Overcall or three way all-in calculation feature has been finally added to ICMIZER. In this article we compare results for various realistic poker tournament spots produced by ICMIZER and SngWiz.
Note: there will be a lot of ICM calculations in this article so its target audience is probably a more advanced player than average.
When ICMIZER was first released 15 September 2011 I have presented a comparison of results with SngWiz. As I said there ICMIZER correctly calculates ICM equities, because it considers 3 outcomes of two players going all-in against each other: win, lose AND tie.
This tie is always a positive result for hero if he/she goes all-in, because if instead we consider only two outcomes Win and Lose, and increase both of their percentages by (Tie%/2) (win% = actual win% + (tie%/2) and lose% = actual lose% + (tie%/2) as SngWiz does we end up with greater probability to bust. Since ICM (and more generally tournament poker) doesn't like busting, increasing lose probability at the cost of tie outcome introduces a serious error in calculations.
This was shown in original article, but there were a lot of arguments about quality of samples in it. And I must agree, some samples were more acamedimcal than realistic. Also initial version of ICMIZER didn't support 3 way all-in calculations. This is no longer the case and now overcalls are taken into account.
Lesson learned and in this article I will analyze and compare 5 different but very realistic tournament spots. Almost of all of them are bread and butter bubble spots without some imaginary ranges.
Each hand analysis will have the following structure:
- SngWiz screenshot of situation and results with details
- A table with results for different hands calculated by SngWiz, representing upper left corner of ICMIZER result grid
- Screenshot of ICMIZER ICM calculations results for this spot
- Link to same situation in ICMIZER
- Comments about the spot and difference in results
Hero facing a push from big stack on bubble of 6 max tournament
http://www.icmpoker.com/icmizer/#wTPf
So in first hand we have middle stack on the bubble and big stack pushes from the button. Typical daily spot. Lets see what kind of mistake SngWiz produces here.
Big pairs (AA,JJ,QQ,TT) - mistake is around 0.1%-0.15% tournament equity. This is quite an amount, but generally mistake will be smaller for paired hands, because they tend to tie more rarely then unpaired hands. Just to give an idea of what 0.15% mistake is - in a 6 max tournament 0.15% of prize pool is roughly 0.15% * 6 = 0.90% of buyin, so that could easily be a ROI for some rather good player on this structure. And such mistake will happen in just a SINGLE hand, while bubble can contain tens of them. But lets look at more interesting hands, namely AX hands which are dealt much more often than top pairs. Here the mistake becomes pretty brutal - AKs - 0.14%, AQs - 0.21%, AJs - 0.25%, ATs - 0.28%, A9s -0.34%. Notice that 0.3% mistake is like a 2% roi mistake in single hand!
Now again - why this results are wrong. Have a look at screenshot of sng wiz screen. Everywhere when 2 players clash there are just 2 outcomes, either one player wins or the other. As I say above, this is wrong and ties do happen. They happen often when you hold AX hand against any kind of reasonable range. Ignoring them produces big errors.
Also notice how 3 way allin spot is analyzed. There are just 4 outcomes there. While in reality there are 13 possible outcomes. Some of them include - all players tie, two players tie and one loses to them, one player wins and two other tie between each other, or there are 6 different ways for 3 players to finish a tournament (namely 123,132,213,231,312,321). ICMIZER precisely calculates probability for each spot and hero ICM EV in each of them, thats why 3 way all-in calculations produce correct results, unlike simplified approach of wizard.
Hero pushing from the button on bubble of 6 max tournament
http://www.icmpoker.com/icmizer/#vRLF
Another typical spot here. As usual tie effect doesn't have such a big impact on results of big pairs but calculations are wrong in wizard. But lets see at push errors for some unpaired hands. AKs - 0.14%, AQs - 0.16%, AJs- 0.17%, ATs - 0.18%, A9s - 0.2%. Roughly the same error occurs in unsuited aces. I wouldn't repeat about the price of such errors. Basically Wiz calculations are just wrong and basing advice on them sounds like losing money each hand.
Hero facing a push from small blind on bubble of 9 max tournament
http://www.icmpoker.com/icmizer/#JsNt
This spot shows that even when there is a minimum number of variables in calculation, mistake can still be huge in Wizard. We are pushed from the small blind on the bubble. So we just need to analyze 3 outcomes (win, lose, tie) when we call, and our EV for fold is the same in ICMIZER and wiz. AA produces only 0.05% error. But look at unpaired hands - AKs - 0.19%, AQs - 0.19%, ATs - 0.26%, AKo - 0.20%, KQs - 0.22%, KJs - 0.25%, QTs - 0.29%. This is a very simple spot, so if you have any doubts you can analyze it on your own using basic ICM calculator and PokerStove for example.
This proves that ties are super important iven in simplistic cases like push from SB to BB.
Hero facing a push from super short stack on bubble of 6 max tournament
http://www.icmpoker.com/icmizer/#rJuw
This spot is inspired by a thread on 2+2. In original hand button shortstack pushed and hero had doubts with 99. If we just flat this we are a afraid that BB will push all-in and we might have to hold our strong hand. So in this calculation we assume that we flat push, then BB pushes 30%, and then we call. As a result we end up in a three way all-in situation and we can see the difference correct implementation makes versus incorrect.
So lets see AA - 0.07%, AKs - 0.13%, AQs - 0.15%, A9s - 0.23%. Notice that in this case wizard undervalues our hand, so real equity is greater than it predicts. But lets look at KQs - +0.11%EV wizard, and - 0.17% in ICMIZER. Mistake is 0.28%, and for the same spot wizard overvalues some hands, and undervalues another. KJs - 0.26%, QJs - 0.51%!, QTs - 0.52%! So far greatest mistakes, 0.52% mistake is a mistake equal to roughly 3% ROI in one hand.
Again the reason is simplified approach to 3 way confrontations. There are a thirteen possible outcomes and Wizard only sees three in this spot.
Hero facing a steal from big stack on bubble of 6 max tournament
http://www.icmpoker.com/icmizer/#uPHz
In last situation Hero is facing a raise from big stack on the button. If he/she shoves BB could call him, and big stack could overcall if he/she decides. If he/she folds, BB could push and big stack will call him. So calculation is rather difficult, lets look at error size.
AA - 0.1%, AKs - 0.27%, AQs - 0.29%, AJs - 0.30%, ATs -0.31%. Really HUGE mistake for all Ax hands, and it grows larger as kicker becomes worse. 0.30% by 6 is roughly 1.8% ROI mistake in a single hand! Also notice that usually AX hands are the hands of interest, we arent playing a lot of 74o or 93o hands, but for them mistake is present also of-course. Its just not so great or important, because we arent going to play them anyway.
KX hands are quite close in results for this spot, KQs only produces 0.08% mistake.
Conclustion
In this article we looked at very different spots. Push, Call, Resteal, Three way all-in spots - all produce big errors, and each of them ICMIZER handles correctly producing superior results compared to SngWizard.
I believe all serious players are interested in most precise calculation results, and ICMIZER provides them now!