Choosing bet sizes is critical to building game trees but also to executing poker strategies. This article focuses on selecting bet sizes for solver game trees but the concepts are applicable to real-world poker as well.
Why must we choose bet sizes?
We must define the action space for poker solvers, as allowing any action quickly blows the complexity of the game to cosmic proportions. Modern hardware can handle anywhere between 1 and many bet sizes per street, and this has become the standard for poker solutions.
How does this affect solution quality?
Most of the EV in a spot can be captured with just one bet size. Having multiple is just a bonus. We are not practically limited by our choice of bet size, as long as we include at least one size that is strategically useful in every spot. For example, in polarized situations we should have at least one large bet size.
How to build a good game tree
To truly know what bet sizes the solver prefers, we need to solve with a variety of sizes and analyze the outputs. However, some general principles can help us build a good starter tree without solving tons of bet sizes.
- Include bets for both players.
- Tune bet sizes per node. For example, river IP typically does not need a small bet size.
- Capped nodes typically only need small sizes.
- Include at least one large overbet size in high SPR spots. Overbets do not bloat the game tree much because child branches of overbets are smaller due to lower SPR.
- Include at least one small size in low SPR spots. Solver prefers betting as small as B10 when SPR is low.
- Include large check-raise sizes OOP and small raise sizes IP. Adjust raise sizes based on SPR.
- Avoid picking sizes that are too close together as they often accomplish the same thing.
- Test your assumptions by adding/removing sizes and comparing EV.
Building good game trees requires a lot of trial and error, but a rigorous approach is often worth it. Otherwise, we risk missing important strategic insights or studying restricted solutions.
The GTO Genesis game tree
To give a concrete example, we present the standard game tree GTO Genesis uses in SRP spots:
| Node type | Options |
|---|---|
| Flop (OOP) | Check, B33, B50, B75, B125 |
| Flop (IP) | Check, B33, B50, B75, B125 |
| Turn (OOP) | Check, B33, B50, B75, B125, B175, B250 |
| Turn (IP) | Check, B33, B50, B75, B125, B175, B250 |
| River (OOP) | Check, B33, B75, B150 |
| River (IP) | Check, B75, B150 |
We offer R50 and R100 for raise sizes and only R100 for re-raises. We also add the all-in size on every node. When OOP is capped (check-called the previous node), we limit their options to check and B33.
Starter game tree
From our experience, some of the sizes are not strictly necessary, especially if you are trying to solve trees on your own hardware. Below is a curated sample tree that serves as a good starting point for a normal SRP solve where we separate by donk, probe, and c-bet to fit as accurate a game tree into as small a footprint as possible.
| Node type | Options |
|---|---|
| Flop donk (OOP) | Check, B33 |
| Flop c-bet (OOP) | Check, B33, B75 |
| Flop c-bet (IP) | Check, B33, B75, B125 |
| Turn donk (OOP) | Check, B33 |
| Turn probe (OOP) | Check, B33, B250 |
| Turn c-bet (OOP) | Check, B33, B75, B125, B250 |
| Turn (IP) | Check, B33, B75, B125, B250 |
| River (OOP) | Check, B33, B75, B150 |
| River (IP) | Check, B75, B150 |
- Raise sizes R50 and R100 IP.
- Raise sizes R100 from OOP.
- Re-raise sizes R100 for both players.
- Add all-in to every node.
- Go all-in if more than 60% of the stack has been bet.
Modify the tree to suit your needs, but this can serve as a detailed starting point if you are running your own solves and just want to get started. Remove bet sizes as you see fit (for example if you are solving a flop that you know never uses B33, you can remove it to reduce solve time).
Applying bet sizes to your poker strategy
Study with bet sizes you are comfortable playing, but also know why certain bet sizes are used in different spots. B200 and B250 are very similar: if you have a solid understanding of what drives small vs. large bets, it won't matter what exact sizing you or your opponents use.