Just one question about betting high at high TC...

[Planisphere]

I was playing heads on with the dealer, and at some point reached really high TC (+6). (I use Hi-Opt II + ASC and I know my plays). But it occurred to me, that the dealer of course has the same probability of getting blackjacks or two tens as I do.

What is the point of betting high when the dealer has the equal chance of getting 21 or 20? (I know by theory that I should bet high...but I do not know the logic behind it ). Are we hoping for the dealer to bust with a ten when he has a stiff hand lower than 17?

[RS]

If you get a 21, you're paid 3:2. If dealer gets 21, you lose even money. If that's all that could possibly happen, you'd have a lot of money really fast.

As far as everything else like splitting, hitting, double downs, I'll let someone else more knowledgeable answer that. Obviously you're going to be in a better situation when you do double, like 9, 10, or 11....but those hands are going to occur less frequently because they consist of 2 little cards and since there are fewer little cards....yeah. I don't know if the ratio between frequency of doubling down opportunities and the increased strength helps you (I'd think yes, but idk for sure) or hurts you. But you certainly gain at least some value from hands like 9v7, 9v2, 8v5, 8v6, 10vT, 10vA, which you normally wouldn't double down, but in a higher count you would. You also gain value from dealer being more likely to bust with a 2-6 showing, although those hands will come less frequently since they are fewer 2-6's in the deck....whether that's a net plus (I think so?) or not, I don't know.

If I'm not mistaken, a majority of your advantage comes from the increased frequency of hitting blackjacks....main reason why 6:5 games are (for the most part) not worth it / uncountable.

[Member Name Hidden]

I've yet to see less than 3-2 at Spanish 21. Hint:Hint:

[DSchles]

If you get a 21, you're paid 3:2. If dealer gets 21, you lose even money. If that's all that could possibly happen, you'd have a lot of money really fast.

As far as everything else like splitting, hitting, double downs, I'll let someone else more knowledgeable answer that. Obviously you're going to be in a better situation when you do double, like 9, 10, or 11....but those hands are going to occur less frequently because they consist of 2 little cards and since there are fewer little cards....yeah. I don't know if the ratio between frequency of doubling down opportunities and the increased strength helps you (I'd think yes, but idk for sure) or hurts you. But you certainly gain at least some value from hands like 9v7, 9v2, 8v5, 8v6, 10vT, 10vA, which you normally wouldn't double down, but in a higher count you would. You also gain value from dealer being more likely to bust with a 2-6 showing, although those hands will come less frequently since they are fewer 2-6's in the deck....whether that's a net plus (I think so?) or not, I don't know.

If I'm not mistaken, a majority of your advantage comes from the increased frequency of hitting blackjacks....main reason why 6:5 games are (for the most part) not worth it / uncountable.

Mostly everything you've written is correct. When the count is higher, you get more frequent naturals, which pay 3:2. Your doubles and splits are more successful (and the dealer can't double or split). You may take insurance. You may surrender. You may stand more frequently than what BS calls for. And yes, if the dealer shows 2-6, he will break more frequently. So, all of the rules of the game conspire to give you an advantage when the count is high.

Don

[Freightman]

Think of it this way.
It's heads up, and over the first 100 hands, they're 100 blackjacks between you and the dealer. You win 50, you lose 50. You've flat bet $100 per hand, so your total action is 100 hands x $100 = $10000.

You lose 50 hands, or 5k, when dealer has Blackjack. You win 50 hands, at 3-2, or 7.5k. Your profit is 2.5k. I'll trade blackjacks with the dealer all day long.

As far as the rest goes, ditto on Don. He gets it right every so often

[RS]

Mostly everything you've written is correct. When the count is higher, you get more frequent naturals, which pay 3:2. Your doubles and splits are more successful (and the dealer can't double or split). You may take insurance. You may surrender. You may stand more frequently than what BS calls for. And yes, if the dealer shows 2-6, he will break more frequently. So, all of the rules of the game conspire to give you an advantage when the count is high.

Don

Thanks for confirmation. I can't believe I forgot about insurance. =\

At the risk of semi-hi-jacking this thread (and my laziness but also general interest), do you know the value of different upcards between low counts and higher counts? IE: At TC=0, a dealer upcard 6 should occur 7.69% of the time (1/13) and will be worth some X value in EV. As the count goes higher and there are fewer 6's remaining, it is less likely than 7.69% (1/13) for a 6 to be the upcard, but when it is, the value is greater than the TC=0 'X' value in EV. Same with other cards, as well as splits and doubles.

In other words:

At a low count, having a 6 upcard is more likely but is also worth less, while in a higher count it is less likely but worth more. How do the frequencies and values break down? Overall, is this an increase in value at higher counts, a similar value, or possibly even decreased value? I'd assume this is a known thing and not asking for specific numbers, but what it is in general? The same would apply for doubling down 9-11's.....the doubles will show up less frequently because there are fewer cards to add up to 9-11, but when they do, they are worth more. How much does the extra value add compared to the decrease in frequency?

Yes, I'll be the first to admit I'm lazy, although, I don't even know how I'd go about finding the answer to this question. Just curious if you know the answer (in general figures) or if it's one of those things that doesn't really matter at the end of the day. I'm mostly just curious and think it's interesting.

