AutomaticMonkey: No-hole-card (OBO) and the "Monty Hall" puzzle

[AutomaticMonkey]

Could the no-hole-card way of dealing a game, where splits and doubles are not lost, change strategy against a 10 or ace when playing such a game?

My first thought is 'no', but being I am not good at mentally fathoming the Monty Hall problem, nor understanding why the push-22 rule changes strategy for BJ Switch (had to prove it to myself empirically with a sim) I'm open to the possibility that being you won't lose your extra bets when the dealer rolls a natural, the house edge on that extra bet becomes zero instead of 100% in case of a natural, and that dilutes the remaining probabilities to the point where the strategy changes.

The particular game I had in mind was Multiple Action, which is essentially a NHC game repeated 3 times.

[Don Schlesinger]

> Could the no-hole-card way of dealing a game, where
> splits and doubles are not lost, change strategy
> against a 10 or ace when playing such a game?

Short answer: no. See BJA3, pp. 51-52, for an analogous, albeit not exactly the same situation, discussion.

> My first thought is 'no',

Keep that thought! :-)

> but being I am not good at
> mentally fathoming the Monty Hall problem,

Aw, sure you can. Try!

> nor understanding why the push-22 rule changes strategy
> for BJ Switch (had to prove it to myself empirically
> with a sim) I'm open to the possibility that being you
> won't lose your extra bets when the dealer rolls a
> natural, the house edge on that extra bet becomes zero
> instead of 100% in case of a natural, and that dilutes
> the remaining probabilities to the point where the
> strategy changes.

Nope.

> The particular game I had in mind was Multiple Action,
> which is essentially a NHC game repeated 3 times.

A bit different in the way the counter sizes his optimal bets, but no changes in basic strategy. See BJA3, pp. 38-39.

Don

[OldCootFromVA]

Look at it this way:

At first, the contestant has a 2/3rds chance of being wrong.

When Monty opens a door, he cannot open the door with the car nor can he open the door the contestant originally picked.

After Monty's door is opened, the contestant STILL has a 2/3rds chance of being wrong; so switching will give him a 2/3rds chance of being RIGHT!

Permutations:

1. Car behind A, contestant picks A: switching bad
2. Car behind B, contestant picks A: switching good
3. Car behind C, contestant picks A: switching good

In #1 above, Monty cannot open A, only B or C.
In #2 above, Monty can only open C.
In #3 above, Monty can only open B.

All other permutations are either reflections or rotations of those three.

Notice, switching is bad only when the contestant has guessed the correct door initially, which only happens 1/3rd of the time. In 2/3rds of cases, switching is good.

Does that clear it up for you?

[Panama Rick]

> Look at it this way:

> At first, the contestant has a 2/3rds chance of being
> wrong.

> When Monty opens a door, he cannot open the door with
> the car nor can he open the door the contestant
> originally picked.

> After Monty's door is opened, the contestant STILL has
> a 2/3rds chance of being wrong; so switching will give
> him a 2/3rds chance of being RIGHT!

> Permutations:

> 1. Car behind A, contestant picks A: switching bad
> 2. Car behind B, contestant picks A: switching good
> 3. Car behind C, contestant picks A: switching good

> In #1 above, Monty cannot open A, only B or C.
> In #2 above, Monty can only open C.
> In #3 above, Monty can only open B.

> All other permutations are either reflections or
> rotations of those three.

> Notice, switching is bad only when the contestant has
> guessed the correct door initially, which only happens
> 1/3rd of the time. In 2/3rds of cases, switching is
> good.

> Does that clear it up for you?

The problem people have with this problem is that once the door is revealed, there are two seemingly equal choices remaining.

The easiest way for one to see what's going on is use more doors. For instance, simulate the game with a pack a cards where the goal is to pick the ace of spades. The player chooses one card, and "Monty" reveals 50 cards, none of which is the ace of spades. After doing this a couple of times, it all becomes very clear.

[G Man]

Ecellent explanation. I use to explain it to people by saying that in fact, the rules are that Monty opens ALL THE DOORS EXCEPT FOR TWO, one choosen at random and the one with the car. Now, if you play this game with 100 doors, it become very clear why you will ALWAYS change door.

[AutomaticMonkey]

> Ecellent explanation. I use to explain it to people by
> saying that in fact, the rules are that Monty opens
> ALL THE DOORS EXCEPT FOR TWO, one choosen at random
> and the one with the car. Now, if you play this game
> with 100 doors, it become very clear why you will
> ALWAYS change door.

Ah OK, so you are going under the (good) assumption that you probably didn't pick the car on your first guess, and it still probably isn't the car, and Monty *knows where the car is* and has helped you by picking everything but that. So with 100 doors, the probability of it being the other door is now 99%.

(Unless of course Monty is screwing with you and only chooses to open additional doors when you DID pick the car on your first shot.)

But in BJ, the dealer (hopefully!) has no knowledge of the cards and always checks for BJ, and only lets you play when he doesn't have it, and normal BJ strategy already accounts for this, i.e., under an ace there is a 1 in 9 chance that there is a 6, not a 1 in 13 chance (infinite deck model).

However in a NHC game, there is still a 1 in 13 chance of it being a 6, and (assumption here) you can think of the dealer's hole card logically like the dealer's draw cards, because they are unknown before you play your hand. And in the equally confusing BJ Switch push-on-22 rule, even though there's nothing you can do about the dealer getting a 22 and pushing, you play differently when this rule is in effect.

So if the dealer's unknown cards affect your strategy in BJ Switch, why wouldn't they do the same in a NHC game? (I know they don't, and believe they don't, just working on the mental gymnastics of it.)

[Don Schlesinger]

> So if the dealer's unknown cards affect your strategy
> in BJ Switch, why wouldn't they do the same in a NHC
> game? (I know they don't, and believe they don't, just
> working on the mental gymnastics of it.)

What's the difference if he finds his BJ early and doesn't let you play, or finds it later, and then takes just your original bet? What's the difference if he slides a hole card early and doesn't look at it, does look at it, or doesn't take it till after you play? All the same thing!

(Of course, as a counter, we waste cards when he looks late. But, this has no effect on the BS player.)

Don