if you sure next card is an Ace , how much u bet ?

how many % of bankroll will you bet

if the ace will sure come to your next hand ?

and how much will u bet if u sure one of the next three card will have an Ace ?

Full Kelly bet 45% of BR - safer to bet 10-20%. If one of 3 cards divide 20%/3 = 7% BR. zg

Can you spread to 3 hands?
If I were certain the next card would be an Ace, about 25% of my days BR.

42.08% There is a whole chapter on this in Exhibit CAA.

Now I don't have Exhibit CAA but that 42% seems awfully high. Sure you have a 51% advantage but two bad beats and you now only have 16% of your bankroll left. Seems like thats a lot of risk to have even though you have a 51% advantage.

http://www.blackjackforumonline.com/content/ACEbjfo1.pdf

Pretty intense article.

With an Ace, you have a good shot at getting a soft hand that needs to be doubled. I'm not putting 84% of my BR on a hand.

You can always double for less. The article above gives the correct strategy for those situations, as well as possible modifications for the strategies for splitting, hitting, surrendering and insurance.

-Sonny-

as a matter of fact, there will be times when you see a hand you might normally double but given the fraction of your bankroll you have riding on the table, you might not double at all...

I only gave the article a quick going over, but it struck me that it appeared to be geared towards a game that offers surrender. As most games don't, the numbers seem off.

Full Kelly betting is a wild ride. Surprise, surprise. As a practical matter, one hopes that your bankroll is big enough that you'll be able to bet the nominal or practical table max in most casinos, should this situation come up.

I agree but I've also never played at a table where table max is anywhere near 42% of my bank roll (given I play lower stakes), thus I'd always betting table max.

beyondbj, do you not have Exhibit CAA, or are you expecting someone to read it to you?

zengrifter, your 45% figure is high. why spout approximations, when the exact answer is available, or haven't you yet received your pdfed copy of CAA?

1357111317, no after two losses (assuming no doubles/splits), you would have 100% x 58% x 58% = 34% of BR left, because you are betting 42% of a BR that is shrinking as you lose.

shadroch, you aren't going to double much, because Kelly implies different strategy as well as a bet size, and no, the article is not geared towards surrender, and no, the numbers are not off.

sonny, you read too much, and need to play more.

It is very frustrating to read recurring threads over the years (decades) on the boards, to solve the problem, to publish the solution (for free!), and then still read new threads where people try to reinvent the wheel or misstate the published solution. Sigh.

Well if all board members had access to the PDF'ed copies I'm sure less reoccuring questions would be asked :grin: :joker:

Anyways, I did have a chance to page through Exhibit CAA for a little while and was blown away by the amount of valuable information. I may have to buy it before this one goes out of print

"42.08%" is also an approximation, because the game parameters have not been stated- S17 vs. H17, doubling rules, number of decks, all of which will affect the exact answer.

The other criterion which will control the correct answer in a real-world situation is the effect of a win or a loss on the player's trip. It defeats the purpose of Kelly betting to disregard the effect of an individual event on the player's future income. Let's say I'm in an environment where I'm getting 8-15% advantage peeks, and I came capitalized to play them at a table max. Winning my known-ace will not allow me to increase my future bets above the table max, while losing it will reduce my trip BR to the point where I'm playing for a crappy win rate all weekend. Something similar can happen in a grind-out counting situation, where I'm counting in a marginally acceptable environment, but subtract 42.08% of my trip bankroll and my resulting win rate makes it no longer acceptable for me to work, I'd choose to spend my time instead doing something I enjoy, thus my future income for the trip would be effectively reduced to zero.

Sorry, but I don't believe your second decimal place is significant, taking all of this into account!

Why don't you read the book or the article (free)? The article gives the answer for other parameters, including H17 and S17. (The other main rule, DAS, doesn't matter for Aces.). Pro21 excerpted the 42.08 because it's the title of the article and is close, regardless of the rules.

