Dennis Bragg: Pushing/Defending In The Blinds: The Next Logical Step
 

So it seems like the next logical step given the past two articles is to take one of the situations and instead of assuming your opponent pushes/calls with xx% of the hands, assume your opponent will use the corresponding table.

Of course then you can rerun the analysis for the corresponding table based on your optimal response. And rerun the first side again with the improved opposite side.

I'm not sure but my hunch is that the two sides will converge to the same table regardless of your starting conditions. In which case you'll have a single set of tables for the "optimal response assuming your opponent plays optimally" Then you could have alternate tables for "assuming your opponents plays 10% tighter and 10% looser".

Your comments at the end of the small blind section noting that with a very small stack you should assume your opponent will (correctly) call with any two cards foreshadow this line of reasoning.

It's possible the two tables will converge to different results depending on the initial conditions. That would be an interesting thing to see. It's also possible they don't converge at all. But I suspect that's not the case.

It would be really interesting the results if your program could be extended to do this analysis.

Re: Dennis Bragg: Pushing/Defending In The Blinds: The Next Logical Step
 

I think the article is great for showing the math behind these decisions. Here is the criticism.....

A large portion of the discussion in the one table tournament section deals with bubble play. I feel that the advice would be very different on the bubble versus playing 5 or 6 handed.

Is this a topic for a future magazine or would the author or anyone else care to comment here?

Re: Dennis Bragg: Pushing/Defending In The Blinds: The Next Logical Step
 

I've already looked into optimal vs. optimal play and am currently writing an article of my own that comments not only on this, but on bubble play as well. I'll hopefully give some insight into just how much adjustment needs to be made on the bubble in different situations.

Re: Dennis Bragg: Pushing/Defending In The Blinds: The Next Logical Step
 

That is an interesting point and I am not sure of the answer. I suspect that the two tables do not converge to the same table simply because the pusher has fold equity. But there probably is an optimal push strategy and a cooresponding optimal call strategy.

I am working on some other simulations right now, but when I get a chance I will try to investigate this some more.

Dennis

Re: Dennis Bragg: Pushing/Defending In The Blinds: The Next Logical Step
 

[ QUOTE ]
I feel that the advice would be very different on the bubble versus playing 5 or 6 handed.

[/ QUOTE ]

I do not agree with this statement, but I would be interested to hear why you think the strategy would be different.

Dennis

Re: Dennis Bragg: Pushing/Defending In The Blinds: The Next Logical Step
 

rabbit, I am looking forward to your article.

Dennis

Re: Dennis Bragg: Pushing/Defending In The Blinds: The Next Logical Step
 

[ QUOTE ]
rabbit, I am looking forward to your article.

[/ QUOTE ]

So am I... [img]/images/graemlins/laugh.gif[/img]

I've submitted my first part which looks at how prize money and bubble situations can affect the EV decisions you have to make. It hasn't been accepted yet, but naturally I'm optimistic. As a second part I'm already working on optimal vs. optimal for SB v. BB (yes it usually does converge) both in the cash game as well as how the answers change in different tournament situations.

Re: Dennis Bragg: Pushing/Defending In The Blinds: The Next Logical St
 

[ QUOTE ]
[ QUOTE ]
I feel that the advice would be very different on the bubble versus playing 5 or 6 handed.

[/ QUOTE ]

I do not agree with this statement, but I would be interested to hear why you think the strategy would be different.

Dennis

[/ QUOTE ]

Because the $ value of chips becomes so warped in many bubble situations. You can easily find yourself in a position where your opponent has you covered doesn't look at his cards, pushes, and you would be incorrect to call with hands as good as AK.

Re: Dennis Bragg: Pushing/Defending In The Blinds: The Next Logical St
 

[ QUOTE ]
Because the $ value of chips becomes so warped in many bubble situations. You can easily find yourself in a position where your opponent has you covered doesn't look at his cards, pushes, and you would be incorrect to call with hands as good as AK.

[/ QUOTE ]

Yes, there are special cases where this is true, like when the pusher is the big stack and you are the second biggest stack. Or when another stack is so small he is about to be blinded out.

The tables only consider chip EV, not $EV. However, I still think they apply to most bubble situations.

Re: Dennis Bragg: Pushing/Defending In The Blinds: The Next Logical St
 

[ QUOTE ]
The tables only consider chip EV, not $EV. However, I still think they apply to most bubble situations.

[/ QUOTE ]

Sorry, but they don't. Even in a somewhat common spot where everyone has about the same stacks and the SB is pushing, the difference between ChipEV and $EV is usually pretty big.

For example, You are in a party SNG on the bubble. Everyone has 2000 chips and the blinds are 100/200.

Folded to the SB who pushes blind.
According to the chart you are correct to call with a bit over 50% of your hands (which would be absolutely correct in a HU match)

However a bubble situation warps the chip value so much. Winning the hand is worth about 38% of the prize pool, while losing it gives you nothing. At the start of the hand, your stack was worth exactly 25% of the pool (everyone was even) so you stand to gain only 13% while losing 25%.

As a result even if your opponent is pushing blind you still need a good hand to call, namely: 66+,ATo+,A7s+,KQo,KTs+ (about 12% of hands)

As an aside, if you opponent knows this then it actually becomes correct to push any two from the SB since the BB cannot call often enough to punish you for your loose pushes.

This just shows how different and counter intuitive proper bubble play can be. If the BB does decide to call then it hurts the SB, but it also hurts himself and the remaining players are the grateful recipients of all that lost $EV.

(Note: the STT forum is full of this sort of analysis)