5 draw stripped deck advice needed

[archmagi]

Hi,

I play in a home game where only 5 card draw with stripped deck is played. To avoid any confusion, it's played with only 7's through to A's, and the 2's through to 6's are taken out of the deck. It's played with 4 people max.

I need advice on how to play a pat straight, which I find very difficult. Because there are only half the cards, all the odds are changed, and hence trips beat straights. If you pat, more often than not it's a straight, and everybody plays accordingly. Of course this makes pat flushes and full houses extremely profitable, but I find that pat straights are negative EV.
I think there are 2 choices:
1) don't play them
2) raise before the draw to either steal the blinds or to eliminate as many opponents as possible and reduce the number of people who can potentially improve their pair to trips. this option requires good post-draw play and anybody who calls a bet is guaranteed to have at least trips. i found people bet against you mostly with at least trips (about 90% of the time), and deciding whether to call or fold at that stage is a painful one.

Any advice will be appreciated.

[bigpooch]

Is the game played PL or limit? What are the antes and/or
blinds? Are openers required? I see that game in this
neck of the woods played NL with total ante = $40 (Canadian
currency) and Jacks or better to open although I suspect
it is also played PL. Also, if it is NL, what are the
typical stack sizes?

[archmagi]

Hi,
This one's NL, the dealer antes $2,. Typical stack size is about $200. Because it's stripped deck, it's K's or better to open.

[Buzz]

Heretic - I never played this game. Here’s some beginner’s math for it.

Before the flop possibilities:
straight-flush-----------16
flush-------------------208
quads-------------------224
full-house-------------1344
straight---------------4080
trips-----------------10752
two-pairs-------------24192
one-pair-------------107520
high-card-------------53040
total----------------201376
check-C(32,5)--------201376

"but I find that pat straights are negative EV."

Really? The probability of being dealt a pat straight is 4080/201376 = 0.0203.
The probability of being dealt trips is 10752/201376 = 0.0534.

Four maximum in the game? Sounds like a game looking for a fish. My best advice to you is make sure you're not it. Remember the old adage: If you can't spot the fish, it's you.

Four maximum in the game? In that case, the individual probabilities and the number of opponents seem small enough to get reasonably close to the true values by just multiplying the individual probabilities by three and thus avoid a more rigorous approach.

Thus, in that case, the probability of at least one of your three opponents having a straight before draw is approximatly 6% while the probability of at least one of your three opponents having trips before draw is approximatly 15%. Those should be reasonably close to the true values to give you an idea of what you’re generally up against. Only roughly once every six or seven deals is one of your three opponents dealt trips.

You should be dealt a pat straight about once every forty nine hands. How should you play it? I don’t know. You’re certainly almost surely ahead before the draw. I’d think you’d also still generally be ahead after the draw. But like I wrote, I’ve never played this game.

"i found people bet against you mostly with at least trips (about 90% of the time), and deciding whether to call or fold at that stage is a painful one.

Hmm. O.K. 90% is close (maybe a bit high). How often does it happen that someone bets against you when you have a straight? If they do it with trips, and then draw two, if you have 789TJ and they're drawing to trip sevens, eights, nines, tens, or jacks, then the best they can do is catch a pair to make a full house. Suppose an opponent starts with JJJ98 and you hold 789TJ. The probability of them improving is (3+1+1+3+0+6+6+6)/231 or 26/231 = 0.011. Not so good for the guy with trips, eh?

Let's try an opponent with AAA98 when you hold 789TJ. In that case the probability of improving is
(3+1+1+3+3+6+6+19)/231 or 42/231 = 0.18. That's better for the guy with trips, but still not good enough to play trips against a pat straight and an all-in bet from you.

You want to suck him along with your straight? Slow play him? Well, I suppose you could play stupidly so that he would have favorable odds to draw.

What if your opponent has a straight flush, quads, a flush or a full house in stead of trips? Well, roughly one time in a hundred when you have a straight you're going to run into one of these and take a bath. That's poker. Probably a bigger danger is your opponent has a better straight than you. Well, (paraphrasing Ray Zee), "You just have to play good poker."

But you're ending up with a negative expectation with your straights? Really? Sounds like "Something is rotten in the state of Denmark." (Hamlet)

Just my opinion.

Buzz

[Gahnia radula]

and hence trips beat straights

Ummm, I think you're confused

yes in a stripped deck the odds change, but trips dont beat straights

What does changes is that a flush now beats a fullhouse

I've played stripped 5 draw at my local B&M and I've never heard of trips beating a straight

Hope this helped

[Buzz]

Heretic - I never played this game. Here’s some beginner’s math for it.

