# UBT Tournament Teaser

Discussion in 'Blackjack Tournament Strategy' started by Joep2, May 17, 2006.

1. ### TXtourplayerExecutive Member

Back to bed...LOL

Thanks Ken, I caught it now. The doctors right, I don't need to be going anywhere for a while and after missing that question going to play in casinos tournaments for sure...LOL.

2. ### tirle_bjMember

DD on hard 20

Good job, Ken! Here's the next question.
Actually DD (78.79%) is 1.77% better than Stand (77.02%). Arlalik and I just figured out the optimum playing strategy for splitting tens in this case.
Here is the question:
You've calculated two different scenarios:
- split but not hit (74.92%)
- split and hit 12 but not 13 (75.17%)
Who can tell us - does the best strategy for Split make any better than Stand? And what is the probability to advance?
Here is the hint...
On the first hand we have hard 12, hit and busted out after getting T.
According to second approach we need to hit second hand 'til 13. So if say we have one busted hand and the other 13 thrugh 16 what are our chances to advance?... O%.
You guys have until tomorrow midnight, after that the answer will be posted. Correct answer will win a Dinner for two.

3. ### ReachyNew Member

Not sure whether any of you guys are awake....

I'd like to have a stab at your question Tirle-BJ but I'm not sure I understand what you want us to figure out. I guess it's about 4am in the US as I write this so I may have to wait for the answer but are you asking whether there is a different strategy for splitting that gives better odds than standing? Or are you asking what we should do with the second split hand assuming the first one has busted?

regards

reachy

Last edited: May 23, 2006
4. ### S. YamaActive Member

the second hand

Reachy, just in case you read this before tirle gets up and have a chance to answer.
It is about what to do with the second hand.
Aftre busting the first hand, do you hit the second one untill its total is 13, or 14, or 15, and so on?

Another good one, guys!

S. Y.

5. ### tirle_bjMember

both hands

Thanks for comments, Yama. Actually we need the optimum playing strategy for both hands and related probability to advance.

6. ### ReachyNew Member

so....

Do we know what hands we've been dealt after the split?

7. ### tirle_bjMember

well...

Reachy, in USA after splitting hands we play out first hand first and then second. The only exception is (A,A).
You need to find out how to play first hand and then based on its outcome how to play second.
Good luck.

8. ### ReachyNew Member

Is the first hand T,2? That's what I'm not clear on. Or are you looking for a best overall strategy for a range of hands?

Sorry.

Reachy

He's asking for the best strategy for whatever hands arise.
You'll need to determine the best strategy for hand one. (Do you stand at 12? Do you stand at 13?)

Then, you'll have to determine the best strategy for hand two given the total of hand one. So, assume hand one is 12, how do you play hand two. If hand one busts, how do you play hand two, etc.

These kinds of questions can quickly get unmanageable for a spreadsheet. It is possible that playing hand two optimally might change what the decision should be for hand one.

I haven't tackled this one yet because I'm busy with other projects today.

10. ### ReachyNew Member

Thanks Ken

Thought that was what I was supposed to do. Massive job!!! Need more time Tirle-BJ!!!!

Incidentally I think I've figured out the infinite deck thing. I've made a table in excell that seems to work. It comes out with the same figures as in your other post.

Cheers

Reachy

11. ### S. YamaActive Member

That's what I suspected but, didn't have time to do the numbers.
Wonder what is the result if we hit not only twelve, but also thirteen, (yep, let's check hitting fourteen, too) on the first hand, and then use the "special technique" for playing the second hand.

S. Y.

12. ### S. YamaActive Member

ain't bj tournaments great?

You open one door only to discover two more.

Also, how to play the second hand if the first one is 21, 20, 19, and 18.
I think, without doing the numbers, that we are stacked with plying "no bust" strategy on the second hand if the first one is seventeen.

S. Y.

13. ### tirle_bjMember

time extention

Well guys, your time is running out, so we're adding another 12 hours with our complements. (May 24th, noon PST)
You're on the right track, Yama - keep going.

14. ### ReachyNew Member

I need to go to bed now. I gave it my best shot but I just don't think I can figure it out. I thought I had sussed the infinite deck calculations but I'm not so sure now. It's the 4 x 10 value cards that bother me. Need Deep Blue computing power...

Anyway, after all that, my plan. If hand 2 is 17+ stand on both hands. Otherwise hit hand 1 to 17+. If you bust, DD on hand 2 regardless (i'm sure the odds are better for DD than hitting or standing after some of the recent posts!!). If successful in hitting to 17+ on hand 1 do not bust on Hand 2 i.e. stand. So basically what Mr Yama said (with a couple of bells on!)

