5CD - Low boat.

[Tilt]

Just bet, and raise to the cap.

[Burdzthewurd]

Boo I hate that line! He drew 2 and two guys stood pat, he MUST go for a checkraise here if his opponents have any mass of brain in their noggins. Fair chance you still might get one of them to 3-bet you and you can cap, but yeah, checkraise that up in case they have straights and would just call your post-draw raise scared.

[Tilt]

No, he has two stand pat players against him. There is very little risk that hes not getting paid here.

If you check, and the next player goes for a check raise with a flush, and the third player has a small straight and checks behind, you get nothing. Very plausible scenario.

If you bet one of these guys is going to raise you. And the third gets trapped.

[Biggle10]

Just curious, do we give any possibility to a full house which would beat twos-full or is that weak-tight thinking?

[Moneyline]

[ QUOTE ]
Just curious, do we give any possibility to a full house which would beat twos-full or is that weak-tight thinking?

[/ QUOTE ]

I don't think you need to be afraid of it, but you shouldn't discount it entirely. I probably wouldn't want to cap the betting after the draw in this hand (unless the other raiser was overaggressive), but the possibility of a bigger boat wouldn't prevent me from making it either 2 or 3 bets.

Just my opinion...

[Moneyline]

Someone should check my math on this one, but this should shed some light on the situation...

According to Super System, the chances of being dealt the following pat hands before the draw are:
A Full House: 693: 1 (.14%)
A Flush: 508: 1 (.20%)
A Straight 254: 1 (.39%)

Therefore, it follows that one opponent will have either a straight or a flush .59% of the time (.2%+.39%)

So, if you hold deuces full of eights, and your opponent must hold one of the three types of hands listed above, he'll hold a boat slightly less than 25% of the time (.14/.59). So you're a little better than 3:1 to have one player beat. In the real world, you're actually somewhat better than that, because A) your opponent may be false carding, and B) since you have a boat it will be harder for your opponent to also hold one because he can't make a boat using deuces and is unlikely to make one using eights.

Now here's where my math is a little shaky... against two opponents in which they both must hold either a boat, a flush, or a straight, I figure you'll have the best hand about 9/16 of the time. However, my math is based on estimates and is certainly underrepresenting your actual chances. In the real world, I put your chances more along the lines of about 11/16 or 11.5/16 (or about 70%) of having the best hand.

I came to this number by creating a matrix. The matrix assumes that each of your opponents will have a straight or a flush 3 times, and a boat once (representing the 3:1 number I arrived at above). Adding up all the possibilites, there are 16 outcomes, 7 of which give at least one of your opponents a full house. However, this method is flawed. As stated above, your chances are better than 3: 1 for each player. Also, with two opponents it becomes more likely that one of them is false carding. It's certainly feasible that the player to your left has a hand like trip sixes, or the player on the button has a hand like trip aces, and has decided to stand pat in hopes of showing down his hand for free.

All in all, I think this adds up to about a 70% chance you are best. It still doesn't prove whether it is better to bet out or go for a check/raise, but I think it does prove that you don't have to be too afraid of a bigger boat.

[Biggle10]

[ QUOTE ]
B) since you have a boat it will be harder for your opponent to also hold one because he can't make a boat using deuces and is unlikely to make one using eights.



[/ QUOTE ]

I'm sure my thinking is flawed, but I'm not sure if this is accurate. Doesn't my having a boat mean that there are more cards of the same rank in the deck? For example, if I had 2222x, wouldn't my opponents chance of getting 4 of a kind actually go up (albeit very small) as I am 'removing' a rank from the deck?
So in this case I'm partially removing ranks, thus making a boat more likely??

[Moneyline]

I'm not really sure... it's probably best to go ask in the probablity forum where people still remember how to do algebra. [img]/images/graemlins/tongue.gif[/img]

[MarkGritter]

[ QUOTE ]
[ QUOTE ]
B) since you have a boat it will be harder for your opponent to also hold one because he can't make a boat using deuces and is unlikely to make one using eights.



[/ QUOTE ]

I'm sure my thinking is flawed, but I'm not sure if this is accurate. Doesn't my having a boat mean that there are more cards of the same rank in the deck? For example, if I had 2222x, wouldn't my opponents chance of getting 4 of a kind actually go up (albeit very small) as I am 'removing' a rank from the deck?
So in this case I'm partially removing ranks, thus making a boat more likely??

[/ QUOTE ]

I'm not doing so hot on algebra lately, but this should not be too hard... Just count the number of full houses.

In a full 52-card deck there are 13*12 different full houses. Each one has 4C3 = 4 possible trips and 4C2 = 6 possible pairs. So that's 13*12*4*6 = 3744 full houses out of the total 52C5 = 2598960 distinct hands. Call it .144%.

With your 3 deuces and 2 eights removed now there are only 11 possible trips. There are still eleven possible pairs, but only one way to form 88 instead of 6. So we have 11*4*(10*6+1*1) = 2684 full houses out of 47 cards remaining. 2684 / 47C5 = .175%.

So, yes, you having a boat makes the chance of somebody else having a boat go up slightly.

The same is probably true of having a flush... let's see.

In the 52-card deck there are 4 suits, each of which can form 13C5 flushes. 4*1287 = 5148 hands out of 52C5 = .198%.

After removing five suited cards three of the suits can still form 13C5 flushes, while one can only form 8C5 flushes. 3*13C5 + 8C5 = 3917 hands out of 47C5 = .255%.