Razzin'

[peterbirks]

Chris Fargas on Twenty-One Outs Twice wrote an interesting article on a Razz hand that he, quite bravely, recounted despite him ballsing it up. Well, he didn't balls up the analysis, but he did get the numbers wrong.

To recap, after four cards, one guy had four to a seven (although Chris could not know this for sure), Chris had four to a 98, and the two other players had caught paint on fourth street. Chris had been bumping it under the not unreasonable theory that he was getting three-to-one for his money and he reckoned that he was better than three-to-one to win it.

In fact, he had the worst of it. He was the dog of four.

It's interesting to break this down a bit.

Suppose the cards are face up and you have 9876 versus A23J after four cards (A2345 is the best low). Which hand would you prefer?

Most players would, I think, correctly plump for the A23J.

Now, suppose you had 982A vs K32A. Which do you prefer now?

Suddenly, the balance of power shifts, and people start preferring the four to the 98.

But this is a relatively simple hand to break down mathematically. Rather than make it the best five-card low hand in a seven-card game, we can despatch the Aces and twos from both hands and make it the best three-card low hand in a five card game.

So, we have 98 vs K3, best three-card low wins with three cards to come. Aces and twos not allowed

I don't have a poker calculator to hand, but clearly if hand B gets two cards seven or lower, hand A needs three cards seven or lower. If hand B gets two cards 8 or lower, hand A needs two 'good' low cards to snap off the 3. If hand B gets two cards 9 or lower, hand A is also likely to need two good low cards to avoid being beaten by the three.

Looking at that I would instinctively make the K3 something like 53% to 55% favourite.

Now, there's one drawback to this analysis, in that betting does not stop on fourth street. It's not enough just to know that the K3 is favourite. We also need to know how things are likely to shift on card five.

If both cards are dogs (ten and above, pairing the hands, etc), 98 becomes favourite, about 60/40?
If both cards are good (seven or below, not pairing the hands), K3 becomes favourite, about 65/35?
If 98 hits and K3 misses, 98 become somthing like 75/25 favourite
If K3 hits and 98 misses, K3 becomes something like 70/30 favourite.

All these are rough estimates in my head, I hasten to add.

So, in none of the above cases is either player going to fold. Card five is likely to result in bet, call, from one side or the other.

If we put the above scenarios as roughly equal in likelihood (25% each) and combined them with similar ofdds for card six (in fact, the hands are more likely not to be helped than helped on card six, but this doesn't change the underlying maths to a significant degree), then we have 16 possible combinations for cards five and six, but six of them (1/1, 1/2, 2/2, 2/1, 3/4, 4/3) restore the status quo.

A further eight (1/3, 1/4, 2/3, 2/4, 3/1, 3/2, 4/1, 4/2) put us into bet, call mode, while just two (3/3, 4/4) put us into bet, fold mode.

The debate here could be that 3/1 puts us into a bet/fold situation where the K3 should quit, while 4/1 keeps us in a bet/call situation where 98 does not quit.

But, on the whole, the fact that there is further betting doesn't really change the situation (apart from increasing the size of the pot). People seem to think that, because the K32A needs two cards for a 'made', it is at a disadvantage to the 982A which needs just one card for a 'made' hand. And, if the game were No Limit or even pot limit, an argument could be made for this.

But in limit, there is no way that there can be insufficient money in the pot to make it wrong for the K3 to call.

it is this that gives us the Sklansky line that the 98 should check here to keep the pot small, thus making it wrong for the King to call on fifth street if he misses. However, the point is that the "leading" hand isn't really leading at all. The King should be betting, not the nine.

Comments

[simong-uk.livejournal.com]

Nice to see some Razz discussion. A couple of things to add though.

1. As always, DAI. I have been playing a lot of Razz this year and am still amazed at how many times I see someone unable to beat what is already on show and still call. And many many current players are happy to go to war with a made rough jack against my smooth 8 draw with several rounds to come. So although the analysis above is good to think of yourself, don't assume that your opponent is thinking on the same lines. Your opponent has likely got a compounded misunderstanding of where they are, but will still hit perfect perfect while you hit brick-pair and then rub you down with the "thanks for the action" type comments.

2. Your analysis is with 2 hands face up. It is good that you think about what will happen on future streets rather than just running the hand hot and cold. I am amazed how ofetn I get called on a street, hit bad while my opponent catches good and he still folds to a bet. I can't believe it jumps out at them as "wow that must have been a crappy call on the last street if the best eventuality is still going to cause me to fold on the next round." But Gawd bless em.

The real aspect of cards not face up is that while you may like to manipulate the pot size and not bet, you may gain more by probing with a bet to see how much he likes his hand. Check-check won't tell you much about the quality of the king, whereas if they can take heat with it you can be sure it must be a loony or very smooth (which may increase your confidence that an A or 2 pairs them if it comes. Then, there are those that will just routinely fold with a King. Against those, never mind the 53-55% stuff, just bet and take it down.