[DSchles]

I don't know the answer, and it's a perfectly legitimate question. I know that high counts make all the things we discussed more valuable, as a concept, so I know that, despite the decrease in frequency, in general, doubling becomes more valuable in higher counts. Splitting also. Insurance, obviously. A dealer upcard of, say, 6 will break much more frequently as the count rises, but, as you say, the offsetting feature is that the 6 will appear less frequently as the upcard. My instinct tells me that, globally, you'll gain more from a 6 in a high count than at a neutral count, BOTH things being considered. But, I don't know how much, and it's conceivable that I may be wrong. :-)

Don

[RS]

I don't know the answer, and it's a perfectly legitimate question. I know that high counts make all the things we discussed more valuable, as a concept, so I know that, despite the decrease in frequency, in general, doubling becomes more valuable in higher counts. Splitting also. Insurance, obviously. A dealer upcard of, say, 6 will break much more frequently as the count rises, but, as you say, the offsetting feature is that the 6 will appear less frequently as the upcard. My instinct tells me that, globally, you'll gain more from a 6 in a high count than at a neutral count, BOTH things being considered. But, I don't know how much, and it's conceivable that I may be wrong. :-)

Don

Ah, darn, I was hoping/expecting this was something that has been discussed or examined in detail. I guess the game hasn't been analyzed 6 ways from Sunday, as they say.

[Dog Hand]

This post contains graphs showing the frequency of a dealer up card of 6, the frequency that the dealer will bust with that up card, and the pre-deal chance that both will happen, all as functions of the HiLo TC for a 6D H17 game.

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

Hope this helps!

Dog Hand

[DSchles]

This post contains graphs showing the frequency of a dealer up card of 6, the frequency that the dealer will bust with that up card, and the pre-deal chance that both will happen, all as functions of the HiLo TC for a 6D H17 game.

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

Hope this helps!

Dog Hand

Those charts are spectacular -- the only thing like that in print. And, as it turns out, I was wrong. :-( (At least I said I wasn't sure and that I could be wrong.) Not easy to apply intuition to something like this. General observation: 7, 8, and 9 aren't affected much in the combined bust rate for higher counts; tens and aces bust more, because their increased frequencies of appearance dominate their tendencies NOT to bust, once they do appear. All the others (2-6) are just the reverse. They bust less, because, although they bust much more IF they appear, they appear with even greater infrequency.

Tricky!

Don

[RS]

This post contains graphs showing the frequency of a dealer up card of 6, the frequency that the dealer will bust with that up card, and the pre-deal chance that both will happen, all as functions of the HiLo TC for a 6D H17 game.

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

Hope this helps!

Dog Hand

Thanks! I think I may even remember reading that post years ago (or something like it with lots of graphs and stuff) now after the fact. Good stuff.

The colors are difficult for me to see, but if I'm reading the third graph correctly, it appears the overall bust rate for a 2-6 upcard decreases on a global or overall scale? Although, it looks like it only goes down a little bit. Looks like the 6 goes from 3.5% at TC=0 to 3.2% at TC=5.

[DSchles]

Thanks! I think I may even remember reading that post years ago (or something like it with lots of graphs and stuff) now after the fact. Good stuff.

The colors are difficult for me to see, but if I'm reading the third graph correctly, it appears the overall bust rate for a 2-6 upcard decreases on a global or overall scale? Although, it looks like it only goes down a little bit. Looks like the 6 goes from 3.5% at TC=0 to 3.2% at TC=5.

Did you miss my post, above?

Don

[Freightman]

Those charts are spectacular -- the only thing like that in print. And, as it turns out, I was wrong. :-( (At least I said I wasn't sure and that I could be wrong.) Not easy to apply intuition to something like this. General observation: 7, 8, and 9 aren't affected much in the combined bust rate for higher counts; tens and aces bust more, because their increased frequencies of appearance dominate their tendencies NOT to bust, once they do appear. All the others (2-6) are just the reverse. They bust less, because, although they bust much more IF they appear, they appear with even greater infrequency.

Tricky!

Don

I was going to needle you on your self confessed error, but decided not to, as we all screw up from time to time, including myself . Of course, I have a question as well.

First, thanks to Dog Hand, for his typical run of the mill, superlative comment and graph. Love his stuff. First, to clarify, as I've seen you comment before without adequately explaining the higher face card bust frequency. So, I think analogy, would be to equate the frequencies akin to median and average.

In most industrial/commercial analysis, averages typically exceed medians. So, applying the concept to the OP, dealer 6 up will bust more frequently than dealer 10 up, on a 1-1 comparison. On that basis, we are far better off with dealer 6 up. However, dealer face up, obviously occurs at 4x the frequency of dealer 6 up, and because if that simple fact, bust frequency of dealer face card is higher than 6 up.

Would you agree, or disagree, with that analogy.

For whatever it's worth, I often play a game with myself (don't believe I've previously disclosed) of calculating my odds of winning a hand, based on my hand and dealer card, adjusted card by card) I find it entertaining as well of the fact, though not documented, can shape ideas for adjusting index play.