Blackjack dynamic programming
Introduction to Neuro-Dynamic Programming (Or, how to count cards in blackjack and do other fun things too.) Eric B. Laber February 12, Eric B. Laber. OPTIMIZATION AND CONTROL Richard Weber Contents DYNAMIC PROGRAMMING 1 1 Dynamic Programming: The Optimality Equation . A RISK-AVERSE STRATEGY FOR BLACKJACK USING FRACTIONAL DYNAMIC PROGRAMMING A Thesis Submitted to the Graduate Faculty of the Louisiana.
20. Dynamic Programming II: Text Justification, Blackjack
It makes sense to write down this is my state, and then make sure that you're always representing it. That's counted out here. Where do we always start? And we know that has one fewer edge, because we just guessed what the last edge was. The second time we call it, it's already memoized, so we don't have to pay for it. It's an experimental perspective.
OK so any pointed questions before we go over blackjack? Before you start blackjack can you go through the rules again? The rules of the game? Well I'm going to do something better than going through the rules. I'm going to abstract the rules away. So I'm going to say that a game of blackjack has, let's start here. So a game of blackjack has a deck. And we have x-ray vision or some other illegal way in which we know what the deck looks like from the beginning.
How many cards in a deck? So say from 0 to 51 because we like zero-based indexing. So the way that the game starts is you get two cards, the dealer gets two cards. What is the only decision that you make in the game if you already have perfect information? So you know the deck already. You don't need to wait for each card to know what it's going to be.
So as the game starts you have to make one decision. Well that's assuming you care what you get each time. So if you have to look at the card then you have to decide each time if you hit or stand. How much to bet? I think our game has that fixed. So it is hit or stand, but I want to restate that.
Because you don't actually have to decide after every card if you want to hit or stand. You know what the cards are going to be in advance. Like how many cards to pick? How many cards to pick. Yeah that's pretty much the same thing. So you don't have to decide every time hit or stand, you know ahead of time I want to hit three times, or I want to hit once. Because you know the entire deck. You don't need to actually look at the cards.
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All right, today we continue our exciting adventure into dynamic programming. I'm excited, super excited. Dynamic programming, as you recall way back before Thanksgiving, is a super exciting powerful technique to design algorithms, especially to solve optimization problems where you want to maximize or minimize something. Last time, we saw how two algorithms we already knew-- namely, how to compute the nth Fibonacci number and how to compute shortest paths via Bellman-Ford-- are really dynamic programs in disguise.
And indeed for, at least for Bellman-Ford, that's how they were invented, was to apply a general technique which we're going to see today in full generality, more or less-- most of this is generality-- in five easy steps. And we're going to see that technique applied to two new problems which are much more interesting than the ones we've already solved-- namely, how to make your text look nice in a paragraph, where to break the lines.
And how to win and make loads of money at blackjack. So lots of practical stuff here, and we're going to see one new technique for general dynamic programming. These are some things I wrote last time. Actually, one of them I didn't write last time.
In general, you can think of dynamic programming as a carefully executed brute force search. So in some sense, your algorithm is going to be trying all the possibilities, but somehow avoiding the fact that there are exponentially many of them. By thinking of it in a clever way, you can reduce the exponential search space down to a polynomial one, even though you're still not being very intelligent you're still blindly trying all possibilities.
So that's the brute force part. In more detail, the three main techniques in dynamic programming are the idea of guessing, the idea that, oh, I want to find the best way to solve a problem. Let's pick out some feature of the solution that I want to know.
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