I know this.

It is being used on the bet where we DO have an advantage, and NOT relative to bets where we DON'T have an advantage.

The single BIGGEST losses in this game come from losing the 4X bet - which we will lose 42% of the time.

The question is: Is recouping THESE losses using a money management strat enough to overcome the house vig?

The concept is about maximizing our +EV bet (the 4x) - our relative advantage over the dealer is 38% playing the above strat.

Increasing based on THIS (and only this) high advantage play, to compensate for losses in the rest of the 0.5% disadvantage aspects of the game is the idea.

ALSO: since the 4X bet is a bet in a vacuum - it always wins when it beats the dealer, and always loses when the dealer beat us, and therefore has NO effect on the blinds and antes, and the blinds/antes have no effect on the 4X bet - then it is best long term to *always* make the 4X bet when there is any +EV against a random hand.

And that is the wider listing of hands I noted, not the smaller list shown at the other srtat sites.

As jmark said: If you want to maximize your gains when you have an edge, bet Kelly.

Kelly is out of context, at least until I can determine what, if any, edge can be exploited as per the strat mentioned above. Kelly only defines a generalized bet size vs edge.

We are limited in bet size to 4x relative to the ante, so Kelly is not directly instructive. Kelly does not help us in determining an ante, as we have no edge On the ante.

We only have an edge on the PLAY bet, and the PLAY bet is fixed to the ante bet, so the ony way to increase it is to alter the ante.

Kelly does not help.

The problem with your theory is that each hand is an independent event.

I realize that. But this is not an even money pure random situation - we are allowed to make a optional bet based on our assessment of EV.

Yes, every hand is an independent event. But we do not raise 4X every hand - only 49% of hands.

And when we do raise 4X, our combined EV for those 49% of hands is 58%. We only lose 42% of the time.

The concept gives us a way to increase our 4X bet.



An alternate concept is to increase the ante until we have a winning 4X bet.

It should be obvious that the point here is to manipulate ante size to allow for the most advantageous 4X bet, leveraging the 4X bet (where we have a decided advantage) to overcome the previously lost ante/blinds (where we do not have an advantage).



if you want to actually analyze what I wrote, and prove me wrong, let's discuss - but I am not going to respond to anymore of these glib "just use kelly" or "you can't do that" comments.

If upping your bet would make a more advantageous 4x bet, and every hand is an independent event, why arbitrarily up it after a loss and not on every hand?

Because of ROR and also max bet size limitations.

Typically the ante can only be 5 to 50.

And again, simply increasing the ANTE will not produce an advantage as even with optimal play, the ante/blind give the house a 2% advantage. This 2% advantage though on occurs in hand that we do NOT place the 4X bet - i.e. 51% of hands.

By scaling to allow us to increase our 4X bet, the winning 4X bets more than cover the losing antes. But we need to scale our optional advantage bet UP to compensate for the ante/blind losses.


ALSO as noted in the post immediately above yours, an alternate method is to increment the ante every hand until you have a 4X win, then drop back to baseline.

The problem here is a limit of 10 increments (if you are having to bet in $5 increments and have a limit of 5 to 50, then there is a limit to the number of times you increment until you have a 4X win.

The house OBV makes money when you lose. So when you win or push, there is no money you need to recoup. Since there is no money to recoup, there is no need to increase the ante.

CONSIDER:


Start at baseline, 5+5. Continue at baseline until you lose in any situation, and increment to 10+10. Continue at 10+10 until you win a 4X bet and then drop to baseline. If you lose at 10+10 (including a fold on the river), then increment to 15+15 and continue until you win a 4X bet then drop to baseline, or in the event of a lost increment to 20+20.

This herein allows 10 losses (of any bet, including a fold on the river) on your way to winning a 4X bet, and any 4X bet win brings you back to baseline.

The worst case scenario is losing 10 4X bets in a row. Is this possible? Yes of course. Even a skilled BJ counter has a certain risk of ruin.

Let's say that you had ten hands in a row that were ALL the top 49% of hands, and you 4X bet them all, and they all lost.

The first half is like a coin toss coming up heads ten times in a row. This is about the same as flopping a pair and making runner runner quads.

But the second half is not, as it is our 58% EV - our 1.38 to 1 - going bad ten times in a row. This is substantially less likely.

And yes that can happen. 12 million to one jackpots are hit all the time. The question is, does this fit a model for risk of ruin that we can accept, AND

So yes, while every hand is an independent event, every hand ALSO allows for an optional bet that improves our EV *WHEN WE TAKE THAT BET*

I think the "sweet spot" is somewhere in between the two.

But the math is a bit harder than I thought, so I think I need to build a full simulation to test/optimize.

If you can't calculate your edge, then how do you know you have one?

Sigh.

I don't know if there is an edge, and I never said I did. I said I *think* there may be an edge. I then opened up the topic for discussion, explaining the concepts.

IMO I need to build a sim to see if this concept is exploitable. At present I am estimating a 1.1% edge, but this may be a phantom.

The *concept* is manipulating the ante to allow an increase in the 4X bets (where we have a decided advantage) to cover previous losses in the 4X bets.

