Check or Bet? Call or Raise?

(continued from previous post)

I want to zero in on one fine point in the Check-or-Bet and Call-or-Raise questions. This is still addressing straight play, i.e. statistically straightforward play with no deviousness.

Even if you have odds to bet first or raise, you may not want to push extra money into the pot. This is if your extra bet does not “pay for itself” statistically.


1. Should I Bet First / Raise ?

Let’s say, for example, that you are on a nut flush draw against 2 opponents, and the pot is large, e.g. the bet is $4 and the pot is already $40. You do not have a made hand yet, but your RHO are 25% due to the flush draw, and the IPO are somewhere around 10%. Well, by that comparison, you certainly have odds to bet first or raise according to the F() function in the last segment. But you usually don’t want to do so in this case because you haven’t made your hand yet. Certainly you’ll call anything, but you don’t want to voluntarily put money in the pot until you have a made hand. This is because IPO is missing something. IPO (when compared to RHO) defines acceptable risk for the reward of the pot. But it doesn’t address the risk/reward of taking an extra risk to win a possible increment to the pot.

We’re talking about straight play here, so there’s no consideration yet of a semi-bluff to get an opponent out. When considering an extra bet (i.e. a first bet or a raise), the size of the pot doesn’t matter, because it is not at risk. Your required odds to call a bet in the above example are roughly 10%, due to the size of the pot.

On the other hand, against 2 opponents you can only win back twice your extra bet, but you will only do so 1 in 4 times. Your required odds to bet first or raise are roughly 33%. Since your RHO are way above 10%, but below 33%, you should call anything but not bet first or raise.

This may seem trivial and you may think you can deal with it by a simple check for a draw hand in the program. But the difficulty arises in complex hands when where in addition to the powerful draw you may have a small pair or some other draw. The bot can’t just eyeball it. Furthermore, in a multiway hand, raising the draw hand often is correct. So we need a way to deal with this effect statistically.


To summarize, defining:

• RO (raise odds) as the implied odds for the incremental bet-first-or-raise, ignoring the current pot, and
• IPOr as the regular implied pot odds but with you raising instead of calling,

when F(rho, ipo) is TRUE but F(rho, RO) is FALSE, straight play for the bot is to check/call, even if F(rho, IPOr) is TRUE.

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Ervin Peretz is a software engineer at a major web search company.
He is author of HoldemKiller, a free online poker bot.