How to play a straight or flush when the board pairs

Question

I am writing a poker game where you play against 5 bots and I just can't get my head around playing straights and flushes. They are solid hands but you can get stacked by a boat or higher.

If opponent bets the pot when the board pairs do you release? I feel like that would make the bot exploitable. About all I can think is call a large bet (more than the pot) like 1/3 the time and keep track of how often opponents bluff and adjust from there. Right now bots are slow playing a flush or straight on flop or turn 2/3 of the time as long as the board is not paired.

Without writing the software part what would you do in position with a nut flush, the board pairs on the river, and opponent bets the pot? Goes all in for 5 pots?

Answer 1

How often should a bot call a human in this situation given different bet sizes is what I now understand the question to be, and with no previous information or statistics to go on. The goal then is to stay the least exploitable as possible while calling enough to start gathering stats to use in further hands.

Here's one possibility that I thought of that admittedly might not be the most optimal but I think it's decent and I'll give some reasoning for it: start out by calling 100% of the time for any bet up to a pot-sized bet and then for bets that are bigger than the pot, call at a rate of 1/(bet size/pot size). For example, in a pot of 100 if the bet is 200, call 1/(200/100) or 1/2 the time; for a bet of 500, call 1/5 of the time.

For a pot size bet, the assumption is that the human player is bluffing (or betting for value with a worse hand) 33% of the time and betting with a stronger hand 67% of the time. With nothing else to go on, this can't be too far off and the smaller the bet is the better the pot odds are for the bot to call.

For over-sized bets, take the example of a bet of 200 into a 100 pot. When the human player is bluffing, the bot calls 50% of the time (loss of 200 for the human) and the bot folds 50% of the time (gain of 100 for the human) which comes out to an EV of -50 to be bluffing. When the human player is betting for value with a stronger hand, the bot will call 50% of the time (gain of 300 total for the human) and the bot will fold 50% of the time (gain of 100 already in the pot for human) which leads to an EV of +200 for the value-bettor. But if the person had instead bet exactly the pot of 100, the bot would have called 100% of the time and there would be an EV of +200, so the person gained nothing by betting more.

Similarly, if the bet is 500 into a 100 pot, a bluff has a return of (1/5)(-500) + (4/5)(100) = -20, and a value bet has a return of (1/5)(600) + (4/5)(100) = 200, which again has no benefit over betting just the pot size.

So if a person knew this, they could increase their (negative)EV when bluffing by betting more, but there would be no EV change by betting more with value hands. It's a little bit arbitrary of a system but you could try something similar and I think it results in enough calls for the bot to start gathering information and adjusting.

Answer 2

Well it all depends on the hand in question, which is why it is very hard to write a really good poker-bot.

Assuming no bluffing is involved, the basics are:

• calculate the range of hands the player could have

• calculate the odds of the player having a hand that beats you vs one you beat inside that range

• compare that to the pot-odds

This would be what you do against a player who is playing at level one of poker, only looking at his hand. The problem lies however in calculating his range, there are reasonable implementations for doing this given a players statistics but you are never really sure as players are not bots themselves and might play strange.

When bluffing comes in the mix it becomes a lot more difficult, you have to consider all semi-bluff options and the frequency with wich he semi-bluffs and add to that the complete bluffs and the semi-bluffs that turn into complete bluffs. This is not easy but given you have those you can add them to his range of hands and do the same as above.

And remember, you need to calculate the odds of a specific hand, not a group of hands, for example there are 6 combinations of AA in a complete deck remember but if you take one A out of the deck (the bot or board has it) only 3 combinations remain.

Another question you might want to ask yourself is how difficult do you want to make beating those bots? What is the purpose of the game exactly?