Key holdem odds to memorize

[Derek in NYC]

I initially posted this in small stakes, where I participate, but then I remembered this forum.

I thought this might be a helpful thread for many players, myself included. I actually have a set of about 40 flashcards that I sometimes review on the bus when Im bored. Anyhow, I thought I'd tap the 2+2 talent pool to increase my flashcards. So here goes my first helpful odd to get the list going:

Odds of flopping a flush draw or made flush with 2 suited cards: 8:1 against

(By the way, does anybody know the odds of flopping two pair or trips holding two unpaired cards?)

[knsmith85]

[ QUOTE ]
I initially posted this in small stakes, where I participate, but then I remembered this forum.

I thought this might be a helpful thread for many players, myself included. I actually have a set of about 40 flashcards that I sometimes review on the bus when Im bored. Anyhow, I thought I'd tap the 2+2 talent pool to increase my flashcards. So here goes my first helpful odd to get the list going:

Odds of flopping a flush draw or made flush with 2 suited cards: 8:1 against

(By the way, does anybody know the odds of flopping two pair or trips holding two unpaired cards?)

[/ QUOTE ]

I'm not sure I understand the usefulness of a lot of these ratios. Sure, knowing how often you'll flop your set, or hit your flush on the turn/river is useful, but past that this kind of knowledge seems pretty limited to me.

For example, when holding un-paired cards, what good does it do you to know how often you flop trips? First off, it is so small that you'll never be able to consider this probability in terms of pot odds, and secondly when you do flop trips you still don't know if it's any good (example: you hold 7 /images/graemlins/club.gif2 /images/graemlins/diamond.gif, flop comes 7 /images/graemlins/spade.gif 7 /images/graemlins/heart.gif 8 /images/graemlins/heart.gif).

This kind of thing is absolutely necessary in blackjack, but it seems to me that there is limited use in hold 'em. (You'd be much better off teaching yourself speed-arithmetic tricks than you are memorizing flashcards, IMO)

Thanks,
Kyle

[gaming_mouse]

Hey Derek,

The chance of flopping a two pair which uses both your cards is 1 in 50, and the chance of flopping trips is about 1 in 77.

2 pair: 9*44/ncr(50,3)=.0202

trips: 3*2*44/ncr(50,3)=.013


Practically speaking, the odds of flopping 2 pair or trips are so low as to be negligible. This is why playing hands like J5o is unprofitable even from the small blind with 8 limpers and a guaranteed check from BB.

Whenever you think to yourself, "Hey, there's always the chance I flop 2 pair," toss your cards in the muck.

gm

[Megenoita]

I think this thread has tremendous potential for value. Derek, I would love to know the contents of your flash cards...could you post or PM? Maybe that's too much of a hassle. It's cool...

Gaming Mouse...you're the man, dude...I love your responses. What limits do you play--just curious. Also, how do I do your computations (that you just wrote) on a retarded calculator? Sorry, I really don't know.

I'll chime in by saying that I think the Super System section on probability that no (other) player has an ace is valuable when you get down to LP play...

M

[Derek in NYC]

to use your example, you are dead wrong if you dont understand why such odds are important to memorize. suppose you hold a trash hand like 8 T offsuit, from the small blind, in a 1/2 structure. 7 players limp ahead of you. should you complete? assuming the bb does not raise, the pot is paying you 17:1 to complete. the only way to know whether this is likely to be worth playing is to know the odds i just mentioned.

[knsmith85]

[ QUOTE ]
Hey Derek,

The chance of flopping a two pair which uses both your cards is 1 in 50, and the chance of flopping trips is about 1 in 77.

2 pair: 9*44/ncr(50,3)=.0202

trips: 3*2*44/ncr(50,3)=.013


Practically speaking, the odds of flopping 2 pair or trips are so low as to be negligible. This is why playing hands like J5o is unprofitable even from the small blind with 8 limpers and a guaranteed check from BB.

Whenever you think to yourself, "Hey, there's always the chance I flop 2 pair," toss your cards in the muck.

gm

[/ QUOTE ]

I don't quite follow how you get that percentage for 2-pair. The combination on bottom makes sense to me, but I don't really get the numbers on top. Aren't there 6 cards that help you at first, 3 for the second, and on the third card (note: Order shouldn't matter here) any of 43 cards (52 - hole cards - card #1 - card #2 - 4 cards that would give you full house = 43) will do.

So for that, I'd get 6*3*44/NCR (50,3), or 18*44 / 19604 = 0.0404.

Where am I going wrong?

