Recent mathematical paper Cornell Univ. Six pages.

How to Gamble If You're In a Hurry
Shalosh B. Ekhad, Evangelos Georgiadis, Doron Zeilberger
(Submitted on 7 Dec 2011)

The beautiful theory of statistical gambling, started by Dubins and Savage (for subfair games) and continued by Kelly and Breiman (for superfair games) has mostly been studied under the unrealistic assumption that we live in a continuous world, that money is indefinitely divisible, and that our life is indefinitely long. Here we study these fascinating problems from a purely discrete, finitistic, and computational, viewpoint, using Both Symbol-Crunching and Number-Crunching (and simulation just for checking purposes).

The PDF can be found here.

I skimmed it but it didn't all make sense to me. I couldn't figure out where they took into consideration how much you win if you win a bet, which would seem to me to be a pretty critical variable; or if they assumed that the payoff is always mathematically fair; or if it doesn't matter. It's probably over my head and better left to the Wizard to translate into English.

Quote: JB

I couldn't figure out where they took into consideration how much you win if you win a bet, which would seem to me to be a pretty critical variable; or if they assumed that the payoff is always mathematically fair; or if it doesn't matter.

Because they are primarily working off of other material, and assuming a complete knowledge of that material. For the most part, they seem to be working off of Inequalities of Stochastic Processes where it is defined that the amount won is equal to the amount bet.

I think the most relevant part of the entire paper is the following:

Quote:

These humans, they are so emotional! That’s why they never went very far.

Quote: konceptum

I think the most relevant part of the entire paper is the following:

Quote:

These humans, they are so emotional! That’s why they never went very far.

Agreed. My emotions almost always overpower my will to play correctly or rationally.

Quote: JB

Agreed. My emotions almost always overpower my will to play correctly or rationally.

Well, I'm not too certain that a purely rational or "correct" approach is at all proper. What is proper is adequate knowledge to know what is officially the correct response and an ability to reason and determine if that is what you want to do.

When I have 16 I know I'm supposed to hit, but I often Stand instead.
After I've been drinking, I know there is something I'm supposed to do with two aces, but I'm too slow to do it.

Each of these two situations involves incorrect play based on emotions, yet Standing on 16 is sensible enough and really means I'm just too pissed at always hitting it and busting. However being too blotto to know what to do when confronted with two aces, means my responses are dulled by booze consumed because it is free.

Each is an emotional response but clearly they are of different quality.

Quote: FleaStiff

When I have 16 I know I'm supposed to hit, but I often Stand instead.

Is this true? I see 52 cards in the deck. 16 have a value of 10, 4 each of 9, 8. That's 24 cards with a value over 7. So my odds are ~50/50 that my next card will be +/-7. So, I'll bust over half the time on anything over 14?

Quote: 135steward

Is this true? I see 52 cards in the deck. 16 have a value of 10, 4 each of 9, 8. That's 24 cards with a value over 7. So my odds are ~50/50 that my next card will be +/-7. So, I'll bust over half the time on anything over 14?

Read up on "Basic Strategy for Blackjack" on the Wizardofodds.com website. It will explain why hitting even when there is a greater than 50% chance of busting is a play that will turn out better for you then standing, in specific circumstances, like 16 versus a 7...

Yeah, you're supposed to hit on 16.

But it is marginal to the point where it is sometimes better to surrender when available.

And, if the dealer has an ace, depending on the rules, it's sometimes better to surrender a 15 as well.