[jellymillion.livejournal.com]

Despite getting my arse kicked at Razz last year from 1/2 to 8/16 (and from pillar to post, come to that) I still love it. I paid a lot of money - for me - for the lesson that there's a reason why 98 and 87 are called "rough". The likely equity split between a made K-high and a paired four-card low was an eye-opener as well.

The interesting players, for me, are the ones who will see maybe 25% of fourth streets, so must be playing many of their useful door cards irrespective of what's behind. After maybe $1000 or so I started to realise what was going on - they were as much playing my board as their own. I haven't yet finished paying to learn how to do this effectively.

[peterbirks.livejournal.com]

I don't think that it's necessarily true that you learn more from betting than from checking. Empirically, checking is more likely to lead an opponent to misstate the strength of his hand towards the loose side, whereas betting is more likely to induce the opposite. The linguistic point that betting tends to obtain more information than checking is because it gives your opponent more options.

A check can elicit a bet or a check.

A Bet can elicit a fold, a call or a raise.

If your opponent is the straightforward type, giving him three choices from which to choose narrows his range down more than does giving him two choices.

However, it's only a marginal gain. First, players are not necessarily straightforward, so giving them three choices of action rather than two is not necessarily desirable.

I've never been a fan of "betting to find out where you stand" because you quite often have no idea where you stand, even though you have bet (particularly against the "won't bet, won't fold" kind of opponent). I can see the gain to be made, but I don't think it is worth it unless other factors are in favour of your bet (these being, the likelihood of eliciting a fold when you are behind, or of eliciting a call when you want to extract value). If you suspect that you are behind and your opponent is passive, check-check gives you as much information as bet-call, and you have saved yourself a negative EV bet in the meantime.

PJ

[simong-uk.livejournal.com]

Razz flip-flops through the streets so much that I believe you should probe regularly. It isn't just about finding out where you are, although it is handy to know as many hands that you act on 5th you will be playing to showdown. That doesn't mean you need to get out of line to probe, but when there are reasonable grounds to suspect that your opponent paired or didn't start out with a premium hand, you should look to bet as a rule. Even if the calculator says 47%, that's close enough - bet it and if necessary regain the bet by checking down on the end or something if it looks close? There isn't that much check-raising going on (I have played 2/4 up to 30/60) out there - unless there is a real live one in the game - just people betting their hand. And as per the first post, although it makes sense to think about the maths to improve, most of the time you will be starting with better cards than your opponent, getting thin value from your edges, benefiting from free cards that you shouldn't have got and then just to make sure you have them in a coffin, a regular dose of suicide with a cinch hand on 5th that goes to the river. Even with average luck it is a very beatable game.

[jellymillion.livejournal.com]

I don't think there's any question that 9876 shouldn't be betting against K32A with the hands showing unless the K3 guy is a monkey.

But there aren't many complete information poker scenarios that I can think of with betting still possible. Well, I can't think of any, but I went to the pub at lunchtime.

Having (76)89 against (32)AK is very different to (98)76. I'd probably check the former, bet the latter - a non-monkey will know he's got odds to outdraw a rough 9 but may cave in when faced with a distribution that includes the very real possibility of a 7, albeit a rough'un.

[peterbirks.livejournal.com]

Hi Mike:

If we are talking specifically about Razz, then in the 9876 v KA23 scenario we have to go back a card. (78)9 will probably not play against (xx)A, (xx)2 or (xx)3. But (87)6 will be raising against (xx)K and may well be playing against the other combinations.

Similarly, (23)K is marginal against (xx)6.

But what remains constant in these "middle cards" vs "good and bad" is that you have an analogy to the high situation of implied odds for the drawing hand. So we can kind of equate the 9876 hand (no matter how distributed) with something like Ah Qh on a board of Qs Ts 9s, while the KA23 hand is more akin to the As Jd holding with the same board.

This would seem to imply that the "good and bad" hands are not only often favourites, but, even when they are not, they have the advantage of knowing where they stand much more often.

If we push this situation over to triple draw (which is a bit like a combination of Razz with no upcards with Irish, in that you have to throw away some of your downcards before you see another card), then you don't have a system of complete information, but you have less partial information.

Suppose here you are headsup with 9873x after one draw of one card (let's assume it's short-handed) and opponent has drawn two after raising pre-flop.

This is a ropey situation because you are often going to be the dog and, even if you aren't, you are probably going to be against a hand that misses and therefore does not pay you off.

As you say, you play differently with different hole cards because these alter your range, but if you put toghether the entire range of up and down cards, I would think that the 9876 combination would be playing a lot of hands without really knowing where he stands.

PJ