Must sleep!!!!

Cheers

Reachy

Reachy, based on your last post, you may be confused about the dealing order after a split.

Split TT, and you'll be dealt one card on the first hand and then you'll have to decide how to play it. Once you stand, you'll get a card on the second ten and proceed from there. In other words, you don't get a sneak preview of hand two before deciding anything on hand one.

Since tirle extended the deadline, I'm working on it.
So far, I have determined the optimal hand2 strategy given the final hand1 total. Here's what I have for that:

If hand1 is stiff, hit hand2 to 17 or better.
If hand1 is 17, hit hand2 to 16 or better.
If hand1 is 18, hit hand2 to 13 or better.
If hand1 is 19,20, or 21, hit hand2 to 12 or better. (Don't bust.)
If hand1 busts, hit hand2 to 18 or better. (Yep, hit hard 17.)

Now I still have to backtrack and determine the optimal strategy for hand one, and figure the overall chance of advancing.

tirle, I think I have it, and the answer to your question: "Is optimal-split strategy better than standing?" is No.

Restating tirle's problem:
BR2 has 262K, bet 100K, doubled a hard 5 for 90K. (Has 190K bet and is stiff now.)
BR1 has 265K, bet 100K and has a pair of tens.
Dealer has 10 up.

For BR1, Doubling for 90K is the best play (78.79%), Standing with 20 is second best (77.02%), and splitting with optimal play post-split is third best (76.34%).

If you split the tens, the best strategy is to hit the first hand to 14 or higher.
Then use the strategy I mentioned in my last post for hand two:
If hand1 is stiff, hit hand2 to 17 or better.
If hand1 is 17, hit hand2 to 16 or better.
If hand1 is 18, hit hand2 to 13 or better.
If hand1 is 19,20, or 21, hit hand2 to 12 or better. (Don't bust.)
If hand1 busts, hit hand2 to 18 or better. (Yep, hit hard 17.)

This whole process succeeds in advancing 76.34% of the time.
Infinite deck used throughout.

17. ### ReachyNew Member

I was confused

My only experience is Global Player and they deal both hands so that's what I based it on. Oops! Now after a good nights sleep I'm going to have another stab at it basedon the information in your 2 posts Ken.

Thing is I told my wife that I was going to win a meal for 2 in Vegas. I'm going to have pay for it myself now!!

cheers

Reachy

18. ### tirle_bjMember

Bravo!

Great job, Ken, no questions asked. The Dinner for two is granted.

Actually we're very glad to have the same results as a confirmation. The only difference is probability.
We got 76.08% (infinitive deck). Of course, it's minor, but for 100% satisfaction here's how we've got to that:

On a first hand by hitting to 14 we have the following probabilities:

P(14) = P(15) = ... = P(19) = P(21) = 8.92%; P(20) = 32.00%;
P(bust) = 5.56%

Now, If we have a stiff on a first hand then by hitting second hand to 17 we get 59.83% to advance. So, if the first hand = 14, 15, 16 then
If the first hand = 17, then by hitting second hand to 16 we get
If the first hand = 18, then by hitting second hand to 13 we get
If the first hand = 19,20,21 then by hitting second hand to 12 (don't bust)
we get accordingly:
P(adv) = 73.71% (first hand is 19); P(adv) = 96.26% (firts hand is 20);
P(adv) = 100% (firts hand is 21)
And finally if the first hand is bust then by hitting secont hand to 18(!)
Based on that we have:
8.92%*(59.83*3 + 60.78 + 67.34 + 73.71 + 100) + 32%*96.26 +
+ 5.56%*42.19 = 76.08%

It would be nice to see your numbers for comparision.

Hope to see you soon at dinner table in Vegas or anywhere else.

I did find a few differences. Here's my comparable list.
h1=16, hit to 17, p=59.83
h1=17, hit to 16, p=62.56
h1=18, hit to 13, p=67.37
h1=19, hit to 12, p=73.74
h1=20, hit to 12, p=96.55
h1=21, hit to 12, p=100.00
h1=Bust, hit to 18, p=42.19

In particular, we differ on h1=17 and h1=20.
The others are close enough to be rounding differences.

20. ### tirle_bjMember

bravo encore

Well, here we go...
You're correct on
h1=20, p = 96.55
12/13*96.26% + 1/13*100% = 96.55%
...and also on
h1=17, p = 60.79
10.35%*35.05 + 10.35%*35.05 + 10.35%*47.12 + 10.35%*59.19 +
+33.43%*96.26 = 60.78%? OOPS we missed (h2=bust * D=17) =
=14.82%*12.07 = 1.79%, so 60.78 + 1.79 = 62.56% WOW