Shoving Range Maths Check

[JaffaCake]

I've dazzled lil Dave on Skype with this hand and trying to work the maths out for it, it's basically a 9bb shove from sb into bb, I'm trying to prive that it's mathematically profitable (before proving it's still a bad idea for ICM reasons)...

Anyone spot a problem in this logic:


"First they assigned the big blind a calling range – all pocket pairs, all suited aces, A-5 off +, K-8 suited +, K-9 off +, Q-9 suited +, Q-T off + and J-T suited. He then fed that range into Odds Oracle and worked out whether shoving 9-3 was a profitable move and came up with the following results:

We have 29.7% against the big blind’s calling range, which obviously has 70.3%. However, if his calling range is correct, he will only be calling 26.6% of the time (as he gets dealt worse than this range 73.4% of the time).

We can therefore work out if we make a profit on average:

When he folds, we make 2.5bb profit, so on average 0.734 x 2.5 = +1.84bb
When he calls, we win 29.7% of the 19bb pot, so 0.297 x 19 = 5.64bb, a loss of (9-5.64) 3.36bb. Therefore the 26.6% of the time he calls we lose 3.36bb, or (0.266 x 3.36), an average loss of 0.89bb.
We can therefore mathematically prove, assuming we have the correct range, that we win 0.95bb every time we make this move (1.84bb when the opponent folds minus the 0.89bb loss when he calls)."

[pleno1]

The cling range seems a little tight.

[JaffaCake]

Don't mind that Pads, kinda made it that way to illustrate the point, just more worried that maths is completely correct the way I worked it out? Odds Oracle comes out as just over 1bb profit overall....but that could be to do with rounding up n stuff?

[hatthehole]

I've dazzled lil Dave on Skype with this hand and trying to work the maths out for it, it's basically a 9bb shove from sb into bb, I'm trying to prive that it's mathematically profitable (before proving it's still a bad idea for ICM reasons)...

Anyone spot a problem in this logic:


"First they assigned the big blind a calling range – all pocket pairs, all suited aces, A-5 off +, K-8 suited +, K-9 off +, Q-9 suited +, Q-T off + and J-T suited. He then fed that range into Odds Oracle and worked out whether shoving 9-3 was a profitable move and came up with the following results:

We have 29.7% against the big blind’s calling range, which obviously has 70.3%. However, if his calling range is correct, he will only be calling 26.6% of the time (as he gets dealt worse than this range 73.4% of the time).

We can therefore work out if we make a profit on average:

When he folds, we make 2.5bb profit, so on average 0.734 x 2.5 = +1.84bb
When he calls, we win 29.7% of the 19bb pot, so 0.297 x 19 = 5.64bb, a loss of (9-5.64) 3.36bb. Therefore the 26.6% of the time he calls we lose 3.36bb, or (0.266 x 3.36), an average loss of 0.89bb.
We can therefore mathematically prove, assuming we have the correct range, that we win 0.95bb every time we make this move (1.84bb when the opponent folds minus the 0.89bb loss when he calls)."

should that not be 8.5-5.64= 2.86, making it 0.77bb ave loss, making the shove + 1.07bb

[JaffaCake]

Yeh I think it is, and that gets me much closer to the Oracle answer, brilliant, tyty for taking the time to check that!

[lucky_scrote]

Just use sng wiz.

You can assign the BB whatever calling ranges you want but if the calling ranges are perfect then shoving 9-3o will certainly lose you a few chips.

I'm assuming there is a 12.5% ante in place in this hand?

I think vs someone who is jamming correctly or slightly wider than for 9bb then I'm not folding Kxs K6+ Q7s+ etc. on phone so can't stove it but that range sounds correct providing its not late stages and have to think about ICM.

[JaffaCake]

Just use sng wiz.

You can assign the BB whatever calling ranges you want but if the calling ranges are perfect then shoving 9-3o will certainly lose you a few chips.

I'm assuming there is a 12.5% ante in place in this hand?

I think vs someone who is jamming correctly or slightly wider than for 9bb then I'm not folding Kxs K6+ Q7s+ etc. on phone so can't stove it but that range sounds correct providing its not late stages and have to think about ICM.

Tx Dan, have rounded the antes to make the example easier, it's a six handed scenario tho deep in the sunday million and the guy was playing the tightest on the table (for the purposes of this). I've made 93o a slight +EV move with my maths, I'm not sure on the 8.5 or 9 in the above tho? Started with 9bb, is it correct mathematically to only use 8.5 as we already have half a bb in (in the sb?). Certainly gets me closer to the Odds Oracle/Stove answer!

[ZZZZZZZROPE]

i use ICMIZER for spots like this.

Giving the bb a calling range of 32% only hands we cant profitably jam are 72 & 32o.

You can copy paste the HH directly into icmizer then adjust the default ranges. top piece of software

[SuuPRlim]

wait for 93 suited imo

[DungBeetle]

I worked it out differently, but agree with your maths.  +0.94 by my reckoning.

Call   Pot at end   Chance   Value
0.266   19   0.297   1.501038


Fold   Pot at end   Chance   Value
0.734   11.5   1   8.441

         Total
         9.942038

[JaffaCake]

Thanks for replies fellas (and LilD for your patience on Skype), finally worked it our long hand and got the maths to add up to the same as Odds Oracle told  me it should be. If anyone's interested this is how it worked out:

First they assigned the big blind a calling range – all pocket pairs, all suited aces, A-5 off +, K-8 suited +, K-9 off +, Q-9 suited +, Q-T off + and J-T suited. He then fed that range into Odds Oracle and worked out whether shoving 9-3 was a profitable move and came up with the following results:
We have 29.72% against the big blind’s calling range, which obviously has 70.28%. However, if his calling range is correct, he will only be calling 26.67% of the time (as he gets dealt worse than this range 73.33% of the time).
We can therefore work out if we make a profit on average:
When he folds, we make 2.5bb profit, so on average 0.7333 x 2.5 = +1.83bb
When he calls, we win 29.72% of the 19bb pot, so 0.2972 x 19 = 5.65bb, a loss of (8.5-5.65) 2.85bb. Therefore the 26.67% of the time he calls we lose 2.85bb, or (0.2667 x 2.85), an average loss of 0.76bb.
We can therefore mathematically prove, assuming we have the correct range, that we win 1.07bb every time we make this move (1.83bb when he folds minus the 0.76bb loss when he calls).

[DungBeetle]

What are the exact numbers?  It's not possible that a probability tree won't come up with the correct answer.

Does the SB have 9 behind and 0.5 in the pot as a posted small blind.  Or 8.5 behind and 0.5 in the pot as a posted SB?

[DungBeetle]

"When he folds, we make 2.5bb profit"

Don't follow this.  Are there antes?

[JaffaCake]

SB has 9bb total, 0.5 in pot. BB covers, has 15bb. Six handed table, antes in, have made them equal 1bb for ease of maths, so 2.5bb in pre