The Apple Barrel Game

[blackjack avenger]

An apple barrel has
50 red apples
50 yellow apples

The game is when the carnie picks a red apple you win!
You stroll buy a barrel and see 10 red apples and 20 yellow ones have been picked and then put in the garbage, so you have an advantage. The ratio is 40 red apples to 30 yellow apples or 4 red apples to every 3 yellow apples. However, there are no seats available for the game.

So you go and watch another barrel game. In this game many red apples are picked so you look away. Then you see there is a seat available at the first game. Of course, you have missed what other apples were chosen, they are in the trash. The carnie shouts "there are only 7 apples left, who is going to bet"?

Would you?

 

[Southpaw]

An apple barrel has
50 red apples
50 yellow apples

The game is when the carnie picks a red apple you win!
You stroll buy a barrel and see 10 red apples and 20 yellow ones have been picked and then put in the garbage, so you have an advantage. The ratio is 40 red apples to 30 yellow apples or 4 red apples to every 3 yellow apples. However, there are no seats available for the game.

So you go and watch another barrel game. In this game many red apples are picked so you look away. Then you see there is a seat available at the first game. Of course, you have missed what other apples were chosen, they are in the trash. The carnie shouts "there are only 7 apples left, who is going to bet"?

Would you?

You stole my apple analogy!!

Mind you this is the best carnie game I have ever seen. 0% HE and the barrel is dealt deeply :joker:

But yeah, you make the bet, as it is most probable that there are 4 red apples and 3 yellow apples left giving you a sizable edge. However, I think the uncertainty of whether or not you in fact have the advantage or not would cause your optimal wager to be smaller than if you were certain that there were 4 red apples and 3 yellow apples remaining.

Spaw

 

[KenSmith]

An unseen apple is an unseen apple, whether undrawn or in the trash.

 

[Southpaw]

An unseen apple is an unseen apple, whether undrawn or in the trash.

I see the light!

 

[blackjack avenger]

Ratio = Ratio?

But yeah, you make the bet, as it is most probable that there are 4 red apples and 3 yellow apples left giving you a sizable edge. However, I think the uncertainty of whether or not you in fact have the advantage or not would cause your optimal wager to be smaller than if you were certain that there were 4 red apples and 3 yellow apples remaining.
Spaw

Is the ratio of red to yellow apples the same from when you left the first game and returned or not?

Isn't
40 to 30 the same ratio as 4 to 3?

 

[ohbehave]

You make the bet but you don't bet the farm because there is still variance, I think is where we're at. That's where your bankroll management and bet strategy enters.

 

[Southpaw]

You make the bet but you don't bet the farm because there is still variance, I think is where we're at. That's where your bankroll management and bet strategy enters.

I think I was wrong. Think about Ken's post for a moment. The game is, from your perspective no different than when you were watching it previously.

Spaw

 

[21gunsalute]

An apple barrel has
50 red apples
50 yellow apples

The game is when the carnie picks a red apple you win!
You stroll buy a barrel and see 10 red apples and 20 yellow ones have been picked and then put in the garbage, so you have an advantage. The ratio is 40 red apples to 30 yellow apples or 4 red apples to every 3 yellow apples. However, there are no seats available for the game.

So you go and watch another barrel game. In this game many red apples are picked so you look away. Then you see there is a seat available at the first game. Of course, you have missed what other apples were chosen, they are in the trash. The carnie shouts "there are only 7 apples left, who is going to bet"?

Would you?

You should include 30 green apples to make a fair analogy.

 

[21gunsalute]

Is the ratio of red to yellow apples the same from when you left the first game and returned or not?

Isn't
40 to 30 the same ratio as 4 to 3?

Unknown. There is no way of telling what the ratio would be at this point. You can use 4 to 3 as an average if you like but you would most likely be wrong. And those 30 green apples never got accounted for. It's possible that all seven apples are neither red nor yellow, but green.

 

[shadroch]

I'd pretend I had a Letter of Marquee and go medevil on the carny for offering a fair game.

 

[blackjack avenger]

Post of the Year

I'd pretend I had a Letter of Marquee and go medevil on the carny for offering a fair game.

