How to Shave 30 Seconds off Solving a 3×3 Rubik’s Cube – 4 Look Last Layer (4LLL)

This tutorial presumes you already know how to solve a rubik’s cube, if you don’t, please start by learning How to Solve a 3×3 Rubik’s Cube in Under 2 Minutes.

Once you have the basic solution down, you may want to reduce your solve time. There are various ways to do that, but this tutorial will focus on solving the last layer in as little as a quarter of the time.

In How to Solve a 3×3 Rubik’s Cube in Under 2 Minutes you learned how to solve the last layer in 4 steps:
Step 1 – Create a cross – F R U Ri Ui Fi.
Step 2 – Align the centers – R U Ri U R U U Ri Ui.
Step 3 – Position the corners – U R Ui Li U Ri Ui L.
Step 4 – Orient the corners – Ri Di R D.

The algorithms you learned are the minimum amount required to solve the cube, they are not however the most efficient. These algorithms do not take into consideration the state of the cube, and many times you have to repeat an algorithm multiple time to solve each step.

In this tutorial you will learn multiple algorithms for each step, with each algorithm matching a cube state. You will have to memories more algorithms but you will always be able to complete each step in one algorithm with no repetition- 4 algorithms in total to complete the last layer.

We will start by orienting the top face, edges first and then corners.

Step 0 – Learn the moves

For reference above are all the move annotations you already know.

In addition to the moves you already know, there are 3 more annotations you need learn:
1) Lower-case letter means turning 2 layers of the corresponding face.
2) B stands for back – the layer facing away from you.
3) M stands for middle – the layer between the front and the back.

How to Beat Rock-Paper-Scissors – Improve Your Odds of Winning the Game.

Rock-Paper-Scissors is suppose to be a zero-sum hand game with a 1 in 3 chance of winning any given round, but is it really a game of chance?

The zero-sum game characterization is based on the assumption that the weapon (rock, paper or scissors) is chosen at random. Most real life experiments will show that, on average, players tend to chose each weapon about a third of the time.
However, who is to say that there is no pattern in the order of the weapon choice?

If players continuously or subconsciously use a predictable strategy to play the game then that’s a weakness that can be exploited.

Continue reading “How to Beat Rock-Paper-Scissors – Improve Your Odds of Winning the Game.” »

How to Play and Win 2048 – Tips, Tricks and Online Game

2048 is a single-player puzzle game in which the objective is to obtain a 2048 tile. A 2048 tile is achieved by combining matching numbered tiles on a 4 by 4 grid.

There are 4 possible moves:
Left to Right” – Right arrow key.
Right to Left” – Left arrow key.
Top to Bottom” – Up arrow key.
Bottom to Top” – Down arrow key.
With every move a new tile (with a value of 2 or 4) randomly appear in an empty spot on the board.

Tiles slide as far as possible in the chosen direction until they are stopped by either another tile or the edge of the board. If two tiles of the same number collide while moving, they will merge into a single tile with their sum value – e.g.: 2 and 2 becomes 4, 4 and 4 becomes 8 and so forth.
The resulting tile cannot merge with another tile again in the same move.

The game is over when the board is full and there aren’t any possible moves left.

In order to reach the mythical 2048 tile, the player must play strategically and maintain enough room on the board to achieve the tile.

How to Solve a 4×4 Rubik’s Cube (Rubik’s Revenge)

Step 0 – Solve a 3×3 Rubik’s Cube

Solving the 4×4 Rubik’s cube is very similar to solving the 3×3 Rubik’s cube, it just requires a few more algorithms to learn, so the first thing you need to do is solve a 3×3 Rubik’s cube.
Refer to How to Solve a 3×3 Rubik’s Cube in Under 2 Minutes.

Moves

Same move notations apply to the 4×4 as the 3×3 cube, with 2 differences:
1. Lower-case letters mean turning 2 layers of the corresponding face.
2. The number “2” before the face letter (e.g. 2R) means moving only the internal layer of the corresponding face.

The Difference Between a 4×4 and a 3×3 Cube

The Center Block

The center – Unlike a center piece in a 3×3, which is fixed and thus represents the color of it’s face, the 4×4 cube doesn’t have a single center piece, but rather 4 center pieces per face which aren’t fixed in position. We will refer to the 4 matching center pieces as a Center Block.

The Edge Block

The edges – Each edge on a 4×4 cube has 2 pieces instead of the 1 on a 3×3. 2 matching edge pieces paired together are called an edge block.

