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Subject: A simple heuristic for calling Tichu rss

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Greg Jones
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When

The prime time to decide whether or not to call Tichu is after you draw all your cards, but before the pass. That's because deciding if you'll call Tichu or not tells you how to pass to your partner. If you'll call Tichu, keep your best card. If not, give it to your partner. They might call Tichu.

Of course, rethink your decision after receiving passed cards, and again up until you need to play your first card.

How

First, count your "cover" cards. These are:

Aces
Phoenix
Dragon
Bombs
Dog, in most cases

If you don't have at least two cover cards, forget it. You probably can't call Tichu.

Now count your "junk" cards. First organize your hand into whatever sets you will be playing. Pairs, full houses, straights, etc. Any cards 2-K that you will be playing as singles are junk. Even consider Kings cards that you'll have to get rid of instead of cards that will help you.

If the number of junk cards is no more than 1 higher than the number of cover cards, plan to call Tichu.

Why

Ok, that was just a little formula. It's not at all clear why you should follow it. The real object is, after the pass, to have at least one more cover card than you have junk cards. Assume in the worst case that you'll need to get a lead to play each of your junk cards. Most of the "cover" cards usually win tricks. The Dog gets you a lead if your partner can win a trick. You want one extra, because otherwise it's not "bomb safe". If you play your last cover card and get bombed, you're usually screwed.

You can pass away up to three junk cards, but you'll probably get two back. And you assume you'll get a cover card from your partner. It's a net gain of 2 in your favor, so you can start out with an imbalance of one on the side of junk, but no worse. However if you start out with only one cover card, you'll get up to at most two and probably have two junk cards passed by opponents to deal with.

The mah-jongg essentially acts as a junk card and a cover. It gives you a lead, but you have to use that lead to play it. So it cancels itself out. Exception: if you have a decent straight with the mah-jongg, you can count it as a cover. You can expect to play the mah-jongg with the straight, and still have the lead to use to play another junk card.

The Dog doesn't count as a cover if you have three or more junk cards. If you pass the Dog, you'll only be able to pass two junk cards. It also cancels itself out. It gets you a lead, but it forces you to keep one more junk card.

Finer Points

The heuristic is pretty good and will usually serve you. However there are some factors that could lead you to vary it a little bit, not the least of which is your level of desperation. If you're way behind and need to make up some points, you might allow yourself one more junk card relative to covers. This will probably result in attempting Tichus that aren't "bomb-safe".

If my opponent has called Grand Tichu, I will pass as if I will call Tichu more desperately. Since my opponent probably has the lion's share of the good cards, if I have almost any, I probably am better off than my partner. I have the best chance to break the opponent's Grand Tichu.

Some covers are weaker than others.

Aces are a bit weak if you don't have the Phoenix and Dragon. They will not always get the lead. However, if you have either the Phoenix or the Dragon, you should probably consider Aces strong at this point. You might receive the other special card from your partner, and then have high confidence in your Aces.

The Dog is a weaker cover. If your partner gives you their best card, they might not have anything left with which to gain a lead. However, they usually do. Even if it's not a strong single card, between you and them you can usually catch a lead on some other kind of trick. Or they might have the mah-jongg.

Bombs are actually a weaker cover. The reason is, if you have a bomb, it is likely someone else does too. There's a tendency in Tichu in general for people to have similar kinds of hands. He who lives by the bomb, dies by the bomb, I say. Don't rely on bombs to get you a lead.

Some junk cards are stronger than others. It's best to assume you'll need a lead to play each junk card, but unless your opponents have almost no junk cards themselves, you will probably get a chance to follow with a King or Queen. Even lower cards like a 7 sometimes get a chance.

Not all sets are secure. Implicit in this strategy is that when you play a set, you retain the lead. Often that's true. Sometimes it's not. If you have lots of small pairs, probably count them toward your junk total as well. In fact it's worse. Your "cover" cards don't cover pairs. When you play a pair you might give the lead to an opponent, and if they're lucky, they can go out without ever leading back to singles. If you have two of a type of set, one high, one low, that's good, because even if the lead of the low one is beaten, you can take the lead back with the high one on the same trick.

Of course, sometimes you gain the lead with a high set when an opponent leads a low set of that type. But you don't want to rely on that, because you can't know whether they have that type of set at all. On balance, though, you might expect to gain as many leads through sets as you lose.

