Last hand. - Hit or stand ?

Last hand, BR1 1356 chips bet 100 and BR2 (me) 1255 chips bet 402.

BR1 stand on his hard 16, BR2 received a hard 17 and dealer up card 7.

- Should I hit my hard 17 or simply stand ? (I am afraid I should hit it..)

But if would be this following scenario: - bankrolls/bets remain the same.

BR1 also stand on a stiff hand, (in fact I don`t think is relevant what BR1 does here with his hand anyway) but this time BR2 receive a hard 18 and dealer 8.

 

Playhunter,

This is a tough play, but I think I would just stand, and hope that dealer busts, thus allowing to advance since you would win by 1 chip. If you hit, you have only 30% of improving your 17 but if you stand, dealer could have 10 in the hole and you lose too, but if someone put a gun to my head I'd just stand hoping dealer breaks.... I thinks some of the tournament experts here could give you more insight though. We shall see. Either way, I do feel it'd be a pretty close call on what you should do.

What'd you end up doing anyway?

 

Yes, by hitting, I successfully improve my hand only 31% of the time, and 69% of the time I bust. BUT when is good it improves from 26% to 62.5% at least !

Well, the real scenario was that my opponent had a 20 and stand on it, I also stand on my 17 which I think was bad, and dealer had a 10 under for a total 17.

 

In this situation, you win if you win your hand and you lose otherwise. Your opponent's hand is irrelevant. Vs a dealer 7, you stand for a 26.1% chance (very quick sim result). Hitting once reduces your chances to ~24.7%.

You would stand vs any dealer up card except an Ace. Vs an Ace you would hit once for a ~19.7% chance vs ~16.5% for standing.

 

No difference here. Your opponent's hand is (still) irrelevant.

 

This is for a game where dealer does not peek for blackjack, or has no relevance either way hitting being the right decision in any of the case ?

 

Whether the dealer peeks or not is not relevant. If the dealer has blackjack, then you lose no matter what you do.

 

That is so right and obvious that I should not even ask .. (where was my mind?) Sorry for that! I think sometimes it just happen to me, hopefully not soon again.

 

The decision to hit or stand is a function of the dealer outcome probabilities.
(E.g. if you stand on 17, what is the probability of the dealer busting, which is then the only way to advance?)

The dealer outcome probabilities are different depending on whether the dealer has already confirmed that the hole card is not a ten. So there is at least the potential for your hit/stand decision to be a different one.

 

As I understand it now, if your only hope is to win your bet, you have to always hit your 17 vs dealer Ace up card to improve your winning chances. And if you are in a game where the dealer does not peek, and he has a blackjack, you are already dead in the water anyway before you knew it, but still have to hit that.

One particularity for GA, is that a dealer blackjack (dealer does not peek on 10) is a push against a player 21, but I think you still have to stand with 17 vs 10.

 

While the above two statements are both true ...

I disagree with your conclusion.

Let
p(ah) represent the probability of success for taking action a on a given hand h
p(BJ) represent the probability of a dealer blackjack.

We need to win our hand totalling n, so the probability of success for a given action on hand h is the probability that the dealer does not have blackjack times the probability of success when taking action a, or

(1 - p(BJ)) x p(ah)

Now suppose that we have identified a situation in a given game where the probability of success for action X on a given hand h, p(Xh), is greater than the probability of success for action Y, p(Yh), or

(1 - p(BJ)) x p(Xh) > (1 - p(BJ)) x p(Yh)

We can now see that regardless of the probability of a dealer blackjack, while the actual expected success rates will change with the probability of a dealer blackjack (as you have noted), the comparison will always hold. That is, action X will always be superior to action Y. Now note that the only difference between the peek and the no-peek games is that the probability of a dealer blackjack is zero for the peek game and is dependent on the dealer's up card for the no-peek game. We can therefore conclude that the playing strategy for this situation would not change due to dealer-peek vs no-peek.

For completeness, note that the equation breaks down when the probability of a dealer blackjack is 1. In this case the left hand side and the right hand side are both zero, indicating, correctly, that the whole situation is irrelevant in a game where the dealer always has blackjack.