Thanks,
Kyle

[knsmith85]

[ QUOTE ]
to use your example, you are dead wrong if you dont understand why such odds are important to memorize. suppose you hold a trash hand like 8 T offsuit, from the small blind, in a 1/2 structure. 7 players limp ahead of you. should you complete? assuming the bb does not raise, the pot is paying you 17:1 to complete. the only way to know whether this is likely to be worth playing is to know the odds i just mentioned.

[/ QUOTE ]

Well, as was mentioned, the odds are so insignificant here for a direct hit on the flop (straight, two pair, or trips) [using the numbers from earlier, the odds of ANY of these are (1 - (1 - .013) * (1 - .0202) * (1 - .0199)) or 5.22%, you're NEVER going to have the direct pot odds to make the call here. I think you're going to lose more on second-best hands than you will make from callers to the river, so that effectively cancels out the implied odds.

[knsmith85]

[ QUOTE ]
to use your example, you are dead wrong if you dont understand why such odds are important to memorize. suppose you hold a trash hand like 8 T offsuit, from the small blind, in a 1/2 structure. 7 players limp ahead of you. should you complete? assuming the bb does not raise, the pot is paying you 17:1 to complete. the only way to know whether this is likely to be worth playing is to know the odds i just mentioned.

[/ QUOTE ]

You're much better off understanding the underlying calculations for these types of situations than you are memorizing, so you can do the math on the fly.

[Derek in NYC]

I was hoping not to have to sit down and do the math, but I dont think you're right. Given unsuited cards, there is some combination where it makes sense to complete from the SB, and perhaps limp from the button behind enough limpers. i want to know where this point is. you're right though, i should consider not only the odds of flopping two pair or trips, but also the odds of flopping a str8 or OESD given an x-gapper. my intuition tells me that some situations arise in limit poker where completing from the sb/button is the correct move, but i can't tell you what the cutoff point is. im happy to be proven wrong, and if so, im happy to concede that this may not be the greatest flashcard in the world, but otherwise, i think the utility of memorizing certain basic odds is quite important to good potodds based play.

[Derek in NYC]

by the way, why would you multiply these probabilities? shouldnt they be added?

[Derek in NYC]

and im sorry to be so dogged, but assuming your number of 5% is correct, in fact there are situations where a call would be correct. either completing from the small blind, or playing from the button in a family pot, would be perfectly fine with a 5% chance of this outcome, particularly given the implied odds you get after the flop if you hit your 19:1 shot.

[knsmith85]

[ QUOTE ]
by the way, why would you multiply these probabilities? shouldnt they be added?

[/ QUOTE ]

You can add them, but then you need to subtract out all the crossover results. The way I did it is much easier.

What I do, is take the probability that the first one does NOT happen AND the 2nd one does NOT happen AND the 3rd one does NOT happen. To get that you multiply together - giving you the odds that you DON'T flop anything good. Subtract that from one to get the odds that you DO flop anything good.

Note that my straight draw calculation is slightly incorrect - I did it for a 3-gapper instead of a 1-gap.

My point about it pretty much never being +EV to complete with junk (3-gap+ off-suit w/o Ace or King), is that you'll end up pouring so much money into second-best pots that you lose pretty much all the benefits of the implied odds. e.g.: When you get a flop like 553x and are holding J5x, your implied odds aren't that great if you're best, and if you do get callers, you're probably beat.

[knsmith85]

[ QUOTE ]
...my intuition tells me that some situations arise in limit poker where completing from the sb/button is the correct move, but i can't tell you what the cutoff point is...

[/ QUOTE ]

I'd say the best test for this intuition, would be to look into a 100,000+ hand PT database, and see how profitable hands like AA or AKs etc. are from the Small Blind. You'll find that they're actually not extremely profitable. (I'm not sure, but I think you'd find that things like 99 or TT from late are more profitable than even the most premium of hands on the SB)

Another key here is that you're not respecting position. When you combine awful position with junky hands that might catch a flop (which could very well be second-best) once in a while, the EV just doesn't work out.

[gaming_mouse]

[ QUOTE ]
Gaming Mouse...you're the man, dude...I love your responses. What limits do you play--just curious. Also, how do I do your computations (that you just wrote) on a retarded calculator? Sorry, I really don't know.

[/ QUOTE ]

To do nCr calculations on a handheld you need a scientific calculator. However, you can do them in google too. Google is also nice because it can handle HUGE numbers, much bigger than any calculator.