Before the <font color="red">draw</font> possibilities:
straight-flush-----------16
flush-------------------208
quads-------------------224
full-house-------------1344
straight---------------4080
trips-----------------10752
two-pairs-------------24192
one-pair-------------107520
high-card-------------53040
total----------------201376
check-C(32,5)--------201376

<font color="red">Looking at the chances of being dealt the various hands, it doesn't seem as though trips should beat straights. Are you sure they do? But look at how rare flushes are.</font>

"but I find that pat straights are negative EV."

Really? The probability of being dealt a pat straight is 4080/201376 = 0.0203.
The probability of being dealt trips is 10752/201376 = 0.0534.

Four maximum in the game? Sounds like a game looking for a fish. My best advice to you is make sure you're not it. Remember the old adage: If you can't spot the fish, it's you.

Four maximum in the game? In that case, the individual probabilities and the number of opponents seem small enough to get reasonably close to the true values by just multiplying the individual probabilities by three and thus avoid a more rigorous approach.

Thus, in that case, the probability of at least one of your three opponents having a straight before draw is approximatly 6% while the probability of at least one of your three opponents having trips before draw is approximatly 15%. Those should be reasonably close to the true values to give you an idea of what you’re generally up against. Only roughly once every six or seven deals is one of your three opponents dealt trips.

You should be dealt a pat straight about once every forty nine hands. How should you play it? I don’t know. You’re certainly almost surely ahead before the draw. I’d think you’d also still generally be ahead after the draw. But like I wrote, I’ve never played this game.

"i found people bet against you mostly with at least trips (about 90% of the time), and deciding whether to call or fold at that stage is a painful one.

Hmm. O.K. 90% is close (maybe a bit high). How often does it happen that someone bets against you when you have a straight? If they do it with trips, and then draw two, if you have 789TJ and they're drawing to trip sevens, eights, nines, tens, or jacks, then the best they can do is catch a pair to make a full house. Suppose an opponent starts with JJJ98 and you hold 789TJ. The probability of them improving is (3+1+1+3+0+6+6+6)/231 or 26/231 = 0.011. Not so good for the guy with trips, eh?

Let's try an opponent with AAA98 when you hold 789TJ. In that case the probability of improving is
(3+1+1+3+3+6+6+19)/231 or 42/231 = 0.18. That's better for the guy with trips, but still not good enough to play trips against a pat straight and an all-in bet from you.

You want to suck him along with your straight? Slow play him? Well, I suppose you could play stupidly so that he would have favorable odds to draw.

What if your opponent has a straight flush, quads, a flush or a full house in stead of trips? Well, roughly one time in a hundred when you have a straight you're going to run into one of these and take a bath. That's poker. Probably a bigger danger is your opponent has a better straight than you. Well, (paraphrasing Ray Zee), "You just have to play good poker."

But you're ending up with a negative expectation with your straights? Really? Sounds like "Something is rotten in the state of Denmark." (Hamlet)

Just my opinion.

Buzz

[archmagi]

Trips beat straights.
I have read in Ciaffone's PL &amp; NL Poker that the rule has been changed in most places so that straights beat trips, but where I am, trips still beat.
And yes, flush beats a full house

[archmagi]

Thanks for the answer, you've got some very valid points.
Yes I'm sure that trips beat straights. Actually, I've lost some sleep looking at your numbers. I still need to put pen to paper, but I found a reference in Ciaffone's Pot Limit and No Limit poker book about split deck draw. He says that you are more likely to get straights than trips in a random deal, supporting the way I thought it was.
He also mentions in the book that despite this, they've changed the rule in most places so that straight now beat trips. Unfortunately that's not the case on this side of the ocean.
As I said, I'm putting pen to paper later tonight.

[Gahnia radula]

Until reading your post I've never heard that

[Buzz]

"I found a reference in Ciaffone's Pot Limit and No Limit poker book about split deck draw. He says that you are more likely to get straights than trips in a random deal, supporting the way I thought it was."

Heretic - Gee, I don't know how to respond. I wrote in my chart that trips occur 10752 times out of 201376, while straights occur only 4080 times out of 201376. I still think those numbers are correct. In fact I'm willing to bet on it.

If Ciaffone really wrote you are more likely to be dealt a straight than trips in a random deal from the shortened deck you have described, then it sounds like an opportunity for you to take some fast money away from me.

But before that actually happens, it's only fair that I show you my set ups and reasoning for the math. Here are my set ups:

ways to have trips before the draw
8*4*28*24/2 = 10752

ways to have a straight before the draw
16*4*4*4*4 - 16 = 4096-16 = 4080

And here's the reasoning:

A word of explanation about trips. There are eight ranks of cards and four ways to take away one of the cards of any particular rank. Then there are 28 ways to choose the next card so as not to make quads. Then, so as not to make a full house or quads, there are 24 ways to choose the last card. Since the order in which you choose the last two cards doesn't matter, you divide by two. I can see another way to set up that problem, but the way I did it seems fine.

