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Roy West's last column and an excercise for the reader..., stdioh, 9. Sep 2003 09:49
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I've been catching up on Cardplayer and I just read Roy West's latest column here: http://www.cardplayer.com/?sec=afeature&art_id=13503

Roy makes a giant blunder in his talk of how to play small rolled up trips and the reason for this blunder is in the math. While he makes valid points about wanting to thin the field innitially with them, a lot of his reasoning relies on an incorrect piece of statistics. Roy states that starting with rolled up trips your chances of tightening up are 2 to 1 against. That statement made me want to shreik.

Now we know that in hold'em if you're holding a set on the flop you are a 2 to 1 to tighten up. The equivalent is thus that if your next two cards are unpaired to eachother and unquadded, you are a 2 to 1. Of course we're also neglecting the other board cards here.

In order to know the real chance of tightening up we must look at each card in order. First, is our quads out live? If so, you need to subtract your opponents door cards from the deck and figure your chance of quads on 4th street. Now subtract this from 1 and multiply the result to your 5th street calculation to tighten up, which will be the chance of making quads there, plus the chance of pairing your 4th street card. But what is the chance of pairing your 4th street card? Well, it is going to again depend on the number of board cards shown and if you've lost any outs there. Based on the number of players in the hand, you know what the likelihood of catching a 4th street card that is live is going to be so now you can work out your chance of tightening up on 5th street.

Now even if you are not tight on 5th street, you're holding XXXYZ. First off, if the field is already thinned, then you aren't as worried about your opponents drawing out on you. If you're facing a large field then you're looking at a large array of doorcards. Lets say that you have 5 opponents still player. You've then seen their 10 boardcards, plus the 2 doorcards of the folder.

So instead of having 7 outs from 47 and then 10 outs from 46, you've got 7 outs from 35 and then 10 outs from 30! That means that if all of your outs are live, the whole way through the hand, you're still a 2 to 1 to tighten up on 7th street!

Of course you're never going to see all of your outs be live at that late stage, there are chances of being beaten by a bigger tight if you get there, etc, etc. The point I'm getting at is that, without looking at other cards, your chance of getting there is much higher than 2 to 1 against when you are on 3rd street. And because you'll be able to play intelligently as the hand progresses, you get great implied odds that you wouldn't see in a hold'em game. The more cards exposed, the more relative outs you have. 4 outs can be very callable even in a smallish pot when you have removed 17 cards from the deck and exposed them.

Now for the excercise. Assume that you are starting with rolled up trips and your 4th card is live. Make no assumptions about whether opponent have eachothers' door cards counterfeited. For the sake of argument you can assume that you haven't seen anybody else's door cards, but *know* that your out to quads is live. Assume though that the game is 8 handed, so 7 cards are exposed that will affect your chances of quads.

What are the chances of making at least a full house by 7th street?

I'll post an answer to this in a reply.
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Re: Roy West's last column and an excercise for the reader..., stdioh, 9. Sep 2003 09:56
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Your chances are as follows:
4th street: 1/42
5th street: 1/10.5
6th street: 1/6.316
7th street: 1/4.634
These are mutually exclusive events.

Summed up, 1/2.028

So with a very small amount of rounding, we can say that if you start with rolled up trips your chances of tightening up are 1 to 1 - a coin flip! Since trips will itself very often be the best hand, all of a sudden you're looking at a much different hand than if you only got there 1 time in 3 (2 to 1).

Now I hope not to offend Roy with this, but I do want to point out that even such illuminated individuals as Roy West (and I do respect his writing and playing very much) make miscalculations. If you make a miscalculation - especially a severe one like this then you can apply good judgement, correct sound logic, expert reads, and everything else to your play but you'll be dead wrong in the end.

As many people say, the most costly mistake is the first one and in this case it is starting with an incorrect assumption and letting that lead you down the path of incorrect play.

I hope that you all enjoyed reading this train of thought.
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Re: Roy West's last column and an excercise for the reader..., PairTheBoard, 9. Sep 2003 21:41
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I'm afraid that the events where up cards get paired are not mutually exclusive.

This is an example of the many kinds of probability problems where it is much easier to compute the probabilty of something NOT happenning. The simplest scenario is to assume you have not looked at your opponents up cards. In that case, the probabilty of NOT improving to a full house or quads is the product of the probabilties of it NOT happenning on any of the subsequent cards, given it has already NOT happenned on a previous one. ie.

(48/49)*(44/48)*(40/47)*(36/46) = 59.8%

If you assume that the 7 up cards for your opponents do not include your Quads Card, but assume nothing about how they relate to your subsequent up cards, then the problem is a little more tricky. The probablity of NOT hitting Quads on your 4th card is now (41/42). But the probality for NOT hitting Quads or Pairing on your 5th card is 1 minus the sum of the probabilties of the mutually exclusive events that you do hit Quads or Pair your 4th card. Ie. 1-( (1/41) + (3/48) ). Notice the chance of pairing your 4th card is (3/48) because you have no information on whether any opponents up cards affect your draw for the pair. The only cards gone from that draw are the 4 in your hand. So:

The probabilities of NOT Quading or Pairing an up card on 4,5,6,7th steets are:

4th: (41/42) = .97619
5th: 1 - ( (1/41) + (3/48) ) = .91311
6th: 1 - ( (1/40) + (6/47) ) = .84734
7th: 1 - ( (1/39) + (9/46) ) = .77871

Thus the probability of NOT improving to Quads or a FH in this scenario is the product of the above four probabities. ie.
(.97619)*(.91311)*(.84734)*(.77871) = 58.8%

So, noticing your Quad Card is not killed by your opponents' up cards, improves your chances for improving to a Full House or better, from 40.2% to 41.2%.

