Join Date: May 2023
Hello all. Long time player, but new to this forum. Hoping someone here can help me with a couple probability questions I have, or point me to the relevant discussion if this has already been asked and answered.
First up - regarding calculating the odds of making one's draw, I tend to use Phil Gordon's "rule of 4 & 2" - count my outs, multiply by four with two cards left to come, or by two with one card left to come, and the result is a close approximation of the odds of making my hand, expressed as a percentage.
Example - OESD with 8 outs on the flop: 8 x 4 = 32%, so I know I'll make my hand somewhere close to 1/3 of the time. Ditto if I have 9 outs (36%). I know I'm 50-50 with 12 outs (48%), and a favorite with 15 (60%).
The numbers aren't always exactly correct, but they're close enough, I think, and after a while I just had them committed to memory, so I don't often do these calculations in real-time anymore.
But what I've never seen discussed within this context is whether or not those calculations should be changed based on the number of players to start the hand. If I'm playing 6-max, 8-handed, or 9-handed, I'd think the calculation might have a slightly different result, because there are more cards out of the deck pre-flop, and less cards left in it post-flop.
So, first question - should I be making adjustments post-flop, assuming that the odds of making my hand are slightly worse when there are more people at the table, because it's less likely all of my outs are still in the deck?
Related to the above, when I'm playing 8-handed, I generally assume that there are four of each suit dealt out pre-flop (2 cards x 8 players = 16, divided by 4 suits = 4 / suit). So, if I've got four to a flush, I don't think about it as having 9 outs left in the deck, I think about it as seven outs, because I assume there were two more of my suit dealt to other players pre-flop.
If I'm playing 9-handed, I just think of it as 4.5 per suit, making my odds slightly worse.
Second question - should I not be making that assumption, and just act as if all unseen cards are all equally likely to still be in the deck? That seems counter-intuitive to me.
Lastly - while the calculation above about the distribution of suits pre-flop in an 8-handed game is pretty simple, what about the pre-flop distribution of each rank of card within a suit?
For instance, if I assume that there are four of each suit dealt out pre-flop, when considering my odds of making a flush, I want to also be accurate in my assumptions about the odds of catching specific ranks of cards when I'm hoping to make a straight or boat up.
If there are four Jacks and four 6's that will make my straight, I don't think of that as having 8 outs, but rather as having something less than 8 outs, because there's some probability that someone was dealt a Jack or 6 pre-flop. I just don't know what that probability is, or how to calculate it.
Does anyone know how that probability, or how to go about figuring it out?
Am I over-thinking this?
Thanks in advance for any help here.