[Closed] Adjusting Pushing Range SB vs. BB 12-15BB

Had an interesting conversation with another German coach about the topic. He said the worse Equity of pushing A2-A6 is overruled by the card removal effect of these hands.

HMm, I think he is right, because the Equity difference is pretty small (old Range 44.83%, new Range 44.97% Equity against the opponents Callingrange). I also did some Calculations with CardrunnersEV, which actually does take cardremoval-effect into account (at least I think so). My example was like:

Blinds: 100/200

Bu 1900
SB 2800
BB 4300

BB is calling with the range you gave him and the result is that the Push with your old pushing-range has an EV of about -0.037 and with the new pushingrange it has an EV of -0.2. Actually I'm not 100% sure if that's correct. But I think at least the tendency that the old range has an higher Ev than the new one is true. I think you could also do the calculations by hand, but I think that's a bit complicated (maybe there's also a smart program, which can do that for you, but I don't know).

According to cardrunnersev you get called 19,9% of the time with your old pushingrange and 20,8% of the time with the new callingrange. I think at least these numbers should be correct and giving these numbers you should be able to calculate the Ev of a push by hand.

There is a simple way to count combinations as you get the equities. Use PokerStove, which reports the number of hands. Here is a specific A2o hand against that 33+ Ax KJs+ KQo range:

393,829,920 games 0.469 secs 839,722,643 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 64.466% 55.36% 09.10% 218040610 35845438.00 { 33+, A2s+, KJs+, A2o+, KQo }
Hand 1: 35.534% 26.43% 09.10% 104098434 35845438.00 { Ac2d }

Divide the 393,829,920 by (48 choose 5 = 1,712,304). You get 230, so there are 230 combinations out of 50 choose 2 =1225 in that calling range when you hold A2o. Let's do 98o:

462,322,080 games 0.579 secs 798,483,730 games/sec

Board:
Dead:

equity win tie pots won pots tied
Hand 0: 62.733% 62.38% 00.36% 288380747 1648545.00 { 33+, A2s+, KJs+, A2o+, KQo }
Hand 1: 37.267% 36.91% 00.36% 170644243 1648545.00 { 9c8d }

There are 462,322,080/1,712,304 = 270 calling combinations when you have 98o.

You can enter 230/1225 = 18.78% and 270/1225 = 22.04% into my program ICM Explorer as the probabilities of getting called, and then use the semibluff button. I think this will confirm that the card-removal effect outweighs the equity difference here.

If you are close to the bubble you should adjust the equity for A2o slightly due to the 18% ties which are each worth more than 50% of a win.