Bonus Points:
Use a similar methodology to show why basic strategy does not change for nopeek-OBO games
Use a similar methodology to show why hit/stand decisions do not change for non-OBO nopeek games
Use a similar methodology to show how split/double decisions can differ for non-OBO nopeek games

 

Oops. That's what happens when I try to think about these things in the wee small hours. Thanks for going through that, Gronbog.

I actually think your first, one-line response to PlayHunter in some ways makes the point more clearly, but I didn't quite grasp it on first reading.

i.e. The hit/stand decision we are faced with is actually -

'If I get over the hurdle of the dealer not having a BJ, what will be the best way to play the hand?'

Whether the outcome of the BJ-hurdle is revealed at the start or the end of the playing of the hand doesn't matter, so we can in fact use the post-peek probabilities in either case.


I wasn't thinking clearly, but I think I had in the back of my mind the impact of the peek effect (https://www.blackjacktournaments.com/threads/4115), which gives us a little extra information, post-peek, about the composition of the remaining deck (and thus might seem to have an impact on both the dealer's and the player's outcomes).

But, again, the thing that cuts through all that confusion is the fact that we can assume the post-peek deck composition from the outset.

So, the only thing remotely noteworthy in all my rambling is that if you set out to use analytical techniques to solve this kind of question, rather than a simulation, then you need to be careful when calculating the probabilities associated with the next card to be drawn, as you have a bit more information than you may realise.

 

That's why my hat is always off to those who can consistently apply analytical techniques correctly. I am not one of them. I find it far easier to get a sim algorithm right once and to then apply it to many problems than to apply an analytical technique correctly even once

 

To make it a rule of thumb, if one needs to win his hand (and a push does not help) in order to advance, he only have to apply basic strategy but with two deviations/exceptions: 1. Hit hard 17 vs dealer Ace, (as Mr. Gronbog explained) and 2. Stand hard 16 vs dealer 10 ! (I am not sure if this deviation should be affected by a negative count ?) Actually one can arrive at these results by comparing doubling down chart with the dealer up card bust percentage chart)

 

Table for A Push is as Goodf as a Loss (or Must WIn 1 Bet)

Your timing is good, I was just going to make the same point. Wong has a section on this in Chapter 8 entitled "A Push is as Good as a Loss". He outlines a few more strategy deviations than you have. I have generated a complete strategy for this which you can find at http://gronbog.org/results/blackjac...one/generated/complete/1.0/p1.X/strategy.html. This chart agrees with Wong except that it does not recommend standing on 16 vs 8 but does recommend hitting 17 vs Ace. I also generated a chart for 3 or more cards which does recommend standing on 16 vs 8 (no need to post it for one change). My chart does agree with BlueLight's result in the sticky thread in this forum topic.

One other thing my chart gives you that is not mentioned by Wong is what to do with your pairs. Note the recommendations for hitting, standing and splitting different pairs. The problem then becomes one of knowing how to play the split hands to realize the expected success rate. There is a separate strategy for playing the first hand of each possible split and there are separate strategies for playing the second hand for each possible first hand result. I can post them all if anyone would be interested.

This chart was generated using iterative simulation of 8 decks, S17 with 75% penetration. Hover your mouse over a given cell to see the simulated percentages for each possible action.

 

I am certain that I may not know what is the optimal strategy to win a full bet after a split. And if is not a big effort, I would be happy to see it.. it may help..

 

Careful What You Ask For

Well, ok. It will take me some time to put all the tables together. I'll warn you now that it's not for faint of heart. More suitable for Rainman types who have eidetic memories.

 

Bear in mind that both Blackjack21 and GameAccount have the unusual splitting procedure that we have discussed before (actually it is also the usual procdure at live tables, here in the U.K.).

That is, a card is dealt to each of the two split hands before the player has to make their first decision.

 

Well, then it is not really necessary for me.. plus a little (more) time consuming on your side.. Do not make it a priority, because certainly it should not be one..

 

Ahhhh, yes. I do recall some discussion of that now. Unfortunately my software does not (yet) support that procedure variation. That would result in a larger set of tables for playing the first split hand.