Sometimes, particularly if you're desperate, you want to gamble that you won't receive two junk cards from your opponent. It's a decent gamble if you're keeping some low sets. For example, if you keep 22233, your opponent might pass you a 2. Great! Or at least a 3. That won't give you a cover, but it doesn't become a junk card. If you have a low straight, a passed card might extend it.

If you're really desperate, hope for a passed card to fill in a low inside or 4-card straight. You might get lucky and an opponent passes you the right card, or maybe your partner passes you the Phoenix. In that case, you count a number of your cards as not junk which normally be junk. Conservatively, count one extra junk card because if you receive the Phoenix you can't use it as a cover, or optimistically, count one fewer junk card because optimistically one card you receive from an opponent will fit into your straight.
 
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David desJardins
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morningstar wrote:
The prime time to decide whether or not to call Tichu is after you draw all your cards, but before the pass. That's because deciding if you'll call Tichu or not tells you how to pass to your partner. If you'll call Tichu, keep your best card. If not, give it to your partner. They might call Tichu.


I rarely think at all about whether I'm going to call Tichu, until after the pass. About half the time, neither player on our side is going to call Tichu, but it's still important to concentrate our high cards in one hand. So I'm thinking in terms of who probably has the better hand, whether my high card is likely to help me more or less than my partner, whether I'm likely to get a high card or not from my partner. Not about whether I'm going to call Tichu at the end of the whole process.
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Greg Jones
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DaviddesJ wrote:
morningstar wrote:
The prime time to decide whether or not to call Tichu is after you draw all your cards, but before the pass. That's because deciding if you'll call Tichu or not tells you how to pass to your partner. If you'll call Tichu, keep your best card. If not, give it to your partner. They might call Tichu.


I rarely think at all about whether I'm going to call Tichu, until after the pass. About half the time, neither player on our side is going to call Tichu, but it's still important to concentrate our high cards in one hand. So I'm thinking in terms of who probably has the better hand, whether my high card is likely to help me more or less than my partner, whether I'm likely to get a high card or not from my partner. Not about whether I'm going to call Tichu at the end of the whole process.


I think in nearly 100% of hands, one partner or the other should have their finger on the Tichu button. That's true even though someone on the other side does too. The only thing is, who's turn comes first? If the other team calls Tichu first, probably you don't, unless your hand is really strong.

It works out to the same thing. Even though you know half the time your side won't be calling Tichu, you should usually only keep a high card if you think your hand might be strong enough to call Tichu. Otherwise, it's not worth the risk of possibly messing up your partner's Tichu. One exception might be if you have a lot of the high cards, but the rest of your hand just looks so bad that you probably can't call Tichu anyway. In that case, your partner probably can't either.
 
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David desJardins
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morningstar wrote:
I think in nearly 100% of hands, one partner or the other should have their finger on the Tichu button.


That seems sort of crazy to me. E.g., it's not unusual that your side exchanges aces with one another, while the opponents have dragon, phoenix, two aces between them. (That will be one side or the other on about 20% of hands.) You're going to call Tichu with a single ace just because your opponents, both of whom have considerably more power, have some flaw that makes them not call Tichu? They may not call Tichu, but that sure doesn't mean that they can't beat you if you call it.
 
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Curt Carpenter
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My brief thoughts would be that deciding whether to call Tichu (especially before the pass) is too nuanced to rely on a simple euristic involving only singletons. When you start discussing the issue of pairs near the end you get at what I'm thinking.

I don't want to get into a point-by-point, except for maybe challenge a couple:

1) The assumption that you will get a cover card from your partner. You certainly can't assume that if I'm your partner. My norm is to pass a power card IFF I have exactly one of them. If I have two or more, then I assume that the chances of my partner having two or more is low (means having two or more of the four or fewer remaining poier cards), and thus we're playing for my hand to be the stronger hand.

2) The assertion that bombs are more likely when there is at least one. I might have to do some bsw data crunching to analyze this. In any case, even if you're right, it's obviously at least as good as an Ace. Not sure how you could argue otherwise.
 
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Matthew M
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My read is that these heuristics are intended for newer players or players otherwise uncertain about how to determine whether or not to call Tichu. I certainly agree that things are far more nuanced, but this is decent starting point. As players gain more experience they will inevitably start branching out from the foundation these heuristics provide.

-MMM
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Greg Jones
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DaviddesJ wrote:
morningstar wrote:
I think in nearly 100% of hands, one partner or the other should have their finger on the Tichu button.


