BQM56

The situation up to now...  

White (me) to play next, now what? I'd say that the top right is an obvious choice, with that much support, is it possible to kill off the solitary black stone and take the corner and center for myself? Or would I have to make a choice? Is there a sneaky trap which might wind me up with both? I went with a, and thought of b, c, d, as I thought that my advantage would be to have an all out shoving match.

Charles Matthews First major concept here - if you want to kill Black outright, don't play contact moves. (See use contact moves for defence.) You don't want anything like a pushing battle.

The situation up to now...  

A play like White 1 here is usually best. It now becomes harder for Black to find eyes in the corner.

Black pushes down  

Charles White plays 3, and then White 5 takes care of Black 4. White would be more concerned about Black 4 at 5 (next diagram).

Black finds a sharp play  

So if Black does make the marked play, White may be cut off in the corner. Black 4 is good. White sacrifices 7 to make a false eye.

Continuation  

If it gets this far, Black has at least succeeded in setting White an interesting life-and-death question, which you might want to consider.

Even on a small board, there are too many variations for exhaustive analysis.

Just one eye in the corner?  

If Black 2, White 3 probably gives Black only room to make an L-group, which is dead. However, White has to be worried about the weakness on the right side - Black peeping at e. But for that, I'd be quite confident of killing Black here.

The L-group  

For example if this happens, Black has (worse than) the L-group in the corner and no serious chances in the centre.

Black fights back ?  

Black should make it tougher for White, using the peeps at 2 and 8. This probably fails, but offers more prospects.

Jasonred Thanks man... but, this situation here scares me! I wouldn't know what to do at all from this point, as now Black ACTUALLY HAS A MOYO, and I have to invade and kill it... the thought that Black might play at a or b next scares me even more...

(Charles I'll give some /Variations.)

Looks like White was too passive with 3. You do not always have to connect against the peep. In this position, White is strong, so resist. Besides, if Black cuts directly (instead of peeping against the cut), Black easily dies. The same is true if White resists the peep.

Resist the peep  

The circle point is the cutting point.

If Black insists on the cut...

White resists, Black fails  

White 5 is an easy way to kill the two black stones.

White Resists, Black runs  

If Black runs to make eye space, he has a long way to go. See SixDieButEightLive for details.

Of course at some point, Black has enough liberties to make the cut feasible.

The situation later... now what?  

Hey, I'm weak, so, for such a ridiculous handicap, you can guess how weak my opponent was, right?