Some Triple Draw thoughts

[peterbirks]

The only game that I could find last night to wile away half an hour or so at TD was 10c-25c ace-to-five. Now, mathematically Ace-to-Five is no different from deuce-to-seven (see the Negreanu equivalence table for proof of this), but what you do not do is just move everything down a digit. So, although it's the same, it feels different.

No matter -- this time I managed to keep my loss down to 60 cents, although I suspect that this was partly down to the fact that at this level even I can spot flaws in some opponents' plays. And it was nice to have a full 6-handed table.

Anyway, I've just put some thoughts on paper about the game. Let's take the principle that a winning strategy in short-handed Hold 'em is to raise 18% of the time, to see about 30% of flops and to win 40%-plus of the flops that you see.

Therefore if we get the same figures on average in TD lowball, we should be a winner. Therefore:

Question One: what kind of hands will I call/raise with to match that percentage?

Clearly position is much more important in TD, because knowing what your opponent is drawing can affect what you do. So a hand that you would dump in the SB or UTG becomes a raising hand on the button. therefore we need to shift the percentage of raises and flops seen downwards quite drastically for SB and UTG, and upwards quite drastically for CO2 and on the button. However, the percentage of hands won when flops are seen should remain the same for all positions (ignoring the BB anomaly when you occasionally get to see a card for free).

I ran an Excel spreadsheet to look for the midpoint 30% of hands (deuce-to-seven) which basically brought you down to 2-card draws to a seven, 1-card draws to a smooth 8 or better, and pat hands up to a smooth 87. Clearly you would have to be stricter when UTG, while you could be significantly looser when on the button.

Now, what ones are raisers? This is tough. Pat hands to a smooth 8 or better, single draws to any seven?

Once again, these move up and down significantly depending on position.

Question Two: What am I aiming for?
Once again, this will change as the hand goes on, depending on your opponents' draws, but I reckon a smooth 8 is a nice target. With a good 2-card draw you have a nice chance of hitting at least some kind of 8 by the end (about 40%, I reckon). With a 1-card draw you are either nearly 50% or nearly 75%, depending on whether your hand contains a straight draw (beware of these hands!). You are still 33%/50% with 2 cards to come.

Question Three: How often will an opponent have a genuine pat 8 or better?

I reckon that in a full six-handed game, an eight-low or better will be out about one hand in 14. I am going to check this empirically.

I have come to some tentative conclusions:

1) Although you can draw to a rough seven, you shouldn't ever draw to a rough 8.
2) Nines are calling hands at the end (when a nine is your last card), but should never be targets.
3) Try always raising with up to a smooth 8 or better, but play limp with the other pat hands when OOP. Don't let anyone force you into breaking, ever.

Comments

[andy-ward-uk.livejournal.com]

"Let's take the principle that a winning strategy in short-handed Hold 'em is to raise 18% of the time, to see about 30% of flops and to win 40%-plus of the flops that you see."

I would be very careful about basing a whole strategy on that assumption ! It might be true, what do I know about triple draw, but surely that can't automatically apply across all games.

Andy.

PS Isn't 2-7 different because straights (and to a lesser extent flushes) kill your hand ?

Yes, 2 to 7 is different

[peterbirks.livejournal.com]

Hi Andy. Mea Culpa.

Of course 2 to 7 is different, even though mathematically the ranking of hands at the end can be compared. If the game wasn't different, you wouldn't have the "beware of the 6" factor in 2 to 7 (you don't hear of anyone saying "beware of the 4" in A to 5). Similarly, although you have debates about the merits of 2-3-4 vs 2-3-7, you don't hear debates about the relative merits of A-2-3 vs A-2-5.

So, although there is a mathematical equivalence at the end, the relative strengths of draws change, as do the relative strengths of cards. If the 6 is relatively weaker in 2-to-7, by implication, the 2, 3, 4, and 7 are relatively stronger than their equivalents in A to 5. I think this is particularly the case with the deuce in 2 to 7 vis-a-vis the Ace in A to 5 (the 2 is relatively stronger than the A).

More strength to the argument of never coming in on a draw in 2 to 7 without a 2!

On the percentage strategy.

[peterbirks.livejournal.com]

First off, we are talking about hypotheses here at low stakes. In other words, if it doesn't work, I'll try something else!

But I have a strong hunch that this theory is correct. After all, you have the same number of players and the same betting structure as in short-handed limit. So I reckon that if you see the same percentage of flops, raise with the same percentage of hands, and achieve the same win ratio when you see the flop, then you are likely to win a similar amount of money.

The flaw in the argument would be if the other players played very differently from the way they play limit hold'em. For example, if everyone else was much more passive pre-flop and much more aggressive on rounds 2 and 3, then your strategy simply would not generate the same number of wins when flop seen. But I suspect that the betting strategy of other players will not be dissimilar to short-handed limit hold 'em. In this sense, TD has more in common with limit Hold 'em than does, for example, PLO.

And, as a starting principle, I like it. Where else would you start?