An interesting exercise

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BradRod

Well-Known Member
At the Mayor's suggestion I recently performed an interesting exercise. I wanted to share my observations from that exercise with the forum.

It goes like this:

Deal hands as if playing one on one with the dealer using only 6 cards. 3 - T value cards, A, 5, 6. The equivalent TC is 18. Play 100 hands.

With such a rich deck to play from I expected it to be a very player friendly run. It was. The end result put me up 20 units after the 100 hands. These were maximum bets because of the high count. What was eye opening was that I lost nearly half of the hands. Still did well because of blackjacks and successful double downs.

I did not count the hands where the dealer got BJ with an ace up. Since I would have bought insurance and would have won the insurance bets. Thses hands were the only (effective) push hands possible with the cards being used.

These Ace up dealer BJ's demonstrated to me that there was not so much to fear in the long run of a dealer BJ in a high count with a big bet out. Because
a. insurance offsets the potential losses and
b. a dealer BJ is still just a 1:1 loss. While the 3:2 player BJ payoff far offset those.

This got me wondering. What are the odds (if surmisable ) of a dealer BJ being Ace up or T up ? is it even ?
 
zengrifter

zengrifter

Banned
This got me wondering. What are the odds (if surmisable ) of a dealer BJ being Ace up or T up ? is it even ?
--------------------------------

It would depend who's dealing! zg
 
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Rob McGarvey

Well-Known Member
"This got me wondering. What are the odds (if surmisable ) of a dealer BJ being Ace up or T up ? is it even ?

If I am understanding your question properly, dealer BJ happens 1 out of 5 with an A showing. In the case you are talking about below 1 per 4 BJ's would be A up.

"Deal hands as if playing one on one with the dealer using only 6 cards. 3 - T value cards, A, 5, 6. The equivalent TC is 18. Play 100 hands.

"With such a rich deck to play from I expected it to be a very player friendly run. It was. The end result put me up 20 units after the 100 hands. These were maximum bets because of the high count. What was eye opening was that I lost nearly half of the hands. Still did well because of blackjacks and successful double downs.

You were also rather lucky. In The World's Greatest Blackjack Book on page 201 it shows two different scenarios. One where you have a 2% advantage and one where you have a 2% disadvantage. You have a 49% chance of doubling your roll betting it all on one chance with the -2 and 51% with the +2. BUT, by playing with smaller amounts, you can increase your chances of doubling by making 100 even sized bets over 100 hands. You have a 98.2% chance of doubling after these 100 hands. On the contrary side, you will have a 1.8% chance of doubling your roll after 100 -2% hands. Better NOT to bet at all against a -2% game, and bet small amounts to grind out the time against your 2% edge on the quick side of this game.

"I did not count the hands where the dealer got BJ with an ace up. Since I would have bought insurance and would have won the insurance bets. Thses hands were the only (effective) push hands possible with the cards being used.

"These Ace up dealer BJ's demonstrated to me that there was not so much to fear in the long run of a dealer BJ in a high count with a big bet out. Because
a. insurance offsets the potential losses and
b. a dealer BJ is still just a 1:1 loss. While the 3:2 player BJ payoff far offset those.

It's great to know what every card left in the deck is isn't it? smile
 
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BradRod

Well-Known Member
Explain further please.

>>It couldn't be even. There are 16 cards with a 10 value and only 4 aces per deck.<<

I guess this is the same source for Rob McG's assertion that 1 in 4 BJ would be Ace up.

My confusion is. I can understand how the 1:4 ratio of Ace to T would effect the possibilty of the hand being a BJ at all-- rather than a T and any other card. I just do not understand how that ratio effects the order in which that A-T combination would be dealt.

Thanks
 
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BradRod

Well-Known Member
>>>>>>>If I am understanding your question properly, dealer BJ happens 1 out of 5 with an A showing. In the case you are talking about below 1 per 4 BJ's would be A up.<<<<<<<<<<<

Please see my question in the next post.

"Deal hands as if playing one on one with the dealer using only 6 cards. 3 - T value cards, A, 5, 6. The equivalent TC is 18. Play 100 hands.

"With such a rich deck to play from I expected it to be a very player friendly run. It was. The end result put me up 20 units after the 100 hands. These were maximum bets because of the high count. What was eye opening was that I lost nearly half of the hands. Still did well because of blackjacks and successful double downs.

>>>>You were also rather lucky. In The World's Greatest Blackjack Book on page 201 it shows two different scenarios. One where you have a 2% advantage and one where you have a 2% disadvantage. <<<<<

What is the player's advantage with a + 18 count ?

>>>>> by playing with smaller amounts, you can increase your chances of doubling by making 100 even sized bets over 100 hands. <<<<<<

Are you saying I shouldn't be making maximum bets with a +18 count. Or did I not play this oversimplimfied simulation correctly ??

>>>It's great to know what every card left in the deck is isn't it? smile <<<

Although it is true that I did know what the remaining cards were , my decision to take insurance or not would have been based solely on the count , not on knowledge of remaing counts.
 
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The Mayor

Well-Known Member
Yes, here is the argument

Yes, half of the blackjack's will be face up.

Here is how it is done (with an infinite deck)...

Let X = BJ.
Let Y = A is showing.
Let Z = T is showing.

Then
P(X given Y) = 4/13.
P(X given Z) = 1/13.
P(Y) = 1/13.
P(Z) = 4/13.

So

Blackjack and an A is showing:
P(X and Y) = P(X given Y)*P(Y) = 4/13*1/13 = 4/169.

Blackjack and a T is showing:
P(X and Z) = P(X given Z)*P(Z) = 1/13*4/13 = 4/169.

They are equal.