That seems sort of crazy to me. E.g., it's not unusual that your side exchanges aces with one another, while the opponents have dragon, phoenix, two aces between them. (That will be one side or the other on about 20% of hands.) You're going to call Tichu with a single ace just because your opponents, both of whom have considerably more power, have some flaw that makes them not call Tichu? They may not call Tichu, but that sure doesn't mean that they can't beat you if you call it.


That statement was assuming that all players in the game are good at Tichu. In a game where all the players are good at Tichu, if you're the last player to play and nobody has called Tichu - well, sometimes things do happen and someone doesn't know they have the best hand - but usually it's a question of manhood to call Tichu at that point.
 
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Greg Jones
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curtc wrote:
1) The assumption that you will get a cover card from your partner. You certainly can't assume that if I'm your partner. My norm is to pass a power card IFF I have exactly one of them. If I have two or more, then I assume that the chances of my partner having two or more is low (means having two or more of the four or fewer remaining poier cards), and thus we're playing for my hand to be the stronger hand.


I don't know, if you have exactly two power cards, the odds of your partner having two or more is 4/9. So I'd say if it doesn't look like you can make a Tichu, you might be screwing your partner out of one 4/9 of the time. That's to say nothing of the Dog, which counts for my heuristic as a "cover" card. In that case, your partner might have the minimum 2, if my calculations are correct, 131/243 of the time.

Debatable whether that's worth it. 5/9s of the time, by keeping the stronger hand, what you might avoid is being beaten 1-2 by your opponents. And in any case, in those 4/9s of the time, when between you and your partner you have 4 of the power cards, some of the time you might win 1-2.

I have a hard time estimating the likelihood of both of those outcomes. I don't think four power cards on your team is always enough to win 1-2, and I don't think having two power cards split between you always guarantees that you lose to a 1-2. One player can use his card to deny the remaining opponent the lead, and lead a low card giving his partner the chance to play a low card, almost as good as if the partner had the lead himself.
 
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Curt Carpenter
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morningstar wrote:
I don't know, if you have exactly two power cards, the odds of your partner having two or more is 4/9. So I'd say if it doesn't look like you can make a Tichu, you might be screwing your partner out of one 4/9 of the time. That's to say nothing of the Dog, which counts for my heuristic as a "cover" card. In that case, your partner might have the minimum 2, if my calculations are correct, 131/243 of the time.

I'm not sure where you get 9 from. I'm only counting 6, aces plus dragon/phoenix. I understand the argument for dog (which makes 7, and I would never count mahjong unless I had a long straight with it), but in my experience the dog is not reliable to count on, so I don't. It's certainly nice for backup, though, and even moreso just to at least know where it is.

So if I have 2 power cards, that leaves 4 out there, or about a 1/3 chance my partner also has 2. The other reason for not counting the dog, is that when I have only one power card and the dog, I almost always keep the dog and pass the power card, whereas with other power cards I almost always keep all if I have at least 2. It just plays differently, and thus factors differently. YMMV.
 
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David desJardins
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morningstar wrote:
I don't know, if you have exactly two power cards, the odds of your partner having two or more is 4/9.


How did you estimate that? It's a little bit high.

0 = (38 choose 14)/(42 choose 14) = 18.3%
1 = 4*(38 choose 13)/(42 choose 14) = 41.0%
2 = 6*(38 choose 12)/(42 choose 14) = 30.7%
3 = 4*(38 choose 11)/(42 choose 14) = 9.1%
4 = (38 choose 10)/(42 choose 14) = 0.9%

So the exact probability is 40.8% which is significantly less than 4/9.

I don't understand the rest of your analysis, but I think the main advantage of tending to keep a top card with two of the top six, rather than tending to pass a top card, is that, how many high cards you have, it's significantly better for both of you to keep your top cards than for both of you to swap them. When you keep them, you're swapping nonfitting small cards for random small cards, which will sometimes fit better. And you're also giving each other more information about what you have. As you increase the probability that you will pass a top card holding two, the probability of your side swapping high cards goes up considerably.
 
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David desJardins
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morningstar wrote:
That statement was assuming that all players in the game are good at Tichu. In a game where all the players are good at Tichu, if you're the last player to play and nobody has called Tichu - well, sometimes things do happen and someone doesn't know they have the best hand - but usually it's a question of manhood to call Tichu at that point.


I guess I'm crazy, but I think if you're good at Tichu, you're calling Tichu based on whether you can make it, not as a test of your manhood.