A word of explanation about straights. There are 16 ways to pick the highest card in the straight, then four ways to pick the next card in line, then four ways to pick the next, four ways to pick the next, and four ways to pick the last. Then I subtracted 16 for those times you'd be dealt a straight flush. I can see another way to set it up too, but the way I did it seems fine to me.

Maybe my math doesn't make any sense to you. Honestly it never made much sense to most of my math teachers when I was in school.

Are we straight on the bet? We play with a deck having twos, threes, fours, fives, and sixes removed. And we just deal out hands - one at a time, or four at a time - whatever you like. I win every time the hand dealt is trips. (How ever much you want to make the wager). You win every time the hand dealt is a straight - and heck, I'll even throw in straight flushes.

Well, gee, you caught me in a soft moment. I'll also throw in quads, full houses - even flushes. You win whenever a five card hand dealt has a straight flush, quads, a full house, a flush, or a straight. I only win if the five card hand dealt is trips. If the hand dealt is anything else, nobody wins or loses. Sound good to you? Too good to be true?

O.K., but this is the end of it, If you opt to have four hands dealt at a time, as they evidently are in your game, I'll give you all the times when both trips and a straight (or other higher hand) are dealt.

Maybe you ought to try dealing out some hands by yourself, just to make sure you really have a winning proposition before we actually meet for the contest.

If you're still game, I look forward to giving you some of my money - or taking some of yours. Maybe I can make a believer out of you.

Buzz

[archmagi]

Hi Buzz,
I'm with you on the trips. It's the calculation of the straight that I'm looking into.
Give me a couple of days on this one, and I'll post my calculation.
Again, thanks for the input

[Buzz]

Hi Heretic - If you’re with me on trips, then straights should be easy to explain.

I do agree that you should spend some time and work it out for yourself.

But if you get stuck, here’s a way to think:

Let’s momentarily forget about suits. We can subtract for straight flushes later. And if we forget about suits, then we have only four possibilities for straights:

AKQJT
KQJT9
QJT98
JT987

Right? (If you can think of another one, what is it?)

Let’s think about picking cards out of a deck to make one of these, but the reasoning will be the same for all of them. Let’s think about picking cards out of a deck to make KQJT9.

What cards do we need to pick out of the deck (either a shortened 32-card deck or a 52-card deck) to make KQJT9? Well... KQJT9 needs a king, a queen, a jack, a ten, and a nine. That’s all it needs - and that’s exactly what it needs. Nothing more, nothing less.

Now how many kings are there in a deck? However many there are, that’s the number of ways you can take a king from a deck and put it in the hand you’re building. Similarly, how many queens are there in a deck? How many jacks? How many tens? How many nines?

There are four kings, four queens, four jacks, four tens, and four nines.

But any one of the kings can go with any one of the queens. For example, the king of spades can go with the queen of spades, the queen of hearts, the queen of diamonds, or the queen of clubs. Thus there are four ways you can put a queen with the king of spades.

Then there are four ways you can put a queen with the king of hearts. And so forth. You should almost immediately see that the number of ways you can put a king and a queen together is 4*4.

Choose any one of those king-queen combinations, the king of clubs and the queen of hearts, for example. There are four ways you can put a jack with that combination. That makes 4*4*4.

And if you take any particular one of those three-card combinations, for example the king of clubs, the queen of hearts, and the jack of hearts, there are four ways you can put a ten with that combination. That makes 4*4*4*4.

Finally, if you take any particular one of those four-card combinations, the king of clubs, the queen of hearts, the jack of hearts, and the ten of spades, for example, then there are four ways you can put a nine with that combination. That makes 4*4*4*4*4.

Therefore, there are 4*4*4*4*4 ways to build a KQJT9 straight from a deck of cards.

However we built a KQJT9 straight, there are exactly the same number of ways to build the other straights. Thus:

(4*4*4*4*4) for AKQJT,
(4*4*4*4*4) for KQJT9,
(4*4*4*4*4) for QJT98, and
(4*4*4*4*4) for JT987,

You can see we’re taking (4*4*4*4*4) four times, or (4*4*4*4*4)*4. That’s the total of number of different ways you can build a straight, picking one card out of a deck at a time, if you disregard straight flushes.

But since we’re listing the straight flushes in a separate category, we have to subtract the total number of possible straight flushes from the number of straights. For clubs four of straight flushes are possible: AcKcQcJcTc, KcQcJcTc9c, QcJcTc9c8c, and JcTc9c8c7c. Similarly there are four straight flushes for spades, hearts and diamonds, a total of 16 straight flushes in all.

Bottom line: 4*4*4*4*4*4-16 = the number of straights.

Hope that makes sense to you. It’s slightly different reasoning than I used in my previous post - and hopefully explains straights better. Of course the bottom line total, 4080, is the same.

I only have one book by Bob Ciaffone in my poker library. I didn’t see any glaring mistakes in it. Are you sure you didn’t misquote him?

Buzz