- The fastest FGS equity calculation algorithm
- What does FGS depth mean and how does it impact calculations and optimal ranges?
- When is it best to use ICM and when FGS?
- Our general FGS depth recommendations for short stacks
The fastest FGS equity calculation algorithm
In this update we’ve completely reworked the FGS algorithms in ICMIZER, which led to substantial increases in both its performance and accuracy.
Despite the lack of appearance changes, this is one of the most significant updates in ICMIZER’s history. Tournament equity calculations based on FGS 1 (which ICMIZER has utilized before update) are now 1,000 times faster. This makes it possible to ‘peek into the future’ a lot further— to look not just one but several hands ahead. The huge benefit of this update is, therefore, that it will allow us to enhance the tangible functionality of the software for you in the coming months. We plan to make calculations and other routine processes perform a lot faster (not limited to FGS), as well as add support for calculating Nash equilibriums in situations with raises, reraises and other bet types for which no support of equilibrium ranges is yet available.
Today, ICMIZER has the fastest FGS algorithm in the world.
So far FGS depths 1 and 2 are available, which let you look 1 and 2 hands ahead, respectively. We’re going to add more FGS depths soon, including 3, 4 and 5.
It’s important to note that each new FGS depth increases the calculation time, and the more players at the table, the more it costs to look ahead an extra hand. For example, for a 6-handed table FGS 2 takes about 0.5 seconds, FGS 3 would take approximately 9 secondss, and FGS 4 would take roughly 3 minutess.
This update also brings knockout tournament calculations using FGS, which many of our users have asked for. FGS 1 and FGS 2 are also available for bounty tournaments.
What does FGS depth mean and how does it impact calculations and optimal ranges?
Previously we’ve described how the FGS model works when it was introduced into ICMIZER (using depth 1).
FGS is a straightforward improvement on the traditional ICM which eliminates one of its main shortcomings: that ICM ignores blind sizes and player positions. For example, if you’re down to two blinds, your position makes no difference to ICM; be it UTG or BTN, your tournament equity will be the same as far ICM is concerned.
Naturally, modeling the future is an expensive process in terms of performance, so FGS calculations take a lot more time than ICM calculations do.
Unlike ICM, FGS does take into account player position and blind sizes when determining tournament equity. For example, if UTG has two blinds in her stack, FGS of depth 1 will see that the big blind will more on the player in the next hand, which will likely have negative repercussions for her stack. Understanding this, FGS will adjust the stack’s equity in this hand. In the same situation ICM would not see that the player is in any danger on her current UTG position.
Perhaps it’s worth explaining that in tournament poker, with each new hand a certain process takes place that has to do with the natural adjustment of all players’ tournament equities based on their position. Put simply, BB loses a lot of equity, SB loses a little equity, while BTN gains equity. (If we go into more detail, usually other positions also gain a little bit of tournament equity that the blinds lose.)
With some combinations of stack sizes and payouts, this pattern of equity fluctuations may vary, but it mainly amounts to the following: BTN goes up, SB goes down, and BB goes down a lot.
As positions rotate, this pattern affects each player and each hand in succession. After the full cycle is over, the equities do even out; but before they do, some positions will enjoy an advantage over others. The well-known ‘buttoning’ practice exploits this pattern in cash games, but in tournament poker it doesn’t apply.
Each additional level of FGS depth makes the model look one extra hand ahead and apply the position-based pattern for that future hand to the player’s calculated equity for this hand.
Consider a 6-handed table and how this pattern will affect the player who’s currently on CO. In the next hand she will be on UTG+1, and then on UTG, on which she will not put up any blinds which are slightly advantageous within the pattern we’re discussing.
On the other hand (no pun intended), consider the player who is currently on UTG+1. FGS 2 will notice that 2 hands from now, the big blind will move on this player, which means that FGS 2 will rate his current tournament equity on CO lower than FGS 1 would.
So, when is it best to use ICM and when FGS?
This is an important question and, luckily or unluckily, one that has no definite answer. Both models calculate equity in their own way and both produce estimates that are off in their own way, too.
We think that the most accurate equity estimate is obtained by using the FGS model which takes into account the full round of hands, i.e. until each player has bet the big blind once. This would correspond to FGS depth that’s one less than the the number of players at the table. But even this statement can be argued with.
In a real game, such FGS depth (players at table minus 1) will not always be available. According to our plans, it will be available for a 3-handed table (FGS 2 and above), 4-handed table (FGS 3) and 5-handed table (FGS 4).
It’s important to understand that FGS calculations at great depths take a lot of time, and the impact of additional depth on ranges may be very minor. If so, faster-performing models like ICM, FGS 1 or FGS 2 are probably more suitable.
However, if future hands have a strong impact, for example if the blinds are high, then we think it’s best to use the greatest FGS depth available. This would help spread the position-based pattern over as many players as possible, thus minimizing the ICM calculation error in the first hand. We will continue to research this and will update you with improved recommendations if any.
(By spreading the pattern I mean that the maximum number of players will have gone through the BB position and will have received a significant equity downgrade, as opposed to just 1 player as per ICM.)
Still, this approach is not fault-proof. For example, if you use FGS 3 for a 6-handed table, the player currently on BTN will have occupied all the early positions but not on BB. Intuitively, it seems that for this particular player ICM would gives a more accurate estimate than ICM 3 would.
Our general FGS depth recommendations for short stacks
3-handed: FGS 2
4-handed: FGS 3 (when it becomes available)
5-handed: FGS 4 (when it becomes available)
6-handed and more: FGS 2 or greater. This recommendation is the most difficult because of the obvious compromise, so approach it on a case-by-case basis. For some situations ICM without FGS may produce the best results.
When will ICMIZER add FGS of depths 3 and more?
We plan to make this happen in November 2016.