Step 1 – Solve the Center Blocks

Identify 2 Opposite Centers

The first step to solving a Rubik’s cube is to figure out the faces. On a 3×3 the color of the face matches the center cube – job done. On a 4×4 cube the center blocks are not fixed – job not done, but rather one has to get all the center blocks in the right spot. The “right spot” would have to correspond to the given edges and corners of the Rubik’s cube.
On a standard cube blue is opposite white, green is opposite yellow, and red is opposite orange. However, if your cube is not standard, the way to figure out the opposite centers would be to match 2 corners that have 2 of the same color, the third color of each corner would be opposing color to the other. e.g, in the above image, 2 corners are matched, the third color on one is blue, and the third color of the other is white, meaning the opposing center to blue is white.

Solve 2 Opposite Centers

Start by making 2 rows of each color. In order to align 2 matching pieces, position them like image above and do a 2R move to align.
Do the same for the opposite color without disturbing the opposite row – for instance do it on the top and left of the complete face, and move it to the back of the complete face when done.

Solve the Remaining Centers. At this point the status of the cube can be one of 5:

1. The rest of the centered are already solved and are in the right position. If that’s the case you are all done with the centers and can move to the next step.

2. The rest of the centered are already solved but are NOT in the right position.
If the centers are on opposite sides, to switch them place one of the centers facing you and use d d F F B B d d
If the centers are next to one another, to switch them place one center facing you and the center you would like to switch with on the left and do di B B d d L L di.

3. Your cube has 2 rows of each color solved.

In the case of the rows being next to one another do a d move to solve the neighboring centers.

In the case of the rows being on opposite sides do a d d B B d d.

4. Your cube has an odd number of center tiles.

In this side by side scenario a d Fi di will make these 2 tiles into a row without disturbing the other centers.

In this opposite scenario a 2d F B 2d will turn both sides into solid color centers.

Note: Make sure that the checkered pattern is reversed to the opposite side. If it isn’t do an F move before you start.

In this side by side scenario a 2d L d will complete the center without disturbing the other centers.

In this opposite scenario a 2d F B 2d will turn both sides into solid color centers.

Note: Make sure that the checkered pattern is reversed to the opposite side. If it isn’t do an F move before you start.

Step 2 – Solve the Edges

As mentioned above an additional difference between a 4×4 and a 3×3 cube are the edges, with the edges of a 4×4 consisting of 2 pieces. Once all edge blocks are in place, you will be able to solve the cube like a 3×3 cube.

Pair up the edges and store them safely

Every solved pair would need to be stored safely in wither D or U face, in place of an unsolved edge.

To replace with an unsolved U use Li Ui L

To replace with an unsolved D use L D Li

How to Count Cards in Blackjack

Blackjack possibly has the lowest house edge of any casino table games, with an edge as low as a 0.28% in favor of the house.

Counting cards is used to lower the house’s edge, or even give the player an edge over the casino. The player edge may range between 0%-1% when counting cards.

The Hi-Lo strategy

The most popular card counting strategy is the “Hi-Lo strategy”, primarily because it is simple to master and yields good results.
With this strategy high cards are given a value of -1, while low cards are given a a value of +1. When added up, they total the running count. Bet amount is placed based on the running count – bets increased when the count is positive and decrease or not placed when the count is negative.

The reason the “Hi-Lo strategy” works is because high cards (10 to Ace) improve the player’s chances of hitting a blackjack, which pays out at 3:2. They also increase the dealer’s chances of going “bust” – since they have to hit on 16 and under. Low cards, on the other hand, are bad for the player – reducing his chances of getting a blackjack, but good for the dealer by decreasing his chances of busting on 16 or under.

If the high to low card ratio is higher than normal – meaning, there are lots of high cards still in the deck, the player can place a bigger bet to increase the amount he stands to win.

The running count

To track high to low card ratio, cards are assign a value between -1 to 1.
Cards 2-6 have a value of +1.
Cards 7-9 have a value of 0.
Cards 10-Ace have a value of -1.

The count starts at 0 every time the decks are reshuffled, and each time a card comes out, it’s value is added to the tally.

Factor in the decks

To get an accurate running count, one must take into account the number of decks left to be dealt.
In order to factor in the number of decks one would have to divide the running count by the number of decks waiting to be dealt. If your running count is +6 and there are 3 decks left, the real count is actually +2.

Betting

Bets are increased when the count is running positive, meaning +2 and above.
Generally speaking, one would want to increase their bet by one unit for each point that the tally goes up.