A TD thought to ponder - multiway pots we like

[*TT*]

Here is an interesting thought to ponder, when is it advantageous to play a hand multi-way vs heads up when playing Triple Draw? I can think of two scenarios so far, I'm sure there are more.

TT [img]/images/graemlins/club.gif[/img]

[F8thless]

I would think that anytime you have an equity edge over an opponent, you want them in. Similar to hold'em, you're going to need a much stronger hand to win than you would in a heads up pot, but when you do you're going to win a much bigger pot, and ultimately have a much higher BB/100.

Any flaws in my logic?

[Soviet Exile]

where we have the number #1 preflop.

where we have position and the other two players are terrible.

[MarkGritter]

No, even in Hold'em there are plenty of situations where you have an equity edge but you prefer that opponents fold instead of call. Generally when the pot is already large, though.

Suppose you have 90% equity in a 10-bet pot. You bet--- would you prefer that your sole opponent call or fold?

In one sense TT's question has an absolutely trivial answer. You don't mind people joining the pot if they are drawing dead. [img]/images/graemlins/wink.gif[/img]

But, the more interesting question is whether there are TD hands whose return increases multiway.

In Badugi, this is somewhat easier to reason about. Suppose you have A23 going into the last draw. Suppose you brick--- do you prefer to be up against one, two, or three players?

Each player has (very roughly) 20% chance of making a badugi.

So against one player you take down a pot containing 2x the number of bets that go in, about 80% of the time. So your return in this case is about 0.6x. (Win 1.6x bets - the 1x you put in.)

With two players you win about 64% and your return is 0.92x.

With three players you win about 51% and your return is 1.04x.

So, it does seem advantageous to keep other players in--- even when you brick you earn more by having their bets in the pot than by having them fold early. (Naturally you are still better off getting them to put lots of money in early and fold later!)

But, in Badugi, an x32A is a fairly strong showdown hand already. In TD2-7 7432x is not a complete hand without that last card, so the odds most likely work out differently.

Here's an example I picked out of thin air: you hold 7432K (previously held QJ) while your opponents have 2678/6T2 and 3568/A9Q.

You are just 36% to win this pot, so you net only 0.08x the number of bets you put in in a 3-way confrontation.

If you convinced the 8653 hand to fold before the draw you become a marginal favorite and net just 0.01x.

If you knocked out the 2678 hand you are a 55% favorite going in to the last hand and net a slightly larger amount (0.10x) in the smaller pot.

However, I think the real power of getting it heads-up consists in standing pat when appropriate. If you are up against the same hands but have a T, you need to break against two players. But against one player you have a 65% edge. This is worth 0.3x the number of bets you put in, a substanital increase over your three-way expectation.

But, then, the T is just one card out of 13, and with a 5 or 6 on an earlier street you'd welcome the extra bets.

I didn't include the effect of the extra money from blinds, either.

One final thought is that multiway pots may actually have more free cards on the turn, and so end up with a smaller pot. How often have you seen 3 players draw one, one and two, and have both of the players drawing one check, giving a free card to the 3rd player? His contribution is probably only 1.5-2 big bets at that point and the failure to extract the third big bet out of him (or get him to fold) means that your EV is decreased.

[*TT*]

[ QUOTE ]
where we have the number #1 preflop.

where we have position and the other two players are terrible.

[/ QUOTE ]

I didn't even consider pat hands in my thought process, good catch. But you have to remember that horrible players get lucky too, we can all catch cards. A horrible player may finish with a K high while we might have 23455 at the end - very frustrating indeed but a reality in draw games, therefore I don't think we should include the quality of the players while factoring in the strength of a multi-way draw, think more about what cards you hold first.

PS: Mark wowed me as usual.

TT [img]/images/graemlins/club.gif[/img]

[*TT*]

Mark - can you work up a spreadsheet to show your multi-way pot equity concept? I'd like to explore this in more detail. I commonly think of equity for the hero to improve, I rarely consider fold equity because its so hard to induce a fold in TD... a concept I need to further explore i my theories.

TT [img]/images/graemlins/club.gif[/img]

[iron81]

Holding a good 2 card draw? You're not a huge favorite to make your hand but if you do its to a 7.

[*TT*]

[ QUOTE ]
Holding a good 2 card draw? You're not a huge favorite to make your hand but if you do its to a 7.

[/ QUOTE ]

I was thinking more along the lines of a 3 card draw like 23xxx from the big blind. Thats a hand that plays better multi-way even though many of your needed outs may already be out there because the pot is large enough that you can safely call bets in the later rounds while letting others drive the action. However 23xxx plays poorly HU, its a hand that you must often fold if the pot is not large enough, even if you improve.

TT [img]/images/graemlins/club.gif[/img]