Deluxe Mat Edition 
This game, also known as Tripoli, is a modern version of the ancient European game Poch. In North America equipment for the game is sold under the names TRIPOLEY®, Rummoli, Michigan Rummy and Royal Rummy. In Australia, I am told it is known as Calliente, and in Germany it is still possible to buy a board for the game under the original name Poch.
The game is in three stages: in the first stage, the holders of particular cards collect the relevant stakes; the second stage is similar to Poker, and the final stage is a Stops game similar to Michigan or Boodle.
Three in One is best for 4 to 7 players (and is possible for 2 to 9). It requires a standard deck of 52 cards, the cards ranking in each suit, from low to high: 2-3-4-5-6-7-8-9-10-J-Q-K-A. You also need a supply of chips for betting, and a board or cloth marked out to receive the various stakes. The layout looks something like this:
Before the deal, each player must place nine chips on the board - one on each of the labelled spaces: ace of hearts, king of hearts, queen of hearts, jack of hearts, ten of hearts, king-queen of hearts, 8-9-10, kitty and pot. It may be that some of these spaces already contain unclaimed chips from previous deals; in this case the new chips are added to these.
The dealer then deals out the cards one at a time, clockwise, to form one hand for each player plus a spare hand. The spare hand does not belong to anyone. Some players will have one more card than others.
If as dealer you do not like your hand you can exchange it for the spare hand. You are not allowed to look at the spare hand before deciding whether to swap. If you do swap, your whole original hand is discarded face down and becomes the spare (you cannot combine cards from the two hands).
Alternatively, the dealer can offer the spare hand unseen for sale to the highest bidder. The person (if any) who buys the spare hand discards their own original hand face down and pays the dealer in chips the amount bid for the spare hand; if you auction the spare hand and no one wants to buy, you still have the option to swap your hand for the unseen kitty. Another possibility is to exchange your hand for the spare and then auction your old hand to the highest bidder. What you cannot do is exchange your hand for the spare and then exchange back - once you look at the spare hand you have to keep it.
Players will keep the same cards for all three stages of the game - there is no new deal before the second and third stages.
Anyone who holds the ace, king, queen, jack or ten of hearts takes all the chips from that space.
If a player has the king and queen of hearts, that player takes the chips from the king-queen space, in addition to the chips from the king and queen spaces.
The chips in the 8-9-10 space can be taken by a player who has an 8-9-10 sequence in one suit (for example 
8-9-10). The 8, 9 and 10 must all be in the same suit, but the suit does not have to be hearts. If two or more players have 8-9-10 in different suits they share the chips in the 8-9-10 space equally, leaving any remainder on the layout for the next winner.
Usually the chips in some of the spaces are unclaimed - these are left on the layout to be won in a future hand. Since more chips are added to each space at the start of each hand, the king-queen and 8-9-10 spaces, which are less often claimed, tend to produce higher winnings when someone does have the right cards.
Before the stops play begins, there is a round of poker. Everyone selects five cards from their hand that they wish to play poker with, separates them from the rest of their hand, and temporarily puts the other cards aside. You do not necessarily have to select the cards that form your best poker hand (you may have cards that you do not want to reveal until the stops part of the game, especially if you play the variation where stakes are collected from the layout in stage three rather than stage one). If you are not familiar with poker combinations, see the ranking of poker hands page for details.
All poker bets are placed in the pot space of the layout. The player to dealer's left begins the betting, and can either bet (putting an additional chip or chips in the pot) or check. If the first player checks, the next player can bet or check, and so on clockwise around the table. If everyone checks, all the poker hands are exposed and the player with the highest hand takes the pot.
If a player bets, it is no longer possible for subsequent players to check. After a bet, players have three options:
The betting continues clockwise around the table for as many rounds as necessary until one of two things happens:
Note that after you have passed / folded, you cannot take any further part in the betting.
If in the showdown, two or more players have equal hands, the pot is split equally between them. Any remainder of chips is carried over for the next deal.
It is usual to agree, before the start of the game, a limit for bets and raises in the poker stage. For example, if you agree a limit of 10, no one is allowed make an initial bet of more than 10, or to raise the bet by more than 10 chips in addition to the number needed to call the previous bet or raise.
