This is a discussion on Why the solomon rule? within the online poker forums, in the Learning Poker section; I have seen this in Harringtons book where he calls it the Solomons rule I think, and PZ state the same rule. Now I was 

Skip to Latest Post made on 23rd July 2012

#1




Why the solomon rule?
I have seen this in Harringtons book where he calls it the Solomons rule I think, and PZ state the same rule. Now I was never any good at maths, and this puzzles me so can some one tell me where my thinking is off please?
If I have 13 outs on the flop I calculate this to being (13:47)x100 = 27.6% to hit my hand. If I multiply this with 2 to see my equity on the river it will be, and instead of 47 ill use 46,5 which is the average amount of cards left after the flop and turn ((13:46.5)x100)x2 = 55.9%. Is this right to just multiply the turn % 27,6 with 2 to get the % or hitting my hand on the river if I dont have to put more money in the pot? If I use the method where I count my out (13) and time it with 2 or 4 I get 26 or 52 which is less than 27,6 and 55,9%. The solomon rule says take the number of outs over 10 and subtract from the number giving me: (13x4)3 = 49. It would make more sence to me if we added 3 rather than subtract it which would give 52+3 = 55 so why is this subtraction of 3 in order to get the right % ? So again, where do I go wrong? I have a feeling that the answer will make my face go red and my mind go "ooooooh of course, I should never have asked" but I'll risk it 
#2




I've not heard of the solomon rule, but the 'rule' of 4 and 2 means you multiply your outs on the flop by 4 (i.e. 13 outs x 4 = 52% equity)
on the turn multiply by 2 (i.e 13 x 2 = 26%). These are 'close approximations, not exact. perhaps the 'solomon rule' is to refine these approximations, I'm not sure but someone on this forum will enlighten us. Cheers. 
#3




The rule of 2 and 4 is a way of approximating the probability that you will improve your hand on the next street (2) or on either the turn or river (4). This is not the same as equity. A key reason is that there are nut and nonnut outs, plus different levels of quality for the latter.
Also, the rule doesn't take the likelihood of further betting into account. For example, if you have a flush draw on the flop, you have 9 outs. But to have them on two streets, you have to see both streets, which can mean calling a bet on the flop, and then, since you'll miss over 80% of the time, calling another bet on the turn where you'll miss around 80% again. Factor in the aforementioned possibility that you'll make your flush and still lose, and you can see that while the rule of 2 and 4 is handy as a guideline, it's only a guideline. 
#4




^^ Prettymuch this. The rule of 4 and 2 is frequently misapplied because people don't consider that they may very likely be facing a bet on both streets. Safer is just to use the rule of 2 twice unless its a situation where you can't face any more bets since one or the other player is AI.
Also, the rule is an approximation, and if you look at the actual formula in books you will see it needs to be modified as OP states. So, he is exactly correct there, but it can be cumbersome to do so so the rule was designed to get you "close enough" odds without a lot of calculations. Now, the actual modification issue that he gets into at the end of his post..... Franky, I have no idea. I used to know the formula and the reasoning behind it. If memory serves I think Harrington spells it out in one of his books. Anyway, the reason that I don't remember is that it really isn't that important. Look at OP's calculations, he's debating the difference between 26 and 27.6% and 52 and 55.9%. I know this will make the "math guys" cringe, but it just isn't that important to get that last 12% accuracy given the amount of time it takes you to get there, especially online where you are likely playing multiple tables and have limited time to make your responses. 
#7




Cheers Arjonius, that makes some cense. So the more outs you calculate for your self the more chance there is that some of those outs will help your opponent and to err on the side of caution you subtract a few % points.
Its not a debate between 55 and 52 but 55 and 49 and if you have more outs the difference becomes much bigger. Maybe academic in most cases but I was puzzeled and curious:) 
#8




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To reconcile this you do the subtraction that you were talking about. Either way, I'm generally not that concerned about it. In NL, bigbet poker a few % points here or there to hit your outs really isn't going to make that much difference. I mean it's all just guess work and approximation anyway. 
#9




I see your point Big.
The thing is that mathematically it seems to me that it would make more sense to add a few numbers rather than subtracting, but hey ho. As you say it is mostly guesswork anyway and point taken. I guess Im just one of these guys with autistic tendensies that needs to know 
#10




re: Poker & Why the solomon rule?
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So while it may be mildly interesting to know the "why", imo, I still think it's not all that important. Especially when multitabling, you just need a quick approximation to get you close quickly so that you can make your choice and move on to the next table awaiting action. We do have a few "math guys" on here, though, and frankly I thought they be all over this. Guess not. So, as a nonmath person, I'm content with the approximation. I always hate to send people elsewhere, but I guess if you really need to know; try Googling it, or head over to 2p2 and try your luck there. 
#11




The actual odds for 13 outs over 2 streets is 48.1% — so the Solomon Rule gets you closer to the truth than the basic 4 rule
Your calculation of 55.9% is sadly incorrect and this is why you are having a problem matching it to Solomon. It is a mistake to simply double the 1 street calculation. It is also a mistake to average the number of cards left over 2 streets (4713)/47*(4613)/46 will give you the odds of not hitting — 51.9% therefore the odds of hitting are 48.1% Hope this helps 
#13




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#14




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However —13/46 is 0.2826 so 28.3% (approx) , I think you must have used 47 anyway 
#15




re: Poker & Why the solomon rule?
BTW we do get quite a lot of threads here about the 2 and 4 rule including this one http://www.cardschat.com/f57/probabi...estion202912/, where from post 8 we discuss the merits of deducting 'outs over 8' or 'outs over 9'.
The op in this thread, ukn742, compares both in a spreadsheet and determines that deducting all 'outs over 9' is much more accurate than 'outs over 8' and I'm pretty sure that you'll find it's better than the 'all outs over 10' that you used in the first post. I've seen Solomon's quoted as 8, 9 and 10, I have no idea which one is truly Solomons but I think 9 is the most accurate. 