Soloman's Formula (from HOH Volume 2)

[ChipLeader]

On page 201 of Harrington on Hold 'Em, Volume 2, a reference is made to Soloman's formula to figure out where you are at in a hand.

You multiply outs by 4, then subtract the excess of the outs above 8 to get an approximate win %.

I dont get the formula, neither in concept or practice. Since i dont really need to understand WHY it works, so long as it can be verified, i just need to know what the second part means.

In the example we have 15 outs, so:
(4 x 15) - (15 - 8), it is the (15-8) portion i dont understand. Is it always -8? If we have 9 outs would it be:
(4 x 9) - (9 - 8)?

[Jordan Olsommer]

[ QUOTE ]
On page 201 of Harrington on Hold 'Em, Volume 2, a reference is made to Soloman's formula to figure out where you are at in a hand.

You multiply outs by 4, then subtract the excess of the outs above 8 to get an approximate win %.

I dont get the formula, neither in concept or practice. Since i dont really need to understand WHY it works, so long as it can be verified, i just need to know what the second part means.

In the example we have 15 outs, so:
(4 x 15) - (15 - 8), it is the (15-8) portion i dont understand. Is it always -8? If we have 9 outs would it be:
(4 x 9) - (9 - 8)?

[/ QUOTE ]

Yes. This gives you 35%, which is close to the actual win percentage with 9 outs, 35.4%

The advantage of the Solomon formula over the Rule of Four (where you simply multiply your outs by 4 with two cards to come) is that for hands with many outs, it's much more accurate. For the 13 situations between 8 outs and 20, the rule of four is more accurate than Solomon's rule for 5 situations, Solomon's is more accurate than the rule of four for 6 situations, and they're equally as accurate in the remaining two. While the rule of four can be way off in situations with many outs (with 20 outs, it's off by 12.5%), Solomon's rule can be way off with very few outs (with 1 out, Solomon's rule is off by 7%).

Overall, the rule of four is more accurate than Solomon's for 11 out of the 20 scenarios of 1-20 outs, Solomon's more accurate than the rule of four 7 out of those 20, and they are equally as accurate for 2. In general though it seems that if you have fewer than 10-13 outs, use the simpler rule of four. Above that, use Solomon's rule which will be more accurate.

[Easy E]

[ QUOTE ]
then subtract the excess of the outs above 8 to get

it is the (15-8) portion i dont understand.
Is it always -8?

[/ QUOTE ]

Please tell me you are kidding... or that you're just learning English as a second language

[binions]

[ QUOTE ]
[ QUOTE ]
On page 201 of Harrington on Hold 'Em, Volume 2, a reference is made to Soloman's formula to figure out where you are at in a hand.

You multiply outs by 4, then subtract the excess of the outs above 8 to get an approximate win %.

I dont get the formula, neither in concept or practice. Since i dont really need to understand WHY it works, so long as it can be verified, i just need to know what the second part means.

In the example we have 15 outs, so:
(4 x 15) - (15 - 8), it is the (15-8) portion i dont understand. Is it always -8? If we have 9 outs would it be:
(4 x 9) - (9 - 8)?

[/ QUOTE ]

Yes. This gives you 35%, which is close to the actual win percentage with 9 outs, 35.4%

The advantage of the Solomon formula over the Rule of Four (where you simply multiply your outs by 4 with two cards to come) is that for hands with many outs, it's much more accurate. For the 13 situations between 8 outs and 20, the rule of four is more accurate than Solomon's rule for 5 situations, Solomon's is more accurate than the rule of four for 6 situations, and they're equally as accurate in the remaining two. While the rule of four can be way off in situations with many outs (with 20 outs, it's off by 12.5%), Solomon's rule can be way off with very few outs (with 1 out, Solomon's rule is off by 7%).

Overall, the rule of four is more accurate than Solomon's for 11 out of the 20 scenarios of 1-20 outs, Solomon's more accurate than the rule of four 7 out of those 20, and they are equally as accurate for 2. In general though it seems that if you have fewer than 10-13 outs, use the simpler rule of four. Above that, use Solomon's rule which will be more accurate.

[/ QUOTE ]

First, if you truly have 9 outs, or have a made hand and put your foe on 9 outs against yours, it's a 36.36% chance with 2 cards to come, not 35.4%.

The difference is using 45 unseen cards v. 47. The reason you use 45 should be obvious.

Second, it's easier to use the rule of 4 until 11 outs, then the rule of 3 until 19 outs. So, 12 outs would be 47%, 13 outs 50%, 14 outs 53% until you hit 68% for 19 outs. Using this method, you will never be more than 1.2% wrong (5 outs at 21.2%) .

For draws over 19 outs, it really doesn't matter since you are 70% to win with 2 to come and should be pushing all in.

Another way to think about it, with 2 to come, 13 outs is even money, 8 outs is closest to 2:1, and 6 outs is 3:1.

[Jordan Olsommer]

[ QUOTE ]

First, if you truly have 9 outs, or have a made hand and put your foe on 9 outs against yours, it's a 36.36% chance with 2 cards to come, not 35.4%.

[/ QUOTE ]

I reached for the closest "outs chart" I could find, which happened to be the one in the liner notes of phil gordon's dvd. I don't know why he has it as 35.4%*, but it's not 36.36% either - it's 35%.