There are plenty of arrangements of the cards where no one of the four players can make Tichu (because the other team can play together against whoever calls). Your passing style makes that more likely, since you're often not concentrating your partnership's high cards in one hand (e.g., your partnership has two top cards in one hand and one in the other, but the player with two thinks his hand isn't so good for Tichu, so he passes one which exchanges with his partner's high card; meanwhile, the opponents do the same).

It occurs to me that if you have strong "table presence" and can pick up whether your partner probably has a good hand or a bad hand, before the pass, then things are very different.
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Greg Jones
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DaviddesJ wrote:
morningstar wrote:
I don't know, if you have exactly two power cards, the odds of your partner having two or more is 4/9.


How did you estimate that? It's a little bit high.

0 = (38 choose 14)/(42 choose 14) = 18.3%
1 = 4*(38 choose 13)/(42 choose 14) = 41.0%
2 = 6*(38 choose 12)/(42 choose 14) = 30.7%
3 = 4*(38 choose 11)/(42 choose 14) = 9.1%
4 = (38 choose 10)/(42 choose 14) = 0.9%

So the exact probability is 40.8% which is significantly less than 4/9.


I didn't bother with the other 38 cards. Of the 4 remaining power cards somebody has to have them, and it's equally likely to be any of the three remaining players.

There are 3^4 = 81 total ways to arrange them among the three players.

There are 4c2 ways to have two of them, and for each 2^2 ways to arrange the other two cards between the opponents = 24.

There are 4c3 ways to have three of them, and for each 2 opponents to give the remaining card to = 8.

There are 4c4 ways to have all of them = 1.

Yeah I miscalculated something. It's 33/81 = 11/27 = 40.8% as you said, not 36/81 = 4/9.
 
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Greg Jones
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DaviddesJ wrote:
I don't understand the rest of your analysis, but I think the main advantage of tending to keep a top card with two of the top six, rather than tending to pass a top card, is that, how many high cards you have, it's significantly better for both of you to keep your top cards than for both of you to swap them. When you keep them, you're swapping nonfitting small cards for random small cards, which will sometimes fit better.


Well, I admit that is an advantage that may be making a weak hand (possibly weaker than your partner's) slightly less weak.

DaviddesJ wrote:
And you're also giving each other more information about what you have. As you increase the probability that you will pass a top card holding two, the probability of your side swapping high cards goes up considerably.


Is there something more advantageous to both holding high cards versus both passing high cards? Either way, you end up with strength evenly distributed between your hands. In terms of information, cross-passing high cards is better than not passing them. Receiving a low card means either "My partner has a strong hand," or, "My partner has no high cards." If you both pass high cards, well, you know at least one high card your partner has.

If you increase the probability that you will hold high cards if you have two, the probability that you'll both hold high cards goes up.

In fact, if you absolutely don't pass high cards if you have two, then every time both partners have two, they won't pass one. But with my heuristic, one partner might pass. It depends on how well the rest of their hand fits into sets.
 
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David desJardins
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morningstar wrote:
In terms of information, cross-passing high cards is better than not passing them. Receiving a low card means either "My partner has a strong hand," or, "My partner has no high cards."


Well, that's not how I play. If I don't have any of the top cards, I'll almost always pass my partner a king or a queen. If you get a 7 from me, it's not because I don't have any top cards. I don't think that would be wise.

When you get a king from partner, occasionally it's because he has a very strong hand (just as sometimes I will pass the dragon from a very strong hand), and that will usually become clear very quickly. But usually it's a pretty clear sign of a weak hand.

From an information-theoretic point of view, if you exclude the very-weak hands that usually pass king or queen and are usually identifiable as such, then you transmit the most information if you pass high about half the time and low about half the time. So that leads to a rule of thumb of passing high on hands that are below average, and low on hands that are above average.

That, in turn, combines pretty well with the observation that about half of hands have two or more top cards, and about half of hands have zero or one.

The more that you pass low or high based on the "fit" of the other cards in your hand, rather than on just power, the more often your partnership will exchange low with low, or high with high. Maybe that cost is justified. But it is a real cost.
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Andrew Garttmeyer
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Im a bit confused here. You talk about how Dog is a cover card (which will get you a lead when deciding whether or not to call Tichu), but you write this:


Most of the "cover" cards usually win tricks. The Dog gets you a lead if your partner can win a trick.

Doesnt your partner actually have to play the Dog for you to take the lead? So the Dog in YOUR hand really isnt a cover card.

 
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Jeff Chunko
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Obviously he's talking about counting the dog as a cover card after passing it.
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