I need help with this play

Althiemers

Althiemers

Do I know you..
Somehow I think I do.
Your Face I seem to recall.
Oh yes...you're the One
I love ...most of all.
A memory from the past.
Love that forever would last.
Wounds in my heart.
Swore we'd never part.
Time..they say will heal.
They know not how I feel.
Thousand miles away.
Thoughts of you everday.
Prayers..I've sent above.
Please Lord..send my love.
Stolen years..filled with tears.
Come now dash my fears,
Memory soon erase.
Time..I have to race.
I'll try.
To remember your sweet face
Oh no..I never cry,
Ok goodbye.


Bonnie Ray

Dedicated
To husbands and wives of alzthiemers.

 

I think I more or less did what you wanted me to do?

Hi Mr Yama

I have reviewed my last answer and I can't see what extra I need to do (other than the calculation for bust vs dealer 20,21 which I will add here).

However I hope these calcualtions are what you asked for in your last post.

player stiff to eighteen/dealer bust plus dealer twenty to twenty-one
13+ - 56.54%
14+ - 55.86%
15+ - 54.98%
16+ - 53.88%
17+ - 52.52%
18+ - 50.87% (My figure for 18+ excludes the numbers for 18 vs dealer 17 although I'm not quite sure why I should do this?)

player eighteen/dealer seventeen

5.41% (which in my previous answer I just added to the figure for 18+ above to give 56.27%)

player nineteen to twenty-one/dealer anything

19+ - 61.99%
20+ - 55.95%
21 - 48.88%

player bust/ twenty to twenty-one

15.46%
Which I omitted from my previous answer.

I'm not sure whether this is what you asked for and if so whether it's correct or not. I hope I'm close as I'm not sure what else I need to do!!!!

Look forward to your reply.

Regards

Reachy

Ps. Just got my copy of "Probability for Dummies" so I'm going to try and follow proper notation in teh future if I can.

 

The aproach

Reachy and others following this thread (if any),
It is difficult for me to follow your train of thoughts, so here is my explanation and detailed aproach to the problem.
The math is not difficult but somewhat toilsome.

The situation.
One player advances. BR1 leads BR2 by little, both made maximum bets. BR2 stands with nineteen (there are other players with pat hands but nineteen is the best hand). BR1 has hard twelve and the dealer shows a Ten up.
We wonder if standing or hitting is a better playing strategy. If hitting, then to what total shall we hit?

Analysis.
If the dealer has a blackjack all players lose their bets and BR1 advances. Evaluating our playing strategies we can disregard chances of the dealer having blackjack or we can use numbers that represent dealer probabilities including blackjack. Either one is good to determine better plays as long as all calculations are performed with one and the same assumption throughout.

BR1 advances only if he has the same result -win/push/lose- as BR2. The same result doesn’t have to be achieved by BR1 having the same hand total as BR2’s.
Calculating chances for standing on twelve is very easy. It will be the sum of chances for the dealer’s bust (both players win max bet), and the dealer’s final hand of twenty and twenty-one (both players lose).
We will not deal with effect of removal at this time, though they offer a better precision and often times are crucial. We can use dealer probabilities for any number of decks. It is important, once again, not to mix probabilities for the specific subset of cards for one side (dealer or player) and full decks (or the infinite deck) for the other side, or one set of numbers in early calculation and another one later.
If we utilize most commonly used six decks as the reference, the dealer will break, make twenty, and twenty-one about 63.64% of the times excluding the dealer’s blackjack (it is 66.45% including blackjacks).
BR1 standing on twelve advances him 63.64% to the next round.

Now, lets look at the chances if we decide to hit. Let’s use infinite deck for this analysis.
The first step is to do calculatations for “hit only once”. Each card from Ace to nine has 1/13th chance of appearing and a Ten have 4/13th chance. Hitting twelve will result in totals thirteen to twenty-one 1/13th of the times and 4/13th for the bust. The lowest total is thirteen so we could tell that we are using strategy “stand 13” -hit to thirteen.

Now we have to calculate total chances of advancing. We will need to go through the entire player’s and all the dealer’s outcomes. It is helpful to go systematically through all outcomes in some order, for example, from seventeen to twenty-one, and then bust. It also may be easier, depending on the logistics of calculations to first go through all the dealer’s result or all the player’s results.
We may also only calculate situation where the player advances, or only where he is not advancing.

There are four distinctive groups when BR1 hits his twelve once and does advance.
Final hand - a stiff (13, 14, 15, and 16), 17, and 18. If the dealer busts all the players win max bets and BR1 advances. If the dealer makes twenty or twenty-one then all the players lose and BR1 advances.
BR1 has 6/13th (61.5%) chances for stiff to eithteen hands times the dealer’s bust, twenty, and twenty-one 63.64% (.2303+.3684+.0377) Together --29.4%
Final hand - 18 and the dealer seventeen. BR1 and BR2 win their hands, BR1 advances. Note that we already calculated chances for BR1 18 and the dealer bust or twenty and twenty-one, but this is a separate case with the dealer having exactly seventeen.
BR1 has 1/13th (7.7%) chance times the dealer’s 12.13% Together --0.93%
Final hand - 19 through 21 and the dealer anything. When BR1 gets nineteen or more he has at least as good hand as BR2’s and advances regardless the dealer result.
BR1 has 3/13th chance times the dealer 100% Toghether --23.08%
Final hand - bust and the dealer twenty or twenty-one. Though BR1 busted he still advances when BR2 loses, so the dealer has to finish with twenty or twenty-one.
BR1 has 4/13th chance to bust times the dealer 40.62% (.3684+.0377) Together --12.5%

When we add it all up we come up with the conclusion that hitting to thirteen gives BR1 65.88% chance to advance.
Hitting to at least thirteen is better play than standing on twelve by 2.24%, excluding the dealer’s blackjacks.

Next step will be to check the chance for hitting to at least fourteen.
Note that it was easier (for me) to work by BR1 outcomes, it creates only four groups. If I went through the dealer’s outcomes I would have minimally more extensive calculations.

S. Yama

 

Fantastic Mr Yama

Thanks for this clear explanation. It is a different approach to the one I have been using and it actually seems a lot simpler and obviously it's more accurate!!! I can see why this approach is correct and mine wasn't so thank you very much for pointing me in the right direction. Now to find another "tournament teaser" to get my teeth into.

One last question. Do you ever play on Global Player at all?

Cheers

Reachy