The other parts of your post are irrelevant here. People were talking about the Kelly bet. It is what it is. It doesn't matter whether you are up or down for the trip, have additional good opportunities or not, etc. Now you do mention one point, "Winning my known-ace will not allow me to increase my future bets above the table max." Gee, I wonder what that article/chapter "CTR-Averse Betting" is all about.

But if you want to talk about "real-world situations" then the topic is almost moot--the answer is almost always to bet whatever you can get away with, which will be vastly underbetting any serious player's bankroll, often less than 1% of BR.

I've read both. The point is that approximations are acceptable in this context.

Right, the (full) Kelly bet is the Kelly bet, but Kelly's theorem in its pure form takes into account bank, variance and expectation, and does not consider the other realities which exist in a casino such as table limits, scarcity of opportunities and the value of a practitioner's time and overhead expenses.


Sure. In most cases the right bet would be the table max. And if the table max is really less than 1% of your BR, no reason not to take most of the soft doubles, right?

Here's a fun one: Full BR is $1M, known next ace, table max is $1000, you have $1000 in your pocket at the time, DOA. What's the best bet?

As a part-time player with a full-time job, absolute bankroll is kind of an existential thing and more relevant are funds I have on my person for immediate use, and funds I have available for that trip/session. "Ruin" in the sense of gambler's ruin doesn't really exist; all that can be ruined is one trip.

"I've read both. The point is that approximations are acceptable in this context."

And my point is that if someone asks a specific, well-defined theoretical question, for which the answer is available, then why unnecessarily introduce an approximation? I'm not saying the second decimal place is critical, but why say 45%, instead of 42%? Pretty soon someone else in another thread quotes the 45%, which then gets approximated to 50%, etc. Approximations are great when we don't know the answer, but here we do!

"[Kelly] does not consider the other realities which exist in a casino such as table limits,"

What about the CTR-Averse article?

"scarcity of opportunities and the value of a practitioner's time and overhead expenses."

You're right. My optimal bet is zero, because it's not worth my time to gamble.

"Sure. In most cases the right bet would be the table max. And if the table max is really less than 1% of your BR, no reason not to take most of the soft doubles, right?"

You usually can't even get away with the table max, but yes, everyone I know DOES make all relevant soft doubles, splits, etc. Contrary to the implication that "real-world situations" complicate this problem, the opposite is true: in the real-world, you bet whatever you can get away with and what you can stomach--very simple. In the theoretical world, the 42.08% answer was unknown for decades, and took some very thorough numerical work to get. The number is very useful for illustrating to many people that Kelly is far more aggressive than most people can stomach, as WRX says.

"As a part-time player with a full-time job, absolute bankroll is kind of an existential thing and more relevant are funds I have on my person for immediate use, and funds I have available for that trip/session. "Ruin" in the sense of gambler's ruin doesn't really exist; all that can be ruined is one trip."

This is the whole point of the CTR-Averse article, but not the point of the question, "How much would I Kelly-bet on a known Ace?"

Actually, the question was how much of your BR should you bet, not how much would I Kelly-bet. While Kelly betting may be the ideal in an absract sense, few people who would ask the question are using Kelly.

"Actually, the question was how much of your BR should you bet, not how much would I Kelly-bet."

True, but I'm picking up the thread from the point where ZG says (post 2 of thread) that the Kelly bet is 45%, because the original question, and the paraphrase "how much of your BR should you bet," doesn't make sense. As an economist, I am constantly irked by the word "should" as used in this context. That word renders the question instantly meaningless. Bet whatever you want! It's just like asking, "Should I order the steak or the salmon?" Dowutchyalike. There isn't anything that you "should" do.

All we can ever do is say: (1) You "should" do abc IF you want to achieve xyz, or (2) You "should" bet abc IF you have xyz utility, or (3) Given that most people empirically feel comfortable betting abc percent of their BR, what economic model would generate an abc solution, and can we then use that economic model to get answers or predictions to other situations that that individual might face, or can we then use that economic model to predict what a group of similar individuals would do in the aggregate?

I've never seen any real-world situation where the answer was anything other than "Bet whatever you can get away with," which may be why ZG steered the thread towards the theoretical Kelly answer.