Straight vs. flush follow-up

[BruceZ]

To clarify, *I* am in no way suggesting that straights should be ranked higher than flushes (c'mon). This was mentioned by the original poster, probably in jest. My point is only that given the structure of Hold 'em (2 cards, a flop, etc.) that it is more difficult to make a straight than a flush the way the game is played because it is easier to flop a playable draw, and easier to complete the draw.

Some have suggested that this is simply because flushes are ranked higher than straights, and this influences the hands that you play. I'll go out on a limb and suggest that this isn't the reason, and it would be harder to make straights even if they were ranked higher than flushes, though it's a good question. I don't think you would play 45o even if straights were ranked higher any more than you would play any two suited cards now, and you wouldn't chase 3 card straights and gut shots any more than you try to hit runner- runner flushes. You don't do these things because you are not likely to make your hand, any hand, not because of the relative ranking of straights and flushes. We play hands that can make both straights AND flushes, and those hands are more likely to make flushes. True you play Axs sometimes, but that is partly for its high card potential, not just for its ability to make the nut flush.

If poker were a game where you were given 7 random cards all at once, then it would be easier to make a straight. Since you have the opportunity to see some of the cards and make a decision on whether to continue, it becomes more difficult to show up at the river with a straight unless you are an idiot and disregard the probability of making your hand. This would be true regardless of whether a straight or flush were ranked higher.

[Collin O'Mahon]

Bruce:

I am having trouble calculating the probability of getting a straight vs. a flush when (a) starting with 87s, and (b) starting with 87o.

Could you show me the math of how to do this...

Thanks

[rigoletto]

I don't think you would play 45o even if straights were ranked higher any more than you would play any two suited cards now, and you wouldn't chase 3 card straights and gut shots any more than you try to hit runner- runner flushes. You don't do these things because you are not likely to make your hand, any hand, not because of the relative ranking of straights and flushes. We play hands that can make both straights AND flushes, and those hands are more likely to make flushes

Hi Bruce. I understand your point, but I'm not sure you are right when it comes to loose LL games. LL players seems to fear flushes a lot: checking top pair on monotone boards or when the flush hits on the turn, folding their str8 draws etc. I think you would see a lot more chasing for straights in these games if the ranking was reversed.

[Veloso]

This is interesting, but ultimately I disagree with you; if straights were ranked higher than flushes, you would play 67o and Axs significantly differently than under the real rules.

Some thoughts:

It's not as hard to see a good flop for connectors as you might think. There are 19600 distinct flops out of any deck of 50 remaining cards. Out of these...

If you hold suited cards, the flush will hit on the flop 165 times (.84%), and a four flush will hit 2145 times (10.9%), so you have a reasonable hand about 12% of the time.

If you hold connectors 45o through TJo, the straight will hit on the flop 128 times (.65%), and an outside straight draw will hit 1760 times (9.0%), so you have a reasonable hand maybe 10% of the time. You're even more likely to flop a gutshot draw than an outside straight draw.

...you wouldn't chase 3 card straights and gut shots any more than you try to hit runner- runner flushes.

Sure you would. Not the 3-card straights, but certainly your gutshots. They aren't good, but they're nowhere near as bad a runner-runner flush draw. You hit your runner runner flush draw 4.2% of the time, and you hit your gutshot draw 16.5% of the time. You'll hit it on the turn 8.5% of the time, even if you don't get to stick around to the river.

It's true that you wouldn't play any two suited cards, but the analogy to 45o doesn't hold up. You don't play Jxs as a flush draw (where you might play Axs), because if you hit your flush, you're worried about a better flush. This doesn't carry over to straights. As far as making straights is concerned, 56o is every bit as good a starting hand as TJo. If the board comes 234 or 347 or 478, 56o is the nuts. Even 789 makes you second nut.

One of the reasons you don't limp with 45o is the fear of a flush. Over 60% of the time, the flop has at least two suited cards. In these situations a third suited card will come on the turn or river about 40% of the time. If the tables were turned, Axs would start being a lot more unattractive. The high card potential is okay with Axs, but it's not the main attraction. How often do you play Axo?

[BruceZ]

Hi Veloso,

Good post.

It's not as hard to see a good flop for connectors as you might think. There are 19600 distinct flops out of any deck of 50 remaining cards. Out of these...

If you hold suited cards, the flush will hit on the flop 165 times (.84%), and a four flush will hit 2145 times (10.9%), so you have a reasonable hand about 12% of the time.

If you hold connectors 45o through TJo, the straight will hit on the flop 128 times (.65%), and an outside straight draw will hit 1760 times (9.0%), so you have a reasonable hand maybe 10% of the time. You're even more likely to flop a gutshot draw than an outside straight draw.


I've done this calculation, so I know exactly how often they flop draws. I think I basically agree with your numbers, but the suited connectors flop 4-flush draws significantly more often than 4-straight draws, it's 9.5% vs. 8.4% or 13% more often (I've been saying 17%, sorry). There are 3 times more offsuit hands, but there is a falloff of how many straight draws they can flop once they get above JTo. I have counted up all of these, and there is an imbalance of 8 out straight draws with reasonable starting hands even if we regard the suited-connectors to be neutral with respect to flush/straight potential.

This issue is being thoroughly discussed in a heated thread on the general theory forum, and if you follow my links, you can find all my calculations. Here's a link (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=329242&page=0&view=ex panded&sb=5&o=14&fpart=) to get you up to speed quickly if you haven't been there. It has my whole argument and links. The subsequent posts are also useful.


Not the 3-card straights, but certainly your gutshots. They aren't good, but they're nowhere near as bad a runner-runner flush draw. You hit your runner runner flush draw 4.2% of the time, and you hit your gutshot draw 16.5% of the time. You'll hit it on the turn 8.5% of the time, even if you don't get to stick around to the river.

Agree, but since they are chased much less often, I have argued that they have a negligible effect on the final conclusion.


As far as making straights is concerned, 56o is every bit as good a starting hand as TJo.

I agree all these hands make the nuts, but the high card potential is important for pairing. Otherwise 65o is weaker than Axs under the current rules, and Axs is very often a marginal hand.


One of the reasons you don't limp with 45o is the fear of a flush.

I agree, but I have argued that straight vs. flush requires a parlay which has a small enough probability that it doesn't change my conclusion. The possibility is often overstated, especially preflop.


The high card potential is okay with Axs, but it's not the main attraction. How often do you play Axo?

The high card potential is what makes it playable, otherwise you'd play any two suited.

I'm waving my hands a lot here, but I believe these things can all be made rigorous with enough effort, but this isn't an important issue to spend a lot of time on.