:laugh:

 

[MangoJ]

Unknown. There is no way of telling what the ratio would be at this point. You can use 4 to 3 as an average if you like but you would most likely be wrong. And those 30 green apples never got accounted for. It's possible that all seven apples are neither red nor yellow, but green.

You can assume a 40 to 30 distribution - and you will win accordingly.

There is exactly no difference between the following scenarios, neither in expectation value (nor in variance!).
The scenarios are ordered in a way that make the absolute equivalency obvious (I hope), by changing minor details with absolutely no effect on the outcome.

(A) After removing 30 seen apples (10 red, 20 yellow), betting on the next apple to be red.

(B) After removing 30 seen apples (10 red, 20 yellow), betting on the last apple to be red.

(C) After removing 30 seen apples (10 red, 20 yellow), betting on the last apple to be red, then burn 63 unseen apples.

(D) After removing 30 seen apples (10 red, 20 yellow), and burn 63 unseen apples, then betting on the last apple to be red.

(E) After removing 30 seen apples (10 red, 20 yellow), and then burning 63 unseen apples, betting on the next apple to be red.

(F) After removing 30 seen apples (10 red, 20 yellow), and then let someone else burn 63 unseen apples, betting on the next apple to be red.

(G) After removing 30 seen apples (10 red, 20 yellow), and then let someone else burn 63 unseen apples but not watching him burn, betting on the next apple to be red.

(H) After removing 30 seen apples (10 red, 20 yellow), and then walk away and come back after 63 apples are burned, betting on the next apple to be red.

If you think two neighbouring scenarios are somehow different (even subtile!), please ask and we can discuss.
I hope this will reduce the discussion (whether A is G) to a way smaller problem. I think the hardest transition to understand is C = D. But it's still a lot easier than A = G.

 

[blackjack avenger]

To the End and Beyond

To add to Mangoj's post:

When you are at the first game; if you could play, it does not matter if the carnie picks an apple from the top or the bottom of the barrel.

Which is what you are doing when you come back for the bet offer with 7 apples to go, you are just picking from the bottom of the barrel.

 

[blackjack avenger]

Vindication is so Sweet

hi lo count
6 deck shoe
tc 1 is an advantage

You innocently stroll by a table during the first hand and you see:
12 low cards, 108 low cards remaining to be played
6 high cards, 114 high cards remaining to be played
8 neutral cards, 64 neutral cards remaining to be played

26 cards, 1/4 deck has been played

approx tc > 1

Then you notice there are no seats available, best to move on.

Later you look and there is a seat open at the first table. Nothing else is available. So you go over to have a look, there is probably 1 hand to be played (1.5 decks to go). Oh, I forgot to mention the table has beauties playing; don't let this cloud your judgement, and the dealer asks if you would like to play?

Do you place a bet?
Do you place a tc1 bet?

If you understand the concepts in the apple barrel game; and the tc theorem, then the choice should be easy.

sorry I have to say it again.
Vindication is sooooo sweeeeet:celebrate

 

[iCountNTrack]

hi lo count
6 deck shoe
tc 1 is an advantage

You innocently stroll by a table during the first hand and you see:
12 low cards, 108 low cards remaining to be played
6 high cards, 114 high cards remaining to be played
8 neutral cards, 64 neutral cards remaining to be played

26 cards, 1/4 deck has been played

approx tc > 1

Then you notice there are no seats available, best to move on.

Later you look and there is a seat open at the first table. Nothing else is available. So you go over to have a look, there is probably 1 hand to be played (1.5 decks to go). Oh, I forgot to mention the table has beauties playing; don't let this cloud your judgement, and the dealer asks if you would like to play?

Do you place a bet?
Do you place a tc1 bet?

If you understand the concepts in the apple barrel game; and the tc theorem, then the choice should be easy.

sorry I have to say it again.
Vindication is sooooo sweeeeet:celebrate

Are you ever going to stop with this nonsense, you play with INFORMATION YOU HAVE that how you play. I have told you a gazillion times, true count theorem does not apply in this case. True count theorem says that the average value of tc does not change on before and after the round IF THE CARDS DEALT DURING THE ROUND ARE COUNTED. I don't know if you remember this from school but when the conditions pertinent to the case are not met the the theorem breaks down.
Let go of your ego and drop it.

