Basic strategy - trying to calculate a flush draw

In Texas Holdem Poker, or in Omaha, trying to figure out the chances you have to complete a flush or a straight, after the flop with two cards to come for example, is quite easy.

Let's say we have two hearts and there are another two on the flop. So, there are 9 hearts out of (52 minus our 2 minus the 3 on flop) 47 cards. We do not count our opponents' cards, as we do not know whether they have a heart on them or not.

To calculate the chance we have to complete our flush, we will do a little trick. We will calculate the chance not to complete our flush first, which is easier.

We will not complete our flush if the turn and river are both not a heart. The chance that this happens is 36/47 * 35/46 * 100%. Note that 36 out of 47 cards do not give a flush on turn, and 35 of 46 ( because a non heart was dealt previously ) do not give a flush on the river. This equals 58,28%.

So the chance for us to complete the flush obviously is 100%-58,28%=41,72%.

In Open Face Chinese Poker, these calculations are not so easy to make. After you are dealt your 5 cards, not only there are 8 cards to come for you instead of 2, but also there are 5 other open cards, for each opponent you have, on the table. But the biggest problem is that with every card that you will be dealt, your opponents will also be dealt another card that may or may not suit you.

With these conditions, its nearly impossible to try to figure out what is the exact chance to complete a flush draw after you are dealt your first 5 cards. To try to calculate the chance for completing a flush draw we must make an assumption. We will assume that we are dealt all the remaining cards right away without all the other players getting any. This way we simplify the problem at hand very much.

So, finally, lets try to calculate a problem. Let's say we are dealt 4 hearts, and we play heads up with another player who was dealt before us 2 hearts and 3 other cards.

Same as before, the chance not to complete the flush is:

35/42 * 34/41 * 33/40 * 32/39 * 31/38 * 30/37 * 29/36 * 28/35  *100%

This equals 19,94%. So the chance to make our flush is 80,06%.

Open Face Chinese Poker Guide: Rules, Scoring and Strategy

Rules at a glance

Chinese Poker is played by 2-4 players with a standard 52 card deck.
Each player is dealt 13 cards.
Every player must arrange his 13 cards in 3 stacks called "settings": The "back" containing 5 cards, the "middle" with also 5 cards and the "front" with 3.
Standard poker ranking is used to rank each setting and compare them to the other players' settings (although some razz or 2-7 lowball variations are not unheard of).
Each player's back must be a better combination than his middle, which must be better than its front. If that condition is not met, this person is "foul".
If you and your opponent do not "foul", you compare your back, middle and low to your opponent ones. Each win gives you a "unit" which is a predefined amount of money. If you win in all 3 settings then you have a "sweep" over your opponent and win 6 units instead of 3.
If you "foul" and your opponent does not, you give him 6 units (and vice versa).
Very good combinations win extra units from your opponent, called "royalties". These are paid in excess of the units mentioned before.
Royalties are agreed before the game. A usual set of royalties is:

A usual set of royalties for Chinese Poker

When more than 2 players play, each one compares his settings in turn with all the others and win or loose units from setting comparison and royalties from each one of them.

Open Face Chinese Poker

This is the most common variation of the game today. Each player is dealt 5 cards face down. Then, starting from the player sitting on the left of the button, all players must arrange these 5 cards face up on their back, middle and front settings. After that, a card is dealt in turn to every player in the same order until everyone has 13 cards, arranged as mentioned before (5 back, 5 middle, 3 front).

Then players compare their settings and win or loose units accordingly, as explained before.

        Fantasy Land

Fantasy Land gets triggered if you get a pair of Queens as your Front hand without fouling. If you manage to make a valid hand with Queens up Front then on the next hand you will get dealt all 13 cards face down right from the deal. This can obviously give you a strong advantage as you are not reliant on draws, and you can place those 13 cards optimally into their 3 hands.

A Sample game

In this game, Player 1 has a better back (a flush, ace high) and better front (a pair of 2's), while Player 2 has better middle (2 pair, jacks over 3's). So Player 1 wins 1 unit from Player 2 (Its 2-1 score).

Also, the royalties must be paid. Player 1 made a flush so player 2 must give him 4 units, and Player 2 made a straight so Player 1 must give him 2 units. So Player 2 must give Player 1 2 units (4-2 score).

So, to sum up, in this game Player 1 won 3 units from player 2.

Here is also a nice tutorial, from Shaun Deeb:

Basic Open Face Chinese Poker Strategy

A good strategy to avoid fouling is to place higher cards in the Back hand, and slighlty lower in the Middle hand, and then the lowest denomination cards in the Front hand.  That way when pairs are made the 3 hands remain in descending order.This approach can be tweaked if say your first 5 cards have 4 to a flush or 4 to a straight. Then you can make this the basis of your Back hand with confidence you'll complete that hand in the next 8 cards.

If you've got a bit more gamble then you might choose to aim mainly for royalty points even as the number of cards left to be dealt get less and less.  By doing so you are taking a bigger risk that you foul your hand.  The rewards can be big for this if you hit, so it is often a balancing act between how big the reward can be and how often you mind giving up a minimum of 6 points each time if you foul.

You should always keep a good eye on what upcards there are on the board as a whole (eg your opponent(s) hands as well as your own) as this will tell you how live your draws are.  You can in fact calculate this very accurately if you are good with odds, hence part of the reason Open-face Chinese is a very skillful game.   

(To give a simple example you could decide that going for a spade flush is going to be a good idea because of the lack of spades currently on the board, or you could decide that a straight draw is a good idea because of the number of live cards still in the deck which would complete that particular straight).

Talking of straights, be careful not to place too much value to making a straight, because the royalty for this is only 2 points in the Back hand.  Remember you could lose 6 points alone by fouling so know when to give it up if it's looking unlikely.

If you seem to be getting dealt a very poor hand (eg after 7 to 10 cards) it can be a good idea to play defensive to try to win one specific hand, because you are looking at just a 1 point net loss by losing 2 out of 3 hands, and a 6 point net loss if you lose all 3.  A good way to do this is to make a strongish hand at the Front (whilst not fouling obviously) because often players have a couple of really good hands (Back and Middle) but the Front hand gets neglected as just any old high card.  Another way (when the deal/board dictates) is to make a strong as possible Back hand but effectively abandon the Middle and Front.

It is also important to factor which hands your opponents are aiming for and what their likelihood is of getting there. For example if it looks like there is a strong chance of them fouling their hand you could change your focus from drawing to a big hand yourself, to just making sure you don't foul.