Ax-suited a loser in loose limit games?

[CardSharkGames]

This is a lengthy post of analysis which seems to indicate that playing Ax-suited (where x is less than Ten) is not profitable in loose limit games. For ease of calculations, $1/$2 limit is assumed.

Say that you play Ax-suited 1000 times unraised. You flop a flush draw about 120 times.

The cost of seeing the 880 flops with no draws = $880.

The 120 times you flop a flush draw, you will make a flush by the River about 40 times.

The cost of the 80 times you see the River with no flush = $320 ($1 preflop + $1 flop + $2 turn = $4 * 80 = $320)

Your total cost of missing the flush = 880 + 320 = $1200.

Just to break even, the 40 times you make a flush, you must make $1200, or $30 of other people's money per pot -- on *average*.

It is very hard to get $30 into a pot even once. If 6 people besides you limp preflop, that is $6. If the flop is raised and 4 people stay, that is $8. If all 4 call the Turn, that is $8 more. If 2 call the River, that is $4, for a total of $26. If you can check-raise the River, which you will not always be in position to do, you can get another $4 and win the required $30, but this is close to a maximum, not an average.

A more reasonable, but still somewhat optimistic average would be $20. Six callers preflop, 4 callers on the flop, 3 on the Turn, and 2 on the River totals $20. But $20 times 40 flushes made is only $800 versus a total cost of $1200 for a $400 loss.

Another source of income are hands which miss the flush but make top pair, two pair, trips or better.

Based on poker odds charts:
Of the 880 times you do not flop a flush draw, you flop:
two Aces about 170 times (with bad kicker - often loses)
two pair about 18 times (may win about half the time)
trips about 1.2 times
a boat about .8 times
a made flush 8 times

When you get two Aces, you will have top pair, but that does not hold up very often in a large, multi-way pot, especially with a bad kicker.

Let's say that you win about 50 pots total with just Aces. The pots for just a pair of Aces will usually not be very large, so say $10/pot for a total of $500. The cost of playing Aces to the River 120 times and losing is, at a minimum, $4 * 120 = $480, for only a $20 gain.

Two pair fair better, maybe winning about half the time in a multi-pot. Again, you won't win very big pots because people are not going to be betting and raising a lot with hands weaker than trips. But say you average $15 for the 9 times your two pair hold up, for $135 and lose $4 on the other 9 for a net gain of about $100.

Trips and a boat may get you another $30 on average, though you will sometimes bet and raise trips strongly and get rivered.

The 8 times you flop a flush, you will almost always win, but you won't get much action. If 6 people limp preflop, 2 may call the flop and 1 the turn for a total of $10. Sometimes someone may call the River, other times they will fold the turn. So say 8*10 for $80.

So we have:
20 gain on a pair of aces
100 gain on 2 pair
30 gain on trips & boats
80 gain on a flopped flush
----
$230 total gain on other hands versus a loss of $400 on flushes
for a net loss of $170.

So we're back to the flushes: to win more than $20 of other people's money per pot requires a lot of raising.

Any raises preflop have a negative expectation because you are at best 16:1 to make a flush (and some of those would be runner-runner which you won't see) and are, at most, getting only 6-7 callers for every $1 you put in.

Raises on the Turn also usually have a negative expectation (assuming you are still on a draw) because you are usually up against only 1-3 players with less than 20% chance of hitting on the river. And if there is a pair on board when all this action is taking place, you may already be drawing dead to a boat or you may get boated on the river.

With three (or four) to a flush on the board, you are unlikely to get a lot of action on the river. You may get 1 player to make a crying calll with a worst hand, but that's about it.

Your best shot at making more money is (re)raising on the flop, but you are not always in position to do that. If the bettor is on your right and you raise, you are likely to knock out the other players rather than build a bigger pot.

Say that out of 120 flush draws, you can raise 60 of them and get 4 callers. That gets another $240 into the pots, but you are only going to win about a third (20) of those pots, or $80 to go against the $170 loss we already calculated. And the 40 of those 60 pots you raise and lose add another $40 to your loss.

If my calculations are anywhere close to accurate, it's hard to see how to make money playing Ax-suited.