Stud Proposition; Interesting Questions

Scenario: A Proposition Bet (no scam involved).


Player A says he will start with a pair of deuces. Player B will take Aces. They bet on each street as in normal 7-Card Stud and do this for as many hands as the contest lasts.


Player A claims he is a good enough player to beat Player B out of money this way, even though he is starting as a big underdog. You (or I) ridicule this contention, knowing that while Player A is an expert, Player B is a good solid winning player though not a true expert. Now a supporter of Player A chimes in and says that all player A has to do is outplay Player B on one street for it to nullify the starting advantage.


Let's say the game is $15-30. Could this possibly be a profitable situation for Player A?


My initial reaction was no, of course not, and then I got to thinking about how sometimes the smaller pair gains a playing advantage over the higher pair (like on the River, where the smaller pair will never pay off unimproved). Also if the Aces obviously make two pair before the River, the smaller pair can usually just fold. However if the smaller pair obviously makes two pair, the Aces may have to keep on coming. So it might be possible that a good player not used to these types of specific situations could make some errors.


For instance, who knows on which street (if ever) the Aces should fold on if the deuces makes two obvious pair? What about if it was fourth street (buried deuces hitting their doorcard)? What about on 5th Street, if split deuces caught a running pair on board? Should the Aces keep coming?


So while it seems hard to imagine that this prop bet could somehow be profitable for the deuces, the supporter of the expert player claimed it would indeed be so for the expert--and it did make me consider a few things I hadn't really thought much about before.


All comments welcome.

Well, in my opinion, it's true that the deuces will outplay aces (assuming both are split) relative to the general percentage of deuces winning the pot. For the following reasons:


1) deuces will NEVER pay off on the river if unimproved


2) deuces will always act last unless they hit an open pair.


3) deuces will fold when aces make an open pair, aces will be forced to call when deuces make an open pair.


4) If the game was hidden at all, aces may call when deuces makes open deuces, deuces will never call when aces makes open aces.


All this being said, there is no way that any reasonable player could lose starting with aces vs. a player starting with deuces. I believe this holds even if the deuces were to randomly have a buried pair or deuces, randomly. Either way, I'd love to play anyone with aces against a known lower pair. I don't care if you put the 5 greatest players together and allowed them to consult!


Now, if you got to see my side card, or the aces were buried and known, that might be a different story, but I'd still prefer the aces, but by much less.

"3) deuces will fold when aces make an open pair, aces will be forced to call when deuces make an open pair."


Depending on when the deuces make an open pair (sixth-street, perhaps), I think the aces WANT to call because it is profitable to do so (pot equity).


Like you, I don't think there is enough skill in the world to play deuces against aces profitably.


Tom D

yes it can if player A is better than player b. the aces are probably a 2-1 favorite heads up. this is a good thought exercise similar to the ones in Poker essays three.


Pat

Yes, of course, the aces want to call when deuces makes an open pair. But this means that money will be going into the pot when deuces are favored, which cuts into the original edge that aces have.


By the way, do you know the general percentage that deuces will beat aces? I think it's around 33-40%, but I'm not certain (I used to know).


My point is that you can't say, well, on average, $100 (or whatever number) will go into the pot on each side and because aces is a 2-1 favorite, aces' equity = $33. It's less because deuces should outplay aces a bit over the course of the hand.

It makes a difference how the pairs are dealt.


If the deuces are always split and the aces always buried, then the deuces are certainly helped.


It should be noted that a great deal of a superior player's advantage is reading hands. If both pairs are buried, then almost all of that advantage evaporates. Each player is playing with all of their cards exposed, until the river, except for the suits of the pair which in rare circumstances affects a flush draw.


If the deuces are buried, then the weaker player will be able to read the hand as well as the expert. At that point, the advantage for the aces is so large that a five or six (at most)rule "system" implemented by a simpleton would win easily. In fact, betting on every street unless facing trips or better would win big for the aces. Many times, the aces will know that the deuces are drawing dead at the river and can even bet the river with impunity.


Even if the deuces are split, the hand reading advantage of the expert is severely reduced. The simpleton will always know if trips are made until the river and usually know if two pair is made.


That is the point. The rules handicap the better player in two ways: 1) weaker cards and 2) reduced value of hand-reading. Thus, much of the expert's advantage (which is being relied upon to overcome the starting hands) is negated by those very starting hands (since they are known). I just do not think there would be enough skill remaining to allow the starting hand advantage to be overcome.

As a follow-up:


The better player is hoping to outplay the weaker player. There are five streets in which he can attempt to close the gap.


The problem is that one street gives him no opporunity to use his skill. Third street is automatic for the aces. He bets.


So, even with split pairs, the better player only has the last four streets to outplay his opponent.


If both catch blanks on fourth street, then that street plays automatic for the most part. Where is the skill?


The terms of the proposition eliminate almost all skill for the game. Thus, a skill advantage is next to worthless.