You are correct in pointing out that your chances of improving to a Full House or better starting with rolled up trips are higher than if you flop a set in Holdem that is not Full or better on the flop. Your chances are significantly better than 1 in 3 but certainly not 50-50 either. In fact, it's close to being right in the middle of the two, especially in the second scenario.
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Re: Roy West's last column and an excercise for the reader..., Harold Pierce, Jr., 10. Sep 2003 04:05
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Isn't the probablity of making quads or a full house actually dependent on the board cards you see as the hand progresses and the number of active player on each street?

Suppose that on the deal your quad card is exposed. Your probability of making quads is then zero. Then suppose on 4th street all of your 4th street card are exposed. Then the probability of making a full house with the 4th street card is again zero. To your amazement this happens on 5th street. To make a full house, you then have to pair your sixth street card and that will depend on how many of your sixth street cards are exposed on the board and how many cards are left to be dealt. Suppose that on 4th, 5th, and 6th steets there are 4 active hands and on 6th none of your cards are exposed. Since there are 16 cards left to be dealt and 3 of these will make your full house, your probability of making your full house is 3/16 or 0.188. The odds against making your full are 4.33 to 1, which is still pretty good. At this point, the pot is huge because you have raising to the max limit on each street.

Suppose on 6th street, however, that all 6th street cards are exposed. You are nowabsolutely amazed, astonished and astounded that your 41% chance of making a quads or a full house fizzled out to zero! You lost the hand to an opponent who missed his flush draw but hit a gut shot straight!!!

-=-MouseEars
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Re: Roy West's last column and an excercise for the reader..., stdioh, 10. Sep 2003 10:08
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In general they are not mutex, but for this example, I made them mutex by multiplying by the likelihood of the previous event *not* happening. If you did the math yourself, you would see that it was reflected in my calculations, though I didn't want to clutter the response with a lot of arithmetic.
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Re: Roy West's last column and an excercise for the reader..., PairTheBoard, 10. Sep 2003 14:21
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Your correct. I could not guess the error in your calculations so could not make sense of them. I see your correction below. Showing the work is good clutter.
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Re: Roy West's last column and an excercise for the reader..., Formless, 9. Sep 2003 20:32
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For rolled up 7s, with 8 players and sevens live on 3rd street:

Full House 31.4%
Four of a Kind 9.5%
Straight Flush 0.01%

I get just under 41%.

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The math in detail., stdioh, 10. Sep 2003 10:20
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It seems that I made one error in my calculations in that I eliminated the board cards from the deck without taking into consideration the chance of them counterfeiting pairs on later streets. Additional board cards do not need to be worried about, but innitial ones do.

Nonetheless, here is the math I used:

Chance of quadding on 4th street: 1/42.
Chance of tight on fifth: 41/42 * 4/41 = 1/10.5
Chance of tight on sixth: 9.5/10.5 * 7/40 = 1/6.316
Chance of tight on seventh: 5.316/6.316 * 10/39 = 1/4.634

Since each of these events takes into consideration that the previous event did not happen, they are mutually exclusive and can be summed to 1/2.0277

Now the incorrect assumption here is that each time we hit a card which is not making us a tight, that card is not reflected in the very fist set of board cards. Obviously we cannot expect this to happen so indeed the number drops from 50% down to about 41%.

Notwithstanding, there is a world of difference between 41% and 33% when it comes to playing a multiway hand like this one.

As pointed out also, it is very important to know your number of outs as the boards change.

Long story short, this is almost always a hand to pump the bejesus out of, since if you are in a small field you want to increase the pot for value based on your trips and if you are in a large pot you are a very big money favourite to improve to a tight. In fact you're a money favourite to improve with only 2 opponents.
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Re: The math in detail., Harold Pierce, Jr., 10. Sep 2003 12:19
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Did you read my post? These type of calculations for stud
poker must take into account all the cards you can see and
the numbers players if you want the true probabilities or
odds.

I have seen such a detailed calculation for 5 stud in an
old book by Livingston. Altho farfetched, the scenario in
my above post is possible.
-=-MouseEars
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Re: The math in detail., PairTheBoard, 10. Sep 2003 14:26
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stdioh and I are making the calculation at the time the first three cards are dealt based only on the information available at that time. Your objection is a little like saying the calculation preflop for flopping a set is not valid because one of your opponents may be holding your Set Card. Maybe they are, maybe not. That information is not available so the calculation is done assuming nothing about the other players cards. In this case, the calculation is done apriori, without assuming any information that will come only later.
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Re: The math in detail., Harold Pierce, Jr., 10. Sep 2003 23:02
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I am semi-aware of the assumptions used in these calculations.
However, in stud poker it is quite possible that you will see on
the deal cards that are pertinent to your hand and these should be
taken into account. It is misleading and a disserve to beginners
if an author fails to make mention of this.