For example, for the 2 pair calculation, try pasting in the following:

9*44/(50 choose 3)

HTH,
gm

[gaming_mouse]

[ QUOTE ]
I'd say the best test for this intuition, would be to look into a 100,000+ hand PT database, and see how profitable hands like AA or AKs etc. are from the Small Blind. You'll find that they're actually not extremely profitable. (I'm not sure, but I think you'd find that things like 99 or TT from late are more profitable than even the most premium of hands on the SB)


[/ QUOTE ]

This is flat out wrong. AA and AKs will be among the most profitable hands from ANY position.

gm

[knsmith85]

[ QUOTE ]
[ QUOTE ]
I'd say the best test for this intuition, would be to look into a 100,000+ hand PT database, and see how profitable hands like AA or AKs etc. are from the Small Blind. You'll find that they're actually not extremely profitable. (I'm not sure, but I think you'd find that things like 99 or TT from late are more profitable than even the most premium of hands on the SB)


[/ QUOTE ]

This is flat out wrong. AA and AKs will be among the most profitable hands from ANY position.

gm

[/ QUOTE ]

Fair enough, but I'm still contending there are no circumstances where voluntarily putting money in the pot is a +EV play for hands like J5x, in a limit game.

[gaming_mouse]

[ QUOTE ]
I don't quite follow how you get that percentage for 2-pair. The combination on bottom makes sense to me, but I don't really get the numbers on top.

[/ QUOTE ]

We assume you have a non-pair hand, like 95, say. To make a 2 pair on the flop which uses both your cards you need 1 nine, 1 five, and 1 card which is neither a 9 nor a 5. We we first calculate how many possible flops fit that description.

The 3*3=9 ways to put one of the remaining 3 fives together with one of the remaining 3 nines. There will now be 44 cards left which are not a nine or a five. Hence 44*9. The total number of possible flops is (50 choose 3).

I just glanced at it quickly, but I believe your calculation is going wrong by implicitly assuming an order, whereas we (as you know) are interested in unordered combinations only.

gm

[gaming_mouse]

[ QUOTE ]
Fair enough, but I'm still contending there are no circumstances where voluntarily putting money in the pot is a +EV play for hands like J5x, in a limit game.


[/ QUOTE ]

And you are quite right (see my earlier response to the OP). The one contention has nothing to do with the other.

gm

[Derek in NYC]

There is a difference between J5o and T8o, etc. In a 1/2 blind structure, in a family pot, completing with T8o from the SB or calling from the button, does not feel that wrong, but Id like to know what the math is.

Im in no way trying to suggest that hands like J5o become playable, but I do think unsuited connectors and 1-gaps can be playable from the SB or the button, given enough limpers.

I just want the math behind it to back up my intuition.

[gaming_mouse]

[ QUOTE ]
There is a difference between J5o and T8o, etc. In a 1/2 blind structure, in a family pot, completing with T8o from the SB or calling from the button, does not feel that wrong, but Id like to know what the math is.

[/ QUOTE ]

Derek,

You are absolutely right here -- and the reason is the T8 off has str8 equity. For example, let's calculate how often you flop a str8 or str8 draw.

Flopping a Str8

<font class="small">Code:</font><hr /><pre>
789TJ
89TJQ
6789T
</pre><hr />

That gives us 3*4^3=192 flops that give us a str8

Flopping an OESD:

<font class="small">Code:</font><hr /><pre>
789Tx
89TJx
</pre><hr />

Take the first possibility. We need to count flops that have a 7, a 9, but not a 6 or a J.

4^2*40=640

But there are two possibilities, so we have 1280 flops that give us a str8 draw. So the chance we flop a st8 or OESD is:

(1280+192)/(50 choose 3) = .075, or aboout 12:1.

This may not seem like a lot, but in a family pot, for a half bet, you now have an easy call.

Note how much more that str8 equity gives you compared with your 2 pair equity, which is only 50:1. It's just not even close.

HTH,
gm

[MickeyHoldem]

and another 64 flops for the DBB...

6 89T Q

not that the odds change very much!

[MortalWombatDotCom]

[ QUOTE ]
To do nCr calculations on a handheld you need a scientific calculator. However, you can do them in google too. Google is also nice because it can handle HUGE numbers, much bigger than any calculator.

For example, for the 2 pair calculation, try pasting in the following:

9*44/(50 choose 3)

HTH,
gm

[/ QUOTE ]

Good resource. I almost feel silly for writing my own arbitrary precision calculator app in java. If i "finish" it before i discover still more resources that render it unnecessary, i'll try to publish it somewhere useful to readers of this forum.

[gaming_mouse]

Mortal,

Yeah, I actually wrote my own too before I discovedred the google one. Good is good enough to handle most problems that come up here, eg, and seems essentially arbitrary precision.

gm