[ QUOTE ]
The difference is using 45 unseen cards v. 47. The reason you use 45 should be obvious.

[/ QUOTE ]

Not unless you have very amiable opponents who have the habit of showing you their hands before you decide on what to do.

*edit: it seems that he calculated it like so: (odds of hitting on 4th st) + (odds of hitting on 5th st) - (odds of hitting both 4th and 5th). Doing this for 9 outs gives you 35.38%.

[binions]

[ QUOTE ]
[ QUOTE ]
The difference is using 45 unseen cards v. 47. The reason you use 45 should be obvious.

[/ QUOTE ]

Not unless you have very amiable opponents who have the habit of showing you their hands before you decide on what to do.


[/ QUOTE ]

Before we go any further, take a minute and read the addenda of Barry's book. I happen to agree with him. If you don't, then we'll just agree to disagree.

[Jordan Olsommer]

[ QUOTE ]

Before we go any further, take a minute and read the addenda of Barry's book. I happen to agree with him. If you don't, then we'll just agree to disagree.

[/ QUOTE ]

p. 286:
"In a heads-up pot, if you know your hand, your opponent's hand, and the flop, how many possible combinations are there for the turn and river?" (emphasis mine)

I agree with him also, which is why 36.36% is incorrect in this case, since we don't know our opponent's hand.

[binions]

[ QUOTE ]
[ QUOTE ]

Before we go any further, take a minute and read the addenda of Barry's book. I happen to agree with him. If you don't, then we'll just agree to disagree.

[/ QUOTE ]

p. 286:
"In a heads-up pot, if you know your hand, your opponent's hand, and the flop, how many possible combinations are there for the turn and river?" (emphasis mine)

I agree with him also, which is why 36.36% is incorrect in this case, since we don't know our opponent's hand.

[/ QUOTE ]

Now read a couple pages later why Barry says using 47 unseen cards shows a fundamental misunderstanding of poker. He has nearly an entire page on why using 45 outs is correct even if you don't know the precise 2 cards your foe has.

[Jordan Olsommer]

[ QUOTE ]


Now read a couple pages later why Barry says using 47 unseen cards shows a fundamental misundering of poker. He has nearly an entire page on why using 45 outs is correct even if you don't know the precise 2 cards your foe has.

[/ QUOTE ]

You mean the one where he says "Once your opponent looks at his hole cards and takes action, those cards are no longer unknown"? Heh, I guess we'll have to agree to disagree then, because to me that sounds pretty silly. I guess I'm just not the caliber of player who can know what two hole cards a person has immediately after they look at them and take action. (yes, I am aware of the fact that once he enters the pot, his hand is no longer random; the players who folded preflop, by virtue of their folding, have also told me that their hands weren't random [for example, I know pretty much for certain none of them held AA or KK] - that doesn't mean I know what they did have or how it affects my hand's chances).

Also, it seems that Sklansky, Malmuth, Ed Miller, and Mike Caro* (authors of HEFAP, GSIH, "Hold 'em Poker", SSHE, and the relevant section of "Super/System", all of which contain reference tables or calculations based on 47 unseen cards for odds on the flop ["Hold 'em Poker" contains a column for 45 unseen cards as well, but Sklansky states this is listed for "head-up no limit insurance situations"]) all have a "philosophical misunderstanding of poker and how to use mathematics to analyze it." Who knew?

*edit: Let's not forget King Yao and Dan Harrington. Upon closer inspection, they also have a "philosophical misunderstanding of poker" according to AoTR.

[binions]

[ QUOTE ]
[ QUOTE ]


Now read a couple pages later why Barry says using 47 unseen cards shows a fundamental misundering of poker. He has nearly an entire page on why using 45 outs is correct even if you don't know the precise 2 cards your foe has.

[/ QUOTE ]

You mean the one where he says "Once your opponent looks at his hole cards and takes action, those cards are no longer unknown"? Heh, I guess we'll have to agree to disagree then, because to me that sounds pretty silly. I guess I'm just not the caliber of player who can know what two hole cards a person has immediately after they look at them and take action. (yes, I am aware of the fact that once he enters the pot, his hand is no longer random; the players who folded preflop, by virtue of their folding, have also told me that their hands weren't random [for example, I know pretty much for certain none of them held AA or KK] - that doesn't mean I know what they did have or how it affects my hand's chances).

Also, it seems that Sklansky, Malmuth, Ed Miller, and Mike Caro (authors of HEFAP, GSIH, "Hold 'em Poker", SSHE, and the relevant section of "Super/System", all of which contain reference tables or calculations based on 47 unseen cards for odds on the flop ["Hold 'em Poker" contains a column for 45 unseen cards as well, but Sklansky states this is listed for "head-up no limit insurance situations"]) all have a "philosophical misunderstanding of poker and how to use mathematics to analyze it." Who knew?

[/ QUOTE ]

By and large, the difference is negligible. If it matters at all, using 45 v 47 with 2 to come certainly matters more to someone like Barry than it does someone who specializes in limit holdem for obvious reasons.

Bottom line, Barry believes using 45 is closer to true. I agree.

And if you look at the 45 chart in Barry's book, you will see using the Rule of 4 through 11 outs, then Rule of 3 after that, is about as close as it gets. Again, the biggest discrepancy through 19 outs is 1.2% (5 outs 21.2%).