Suppose your are dealt three to a middle straight such as (7,8)9
and the board show 7 of the 8 outs. In this case, your probability
of making a straight most certainly is not 0.19 as given in standard
math tables. Indeed, it is gut shot. And if the last out appeared on
4th street, the probability of making the straight is zero.

In draw games, Hold'em and Omaha, you see only your cards and can
make no assumptions about the cards in other players' hands or in
the deck. Thus, the draw and flop probabilities are exact.

Frankly, I think too much of a fuss is made over odds altho these
are improtant for understanding the basic structure of any poker
game. In most poker games, the action is so fast that one simply
doesn't have time to do these calculations on the fly unless your
are math genius. Those mouse pads with the basic stud info on
them that StudStrategy.com is now selling will be a real boon
for on-line beginers and average players.

-=-MouseEars
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Re: The West in detail., timmer, 10. Sep 2003 19:13
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on 10. Sep 2003 10:20 stdioh wrote:

>
> As pointed out also, it is very important to know your number of outs as the boards change.

you , my friend have discovered one of the prime reasons stud is a much harder game to advance your understanding of the mathamatical aspects compaired to hold em.

the fact that the base odds calculations are not fixed as in hold em but are constantly changing due to the number of cards on the board. make the odds aspects of the game much more difficult.

now take into account that in low limit stud with the rake being as much a factor as it is and the fact that most bets you make need almost a 20% over lay. You might begin to understand what Mr West is getting at.

The facts are that a bet not lost is worth *more* than a bet won. Primarily because of the size of the rake. when you begin to account for this huge factor you might begin to glimps upon why MR West directs his Low Limit players to play as carefully as he does.

Besides if you bet the bejezzus out of your trips you will likely find that you win a small pot with a hand capable of winning a much larger pot or you put many bets into a pot that you might possibly lose if you dont improve.

Also by putting many small bets in before 5 th street against many players makes playing pure draws much more attractive for most LL stud Players.

( Im not saying it is correct due to the implied odds vs the total number of bets these draws must put in to see all the cards. However many times it is quite correct on a street by street pot odds basis and sometimes even over all)

In fact in some cases it may be correct to limp along keeping the pot small untill you get to 5th street where the bets double. thereby denying the pure drawsthe odds they they need to continue but still managing to get a pot large enough to continue on hoping for a FH for those times you get in trouble on 6th.

If you read Mr wests book carefully and with the aforto mentioned things in mind you will find that his strategy although not explaned nearly as thoroughly as the 2+2 publications have quite a bit of validity and are in almost every case descibed with in it, correct for those players, those limits, and those opponents, you can expect to find in the games he writes about

now its obvious that you will win a bunch of money with trips that goes with out argument. However winning the most and losing the least when you win / lose with them is what seperates the good stud player from the bad stud player.

timmer
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Re: The West in detail., stdioh, 11. Sep 2003 15:37
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You make fair points and I'm not so much trying to trash Roy (I really do respect what he has to say) as make a point that in this case, his views are unconventional to say the least.

Generally speaking, the simple solution is the correct one, and in poker that bases down to "get your money in there when you have the best of it."

Now when you're playing against real poker players this can't be followed so directly. There is deception and counter deception. When you're in a game with a bunch of loose passive players, however, playing passively yourself is not the way to beat them. You need to agress, even when you will quite frequently be drawn out on. It is important to make them pay when they have the worst of it so that you get their money when they more frequently don't improve.

And to make an argument in one breath that you shouldn't thin the field since you want to bring more of them along and in the next breath say that you're in danger of getting drawn out on is a bad idea. If you don't want to be drawn out on, raise some people out of the pot.
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Re: The West in detail., timmer, 11. Sep 2003 20:07
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on 11. Sep 2003 15:37 stdioh wrote:

> And to make an argument in one breath that you shouldn't thin the field since you want to
> bring more of them along and in the next breath say that you're in danger of getting drawn out
> on is a bad idea. If you don't want to be drawn out on, raise some people out of the pot.

but it is a poker reality bad idea or not.
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Re: The West in detail., stdioh, 12. Sep 2003 09:07
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I guess you could say that it is the eternal struggle. Do I cap preflop with AA or not pretty much fits into the same pigeonhole.
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Re: The West in detail., timmer, 20. Sep 2003 11:34
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on 12. Sep 2003 09:07 stdioh wrote:
> I guess you could say that it is the eternal struggle. Do I cap preflop with AA or not pretty much fits
> into the same pigeonhole.

yeap, right on top of "it depends".

timmer
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Re: The math in detail., timmer, 10. Sep 2003 19:14
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did I mention that most these calculations are done hot and cold 7 handed ?
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