 

[HockeXpert]

An apple barrel has
50 red apples
50 yellow apples

The game is when the carnie picks a red apple you win!
You stroll buy a barrel and see 10 red apples and 20 yellow ones have been picked and then put in the garbage, so you have an advantage. The ratio is 40 red apples to 30 yellow apples or 4 red apples to every 3 yellow apples. However, there are no seats available for the game.

So you go and watch another barrel game. In this game many red apples are picked so you look away. Then you see there is a seat available at the first game. Of course, you have missed what other apples were chosen, they are in the trash. The carnie shouts "there are only 7 apples left, who is going to bet"?

What % of your b/r would you bet assuming full kelly? What % of your b/r would you bet if the next apple was yellow?

 

[blackjack avenger]

Take a Deep Breath

Are you ever going to stop with this nonsense, you play with INFORMATION YOU HAVE that how you play. I have told you a gazillion times, true count theorem does not apply in this case. True count theorem says that the average value of tc does not change on before and after the round IF THE CARDS DEALT DURING THE ROUND ARE COUNTED. I don't know if you remember this from school but when the conditions pertinent to the case are not met the the theorem breaks down.
Let go of your ego and drop it.

Instead of just saying I am wrong, critique the apple barrel game! You have counted the first round (INFORMATION YOU HAVE), then you have a ratio, then you know what the final round will be! Just focus on the apple barrel game and Mangoj's respone and my one follow up to him.

FORGET THE APPLE BARREL GAME, GO TO "FROM APPLES TO MARBLES" A FEW POSTS DOWN

 

[blackjack avenger]

Crush It

What % of your b/r would you bet assuming full kelly? What % of your b/r would you bet if the next apple was yellow?

You would crush this game, you have a 4 in 7 chance of winning on the first hand that you could not play and on the last hand that you get to play.

If all you got to do was watch the first third of the barrel picks; close your eyes, and then decide if you want to play the last hand or not you would crush this game.

Of course I have never said this is better then seeing all apples picked, but the above is quite possible.

You have to think in ratios of red to yellow apples and how they hold true on average through the whole barrel sample.

 

[ohbehave]

The TC theorem doesn't break down here. What if it was groundhog day for the rest of your life and you had to keep seeing this same shoe every day. Same setup, you see the first hand TC~+1 but never see any of the rest of the shoe and can only play the last hand.

The answer is easy. You play it because the first hand sets up the shoe for a player advantage. If played forever, some of the last hands will ultimately not be favorable but the majority will be favorable to the player. And all together all those last hands will average TC+1.

 

[blackjack avenger]

From Apples to Marbles

Whoever started this apple thing obviously had no clue:grin:
joking southpaw

all ego aside

Some of you need to go to the store and buy:
50 red marbles
50 yellow marbles

take out 10 red marbles
take out 20 yellow marbles

the ratio is now:
40 red
30 yellow

the ratio is now 4 red to 3 yellow

Put the marbles in a dark bag
Would you bet on the next marble being red?

shake the marbles up in the bag
would you still bet?

shake the marbles in the bag 1 million times
would you still bet? for each bag shake?

split the marbles into 2 different bags
would you still make the bet?

split the marble into 10 different bags
would you still make the bet?

there are 70 marbles left
put them in 70 different bags
would you still make the bet?
line the 70 bags up, does it matter if you bet on the first or the last bag?

Why would anyone make an argument that any of the above bets need to be different? They are all the same bet, same ev

Now, some of you hopefully can now see the jump in logic to blackjack.

the marble bags analogy show that the distribution through a shoe does not matter once you have a positive TC. One can bet on the next hand of the shoe or the last.

Would you play this bj game?
You see the first few hands, it's always tc10
However,
you only get to play the last hand of the shoe
shuffle repeat
you would crush it, because its a tc10 bet
If it's a tc2 seen with the same rules, you would win