Chance of dealer busting of each upcard at various index count

[Freightman]

It is, but not in isolation. It's not something most people would have the time or expertise to evaluate on the fly. That's why there are tables and indices to tell you what to do.

I do. This can be refined beyond indices. I would add that most players wouldn't know exact indices of A7 or A6 v 2. Suffice it to say simple rule of thumb suggests higher TC required for lower second player card. The unknown regaled system would refine this a bit further.

I really don’t like A6 v 2, but A7 v2, under proper circumstance, will draw a comment akin to - hmm, that’s a risky double, slowly putting the chips on the table. Of course, QTC is a factor.

[Dog Hand]

Comments and questions on each of the above charts:

1. Norm, why does the bust rate show at about 23% and not the traditional 28.6%? I see two possibilities: 1) This is for BEFORE the dealer checks for a natural under tens and aces; and/or 2) This is for a lone player, where the dealer doesn't complete his hand if the player breaks. Note that the footnote says for 1, 3, and 6 players. But there's only one graph! And, I'm guessing that it's for a lone player.

2. For Dog Hand, while the charts are great, NONE actually shows the global dealer bust rate against ALL upcards combined, according to true count. And, I think that was the OP's question. Norm's chart shows this, but with the objections I have mentioned above.

So, to conclude, what I'd like to see is a graph of the dealer's global bust rate, across all counts, for PLAYABLE hands, where the dealer is required to complete his hand. (I know what the graph looks like, but I still haven't seen it anywhere here.)

Don

Don,

I somehow missed this comment when you posted it years ago.

To answer your comment #2, I ran two 2-billion-round sims: one for a H17 game; the other for a S17 game. I used Norm's excellent "Dealer Must Complete Hand" option to force the dealer to draw to at least H17 or S18. Below is a graph showing the results for H17 and S17 6D games.

Dealer Bust Rate vs HiLo TC.jpg

I truncated each graph to show TC's only in the range of -10 to +10: the remainder of the TC's comprise less than 0.1% of the rounds.

The overall Bust Rate is 28.57% for H17 and 28.19% for S17.

The highest bust rate for H17 occurs at a TC of -2: 28.63%. For S17, the highest value of 28.25% occurs at both -1 & -2.

Hope this helps!

Dog Hand

[Freightman]

Don,

I somehow missed this comment when you posted it years ago.

To answer your comment #2, I ran two 2-billion-round sims: one for a H17 game; the other for a S17 game. I used Norm's excellent "Dealer Must Complete Hand" option to force the dealer to draw to at least H17 or S18. Below is a graph showing the results for H17 and S17 6D games.

Dealer Bust Rate vs HiLo TC.jpg

I truncated each graph to show TC's only in the range of -10 to +10: the remainder of the TC's comprise less than 0.1% of the rounds.

The overall Bust Rate is 28.57% for H17 and 28.19% for S17.

The highest bust rate for H17 occurs at a TC of -2: 28.63%. For S17, the highest value of 28.25% occurs at both -1 & -2.

Hope this helps!

Dog Hand

Nice graph. Question that still remains is bust rate for each dealer up card 2-6) at various true counts for the relevant hand at the time in question - higher the upcard higher the bust rate, higher the TC higher the bust rate.

Further, it seems to me that truncating the negative values will slightly skew the results.

[21forme]

I would add that most players wouldn't know exact indices of A7 or A6 v 2.

Perhaps, but you can get yourself into trouble guessimating. The general rule of thumb is if you don't know the index, play BS. Deviating from BS on gut feelings or guesses can do more harm than good.

[Norm]

Generally speaking, an incorrect hit/stand index that is nor far off is better than no index at all. That is one of the reasons compromise indices can work, if they are generated carefully. Of course, using BS is basically using an incorrect index. 'm agreeing with your statement that you can get in trouble if your gut is bad.

[Freightman]

Perhaps, but you can get yourself into trouble guessimating. The general rule of thumb is if you don't know the index, play BS. Deviating from BS on gut feelings or guesses can do more harm than good.

I don’t guesstimate.

[Secretariat]

Generally speaking, an incorrect hit/stand index that is nor far off is better than no index at all. That is one of the reasons compromise indices can work, if they are generated carefully. Of course, using BS is basically using an incorrect index. 'm agreeing with your statement that you can get in trouble if your gut is bad.

Norm can you answer my earlier question which was

Norm can you explain why you think dealer bust rate is meaningless?
I don't understand.
When standing on our stiffs, bust rate becomes everything!
I would certainly like to see that feature on CV at least when standing on our stiffs.

[Norm]

Whether or not the dealer draws, and therefore may bust, depends on what all the players at the table do (assuming the dealer does not have a stiff). If any one of them does not bust or BJ, the dealer must draw. (Somewhat different with ENH) The more players, the more likely the dealer will draw, and the more likely the dealer will bust. All that matters is the probability of you winning your particular hand, not an overall dealer bust rate which may depend on the hands and actions of other players.

If you stand on a stiff, the dealer must draw and may bust. The odds of that happening are critical. But, the dealer may or may not draw and may or may not bust anyhow even if you hit and don't bust depending on other players. That overall bust rate is meaningless. What matters is the probability of busting assuming a heads up game at a specific count, not a general stat.

[Secretariat]

What matters is the probability of busting assuming a heads up game at a specific count, not a general stat.

That's exactly what I would like to see, bust rates at specific counts vs dealer up card. It's easy to figure out with the count and side count(s) if the dealer bust odds are larger or lower than normal but it's impossible to quantify precisely. Training with CV with an option of seeing the dealer bust odds (especially heads up) at the actual deck compositon could give a better perspective and "feel". Have no idea how much of a programming effort it would take on your part though. Just a suggestion.

[Dog Hand]

Nice graph. Question that still remains is bust rate for each dealer up card 2-6) at various true counts for the relevant hand at the time in question - higher the upcard higher the bust rate, higher the TC higher the bust rate. <snip>

That's exactly what I would like to see, bust rates at specific counts vs dealer up card. <snip>

Freightman and Secretariat,

I direct your attention to the second graph of this old, old post:

https://www.blackjacktheforum.com/sh...ncy-vs-HiLo-TC

That graph shows the dealer bust rate versus HiLo TC for each dealer upcard for a 6D H17 game.

As Freightman correctly predicted, for the small upcards of 2-6 the dealer bust rate increases with both upcard value and TC (with some small exceptions at extreme TC's).

Hope this helps!

Dog Hand

[Secretariat]

Thanks Dog Hand. Two really nice graphs. The effect of ratios of 789s on top of the TCs would be a nice addition for my game but I'll certainly print those graphs and add them to my personal "jewels".

[Freightman]

Dog Hand
Thanks for your usual high end works. You also said

As Freightman correctly predicted, for the small upcards of 2-6 the dealer bust rate increases with both upcard value and TC (with some small exceptions at extreme TC's).

Just in the last week or two, at high TC and very ace rich environment, I drew to a 3 card 20 against dealer 10 thinking - oh shit - and dealer back door getting his bj. I can’t of the number of times, in similar environments seeing my stiff v dealer 6 drawing 10, and then the dreaded dual number card - as well dealer 5 drawing 10 and AA.

Im presuming the above refers to the skewing you refer to in positive extremes.

[aceside]

Especially with an ace poor deck?

I agree with you. The dealers’ bust rate critically depends on the density of aces in the remaining deck. The more aces, the less likely the dealer will bust; therefore, a player should play one hands. Otherwise, play two hands when TC>+1. I proposed this technique a year ago to seek you guys confirmation, but to no avail.