--Mayor
 
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Rob McGarvey

Well-Known Member
The Fact of The Matter Is

A BJ is composed of two cards, one an Ace the other a 10. The ratio of 10 to A will be 4 to 1, and over the long run your BJs will be A,10 A,J A,Q, and A,K, half A up and half the 10 J Q K up.
 
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Rob McGarvey

Well-Known Member
>>>>You were also rather lucky. In The World's Greatest Blackjack Book on page 201 it shows two different scenarios. One where you have a 2% advantage and one where you have a 2% disadvantage. <<<<<

What is the player's advantage with a + 18 count?

Let us guess that it is 9%. With TC+1 we play even in multi deck, TC+2 we get the edge, so using .5% per C ruff estimate let's say 9%.

>>>>> by playing with smaller amounts, you can increase your chances of doubling by making 100 even sized bets over 100 hands. <<<<<<

Are you saying I shouldn't be making maximum bets with a +18 count. Or did I not play this oversimplimfied simulation correctly??

If we are going to use 9% of our bankroll as our max bet, yes, we would be betting too much. Half Kelly or quarter Kelly, or a top max bet no matter how high the count gets, possibly 2% is what Igor K (Humble) is suggesting in the long run grind of the house. He uses 1/100th of the bankroll, or 1%.

>>>It's great to know what every card left in the deck is isn't it? smile <<<

Although it is true that I did know what the remaining cards were , my decision to take insurance or not would have been based solely on the count , not on knowledge of remaing counts.

Very good. Was this exercise only an insurance exercise? I think there is a lot to learn from exercises like these, and that is why I thru the maximum and minimum boldness as it is called in the book into the exercise.
 
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The Mayor

Well-Known Member
Re: The Fact of The Matter Is

I am not sure you understand the question, Rob.

But, the answer is that 1/2 of the dealer's BJ's occur via an A up, and 1/2 occur via a T up. That is just how it goes. Now, if an A, the dealer is 4 times as likely to have a BJ as if he is showing a T, but on the other hand, the dealer gets a T up 4 times as often as an A. Hence it evens out.

--Mayor
 
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BradRod

Well-Known Member
<<<<<<<If we are going to use 9% of our bankroll as our max bet, yes, we would be betting too much. Half Kelly or quarter Kelly, or a top max bet no matter how high the count gets, possibly 2% is what Igor K (Humble) is suggesting in the long run grind of the house. He uses 1/100th of the bankroll, or 1%.<<<<<<<<

I thought that kelly criteria was based on player advantage. No more no less in order to double the BR before depleting it.

You are suggesting that there is another criteria to follow for bet ceiling based on something other than BR and TC ? This seems to disregard the players advantage in betting. At what counts would you do that ?

>>>>>>Very good. Was this exercise only an insurance exercise? I think there is a lot to learn from exercises like these,<<<<<<<

The exercise was not only for insurace but, I think for general expectation at a high count.

>>>>>>>>> and that is why I thru the maximum and minimum boldness as it is called in the book into the exercise.<<<<<<<<

i did not understand this
 
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Rob McGarvey

Well-Known Member
Re: The Fact of The Matter Is

"I am not sure you understand the question, Rob.

I'm sure I didn't get the drift, as I said from my first post, if I am understanding the question correctly, or the point of the exercise. I assume there is a point to it somewhere, and that it had to do with betting the advatage to some degree. This written medium and pop up posting leaves a lot to be desired.

"But, the answer is that 1/2 of the dealer's BJ's occur via an A up, and 1/2 occur via a T up.

Of course.

"Now, if an A, the dealer is 4 times as likely to have a BJ as if he is showing a T, but on the other hand, the dealer gets a T up 4 times as often as an A. Hence it evens out.

All makes sense. 1 out of 13 will be A up, 4 out of 13 ten up, 8 out of 13 2 3 4 5 6 7 8 9 up, and if and when the dealer has a BJ it will be 50% A up and 50% ten up.

What is the point of the original exercise you set the man out to do? That would help in this discussion.
 
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Rob McGarvey

Well-Known Member
<<<<<<I thought that kelly criteria was based on player advantage. No more no less in order to double the BR before depleting it.

You are suggesting that there is another criteria to follow for bet ceiling based on something other than BR and TC ? This seems to disregard the players advantage in betting. At what counts would you do that ?

I am justing pointing out "minimum boldness" to you, many small bets instead of larger ones. "Max boldness" is plunging your entire roll on one shot, the proper play against a neg ex game. Some players will never bet more than 1% of their bank, some use 2%, even if your advantage is 9%. We are still working with risk of ruin here.

>>>>>>Very good. Was this exercise only an insurance exercise? I think there is a lot to learn from exercises like these,<<<<<<<

The exercise was not only for insurace but, I think for general expectation at a high count.

>>>>>>>>> and that is why I thru the maximum and minimum boldness as it is called in the book into the exercise.<<<<<<<<

i did not understand this

If I had a flat bed scanner I would put the pages up here for you to view. It's hard to get a grip on things this way.
 
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T-Hopper

Well-Known Member
Wrong


You were also rather lucky. In The World's Greatest Blackjack Book on page 201 it shows two different scenarios. One where you have a 2% advantage and one where you have a 2% disadvantage. You have a 49% chance of doubling your roll betting it all on one chance with the -2 and 51% with the +2. BUT, by playing with smaller amounts, you can increase your chances of doubling by making 100 even sized bets over 100 hands. You have a 98.2% chance of doubling after these 100 hands.
​

I'm sure the book says nothing about having a 98% chance of winning after just 100 hands.
 
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BradRod

Well-Known Member
Re: I must say that the quality of discussion...

.. is climbing fast around here! zg

has a way to with your contribution .... although i must say that i find your messages mostly abit cryptic ...

brad
 
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