All players pick up their cards, putting their poker cards back together with the remainder of their hand, and play a game of Michigan. The winner of the pot in the poker stage begins the play by leading a card face up in front of them. If there was a tie for the pot, the first of the winners in clockwise order starting to the left of the dealer will begin. The card led can be of any suit, at the player's choice, but must be the lowest card that they hold in that suit (it need not be the absolute lowest card in their hand - they might have a lower card in another suit).
The player who holds the next higher card of the led suit must play it, placing it face up on the table in front of them. Then the player with the next higher card of the suit must play that, and so on until either the ace is reached or no one can play because no one holds the next higher card of the suit. A card on which no one can play is called a stop card; this can happen because the next higher card of the suit is in the spare hand, or because it has been played previously.
When the end of the sequence is reached, the player who played the ace or stop card begins again. They can lead any suit except the suit just played, and they must play the lowest card they hold in the suit they choose. The player with the next higher card of the suit led plays it, and so on until another stop is reached.
The play continues like this until someone runs out of cards, at which point the play ends immediately. The player who played all their cards wins all the chips in the "kitty" space on the layout, and in addition wins from each other player a number of chips equal to the number of cards they had left in their hands.
If a player who has just played an ace or stop cannot lead again, because all their remaining cards are in the same suit that was just played, then the turn to play passes to their left hand opponent. If that player also has nothing but the suit just played, the turn to start passes around the table until a player is reached who has some other suit to lead. If no one has any other suit the play ends, and everyone puts into the kitty a chip for each card they have left in their hands. These chips stay on the layout to be won by the winner of stage three of the next deal.
The game can continue for as long as the players want. When you decide to stop, there will probably be unclaimed chips in some of the areas of the layout (often on the king-queen and 8-9-10 spaces). Rather than just sharing these chips out among the players, it is usual to play for them. This can be done by playing an extra round of poker: do not place any new chips but deal just five cards to each player and play as in stage two; whoever wins takes all the chips from the layout. If there were a lot of chips left over you may prefer to divide these into several pots and play a game of poker for each.
A popular variation is to omit stage one, and instead to play that the layout stakes are collected by anyone who plays the relevant card during the Michigan stage. To collect the king-queen stake you have to play the queen and king of hearts consecutively. To collect the 8-9-10 stake you have to play the 8, 9 and 10 of any suit consecutively. This makes the game slightly more interesting, in that if you are dealt a high heart or a sequence, there is no guarantee that you will collect the stake for it - someone might run out of cards before you have a chance to play it. Rummoli is played this way.
Some play that the suit of the pay cards on the layout is decided by whoever is prepared to pay the largest amount. Players bid in turn, starting with the dealer, and going around the table as many times as necessary until all except one player have passed. The high bidder then adds the amount of the bid to the kitty and chooses the paying suit. In this version the stakes on the pay cards are collected during the Michigan stage, as in the variation described above.
Some play that the sequence on the layout is 6-7-8 or some other specific sequence, rather than 8-9-10.
Some play that the poker betting is begun by the dealer, rather than by the player to dealer's left. Some play that the Michican stage is begun by the dealer, or by the player to the dealer's left, rather than by the winner of the poker.
Some play that everyone must play with their original cards - there is no swapping or auctioning of the spare hand.
All the variations given on the Michigan page are possible for stage three.
Some play that the first lead in stage three must be the lowest card in the player's hand. They have no choice unless they hold equally low cards in two or more suits. Subsequent leaders can choose the lowest card of any of the other three suits as usual.
Another possibility is to require that alternate leads are red and black. The first player must begin with their lowest black card. If the leader has two equally low black cards (for example 
2 and 2) they can lead either. Play continues as usual until someone plays an ace or stop card; this player must then begin again with their lowest card of the opposite colour - so the second sequence of plays will be red, the third will be black, and so on. If the player to lead has no card of the appropriate colour, the turn to lead passes to the left. If no one has a card of the right colour the play ends and everyone pays a chip to the kitty for each card in their hand. Since this version removes practically all skill from stage three (there is usually no choice of what suit to lead), I cannot recommend it.
Rick Leibold has sent me details of a variant called Cosmo, which was made by H. E. Kinnee Company in Detroit. This has a special board with cut-out windows displaying the suits of pay cards, the details of sequence and so on. These are printed on a second board behind the first and are changed each deal by means of a central handle. Only stage three is played, with alternate red and black leads.
From the Tams11 lobby you can obtain a Windows Michigan Rummy game that can be played solo or on line against live opponents.