The game is for 4 players, and is played on an 8x8 grid (a chessboard will work well). You also need 8 markers for each player (colored chips or beads would work fine), a fair pile of coins/tokens (you could gamble real money), and 3 six-sided dice.
Setup: Each player antes 8 coins into the pot and places one marker at the base of each column along the board. The columns (or, equivalently, the markers) are numbered, left to right, 2 3 4 5 7 8 9 10. Note that there is no 6. This is from the perspective of each player, so your 2 column will be the 10 column for the player sitting opposite you. Determine who plays first however you like; a normal set is four games, with each player starting once. Play proceeds to the left.
Gameplay: On your turn, roll 3 dice. Add two of the dice to determine which marker to move and the third to determine how far to move it. So a roll of 2 2 3 could be used to move the 4 marker 3 spaces or the 5 marker 2 spaces. Whenever you move a marker, you add a coin at the base of the column. When your marker reaches the far side of the board, you take coins from the pot equal to the number of coins in that marker's stack, empty the stack, and return the marker to its starting position.
There Are No Sixes: The main complication is that there are no sixes. Any time a die turns up 6, you must reroll it. You add an extra coin to the column for each set of rerolls. In addition, there is no 6 column, so on a roll of 1 2 4, you could use the 1+2 or the 1+4 for column choice, but not the 2+4. On a roll of 3 3 3, all three dice are rerolled.
Stealing: If your marker lands on another player's marker, you take all the coins from the corresponding stack and add them to your stack. You then move the other player's marker back one square. If your marker would pass over another player's marker, you can steal one coin (take it from his stack and add it to yours) as you pass over, or choose to move less than the full amount and land on his marker, stealing the entire stack.
Winning: The game ends when the pot is empty, or when one player runs out of coins. The winner of the game is the player with the most coins. In a multi-game set, you can tally net score and redistribute coins each game (settling up at the end if you're playing for money), or just play until somebody runs out of money.
Variations: A simple variation is to play on an 11x11 board with markers running 2-12 and not reroll sixes. Another is to number the markers instead of the columns and allow the players to choose how to order them. More interesting is the Foresight Variation.
To play the Foresight Variation, you need a whole pile of dice -- theoretically as many as 60, but 20 or 30 will probably suffice. Dice are not rolled each turn, but are instead rolled in advance, and upcoming rolls are visible to all players. Whenever a player doesn't have any rolls visible (including at the beginning of the game), he rolls one die (rerolling a six) to determine how many advance rolls to make. Sixes are not rerolled until the turn when that roll is being used, adding a degree of uncertainty to the foresight. Otherwise, the game is played as normal.
I designed this game for a piece of fiction, but I think it will be fun and interesting, and it has the feel to me of a time-worn classic, like chess or mahjong. The only problem with it is that I don't have a name for it. Suggestions are welcome...