuses will change many of the index numbers for pairs and straight
flush draws.
Hope this helped and that I didn't make any major mistakes.
Good luck and have fun!
-M
No Natural Blackjack:
--------------------
Uncontested Player BJs happen roughly 4.55% of the time in a 4 deck
game. You lose 1/2 of a unit every time this happens, so you have a
disadvantage of 2.275%. But another factor is that you also lose the
fact that you win against a dealer 21. I think the dealer gets 21
about 9% of the time (not sure if this includes BJs or not) so 9% of
the time that you have BJ you are also pushing instead of winning.
This costs you another .4% so the total EV effect is -2.675%.
3 of a kind bonus:
-----------------
The probability of getting 3 of a kind in first 3 cards dealt is the
chances that the 2nd and third card are the same as the first one
which is: 15/207*14/206 = .0049 Now you also get a second chance if
you split the pair. With multiple deck basic strategy, you split
roughly half the time. Then the other half of the time, there are a
lot of hands that you won't hit (like 10s,Js,Qs,Ks and other pairs
against certain dealer up cards). On these hands you will never even
get a 3rd card, so they reduce the chances of getting the bonus. This
happens about 1/3 of the time. So we have:
.49 * 1/2 * 2 (half the time you get 2 tries because you split)
+
.49.* 1/2 * 2/3 (the other half the time, only 2/3 of hands get
another card)
---------
.0065
It's worth 3 units every time it happens, so the EV addition is .0065
* 3 = .0195 or 1.95 percent.
Straight Flush bonus:
--------------------
First, I will just determine the chances of getting a straight flush
on any first 3 cards out of 4 decks. The Aces and 2/K act differently
from the rest because I assume you can't have a straight go "around
the horn" and I also assume that Ace can be high or low.
For example, starting with an Ace (which will be 1/13 of the time) you
then have 16 cards that could continue a straight flush (the 2,3,K,Q
of the same suit). After drawing any one of those, there are now only
4 possible cards left that can finish the flush (2 if you drew the 3
and so on).
Ace: 1/13 * 16/207 * 4/206 = .000115
2/K: 2/13 * (4/207 * 4/206 + 4/207 * 8/206) = .000173
Rest: 10/13 * (8/207 * 8/206 + 8/207 * 4/206) = .00173
--------------
Total: 0.002018
But there are a number of starting hands where you would stand and not
get a 3rd card, such as all hard 17 - 20. I estimate that these make
up about 1/3 of the total hands, so we will multiply our probability
of getting the straight flush by 2/3 for a final total of .00135. To
be simple, let's say it is worth 4 units all the time, so the added EV
is .54
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