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Originally Posted by DonkeyStars
Right well I've just discovered an even BIGGER rig.
I applied those filters and unchecked the 'one pair on flop' filter, so it just gives me all the TPTK hands.
In 160k hands of data (filtered out rigged 2nl zoom and some playmoney games I played when I was a beginner and didn't know the rules), I've only made TPTK 709 times.
709 times out of ONE HUNDRED AND SIXTY THOUSAND HANDS.
In order to make top pair top kicker you first must have an ace in your hand. The odds of being dealt an ace is 4 out of 52, or 7.6%.
I don't know if TPTK precludes AA - I would have to say it does - so that means you have AK-A3. (we can exclude 2 because 2 cannot be Top Pair, ever. It can be bottom trips, or even bottom quads, or bottom boat, but not top pair). We shoudl probably exclude 3 as well because the only way A3 can make TPTK is on a 322 board. So lets go with A4 thru AK. So that's 10 cards out of 13 that can give you a flopped TPTK possible hand, and there's 4 of them out there.
That means 40/52 times you get an A you'll get a TPTK potential. 7.6% * (40/52) = 5.9%. So, 5.9% of the time you'll get a hand with TPTK potential.
On the flop you need EITHER to be holding the KING and to hit an Ace (of which 3 are left) OR you need to hit the other card (of which 3 are left).
AK hitting the A is a bit tricky to work out so lets focus on just the other card - whatever you're holding - K-4 - your odds of hitting TPTK with Ax are, AT BEST, 3/50, or 6%. The lower your kicker, the weaker your odds, because with AQ not only do you have to hit a Q but the K cannot come out, and with A4 you can only have TPTK on a 432, 433, or 422 board.
but lets use 6%. Your inflated 6% of hitting the flop with TPTK times your 6% chance of having the TPTK potential = 0.36%.
160,000 * .036 = 576.
We can therefore conclude that if it's rigged, its rigged in your favor.
Except that we can't conclude that at all because the variation between your 709 and the 576 it should be is about eight-hundredths of a percent. (0.0008 , or 0.08%)
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You hit a pair on the flop about a third of the time.
Wrong. The odds of flopping a pair are 6/50, or 12% - about a sixth of a time.
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Half of that time it will be the top pair.
Wrong. It has at best a 1/3 chance of being top pair, and you can't look at that in a vacuum.