Kelly is not instructive here until we determine the strategy. After the strategy and edge (if there is one) is determined, the Kelly will be instructive in terms of bankroll size.

HOWEVER, you can't just say that Kelly indicates betting a certain amount, as that does not apply HERE, since we are looking for a way the LEVERAGE the 4X bet size.

If the PLAY bet were NOT limited to 4X - i.e. we could bet whatever we wanted - then we would have a substantial edge, and KELLY would indeed be instructive in terms of the proper bet size for the PLAY bet.

That is not the case, though.

In order to leverage/manipulate the 4X bet, the ante size must be adjusted and the house has a decided advantage regarding the ante/blind. Thus it may be impossible to make the needed variations to accommodate.



Regardless, at this point it seems the concept is not attracting much interest here. I nevertheless am interested to see what the final simulation will provide. Among the things I see needing optimization would the be *amount* to increase antes, the "key" that causes an increase or decrease, and the probability that such a set a actions will "fit" within the betting limits at a casino.

Okay, while it seems intuitive that if a hand like 22 is +EV against the dealer and should always be bet max preflop - there are other factors.

The reason that WoO and other do not have it in the preflop strat is that there is a GREATER advantage to waiting until the second or third decision point to bet, or fold to minimize losses.

Thus the preflop strat:

33+
All Aces
All suited Kings
K5o+
Q6s+
Q8o+
J8s+
JTo+

Are all hands that are 60% favorites against a *random* hand. And these are 37.7% of hands.

Interestingly, the wider range I was originally considering (49%) gives a 58% advantage against a random hand.


SO: We are 1.65 to 1 to *be dealt* a hand that we will 4X with, and when we are, we are 1.5 to 1 favorite to win.

The return on the 4X bet is about 26% with most pay schedules, ignoring all hands where we do not do the 4X raise.

Return on the 2X raise is 17%.

Return on the river call is - 7.6%
Return on folding is - 38%


These return percentages though do not take into account the specific amount at risk, though - these are all only return percentages relative to the ANTE.

For instance, those times we WIN the 4X bet, the GROSS return is 113% - but when we LOSE the 4X bet the gross return is -87%.

For the 2X bet it's 44% and -27%. The cumulative for 2X/1X/Fold is -29%.

Losing one 4X bet is three times as much as the combined 2X/1X/Fold hands.


We get a 2x/1x/fold hand 62.3% of the time. Cumulatively these 62.3% of hands are losers - but when we lose a 4X bet, it substantially overshadows these smaller losing hands.

Now, with the concepts being discussed above - if a loss of a 4X bet is the key point, that results in incrementing the ante to allow a larger 4X bet - then when we win a 4X bet we decrement as the 4X bet win substantially covers the smaller losses.


Obviously, increasing the ante to allow a larger 4X bet ALSO increases the size of losses from the 2x/1x/folds hands, that will occur from the point of increase to the point of a 4X win.


And more clearly, this is the question of what is the key point for decrementing - and would it necessarily be related to any non- 4X hands along the way?

AND would the fact that these smaller hands are included at the increased level negate any attempt at recouping the previously lost 4X bets.


Or put another way, can se see an advantage by immediately reducing the ante after a 4X bet win, since even as an independent event, the NEXT hand is most likely to be a non-4X hand.

So this discussion is about betting a D'alembert on a hypothetical, possible edge? Heh.

Um no, the 2% edge on the ante bet is a result of averaging all the possible hands. So when you aren't raising 4X ante, you have a bad hand and the house has a huge edge on the hand. And the problem with your method is, you lose more money on the ante/blind when you increase your bet. And you can't control when you receive a hand worthy of a 4X raise.

This game is a winner for the house thanks to the ante/blind bet. The blind bet only returns 68.5% back longterm while the ante only returns 83.5% back longterm. You spend one bet each on these, so you need to gain 0.5 antes based on your play bet just to break even. The wizard and discount gambling have proven this is not possible given a random game.

No.

At last a salient comment that actually brings up the most relevant points - I am just coming to this conclusion for the most part.

BUT

Consider if we reduce the ante size immediately following a 4X bet win, as the probability that the next hand is always 62.3% that it will not be a 4X hand.

Of course there is a point where we can no longer lower the ante - as well as there is a point where we can no longer increase the ante.

Naturally in a pure random game the next hand after a 4X win could easily be yet another 4X hand, we make less if we lower the ante, and when we have increased the ante, a long string of 2x/1x/fold hands certainly makes a dent in our stack.

Whenever you advocate changing your bet size based on winning or losing a previous hand you have a serious problem.

Right and the fact that it's not a 4X hand 62.3% of the time helps form the basis of the house edge, which is 2.185% of an ante. Your betting strategy does nothing to change that since you must place your wager before your hand is dealt to you. It will behave similar to a Martingale. Generally you'll come away a small/moderate winner, but you have a small chance of being a gigantic loser. The weighted average of all the scenarios still will cost you 2.185% of the total amount of the antes wagered.

Now if somehow we can successfully cheat and be able to increase the ante amount after we saw our hole cards, then that's a different story.

Wherever you are arrogant, you should post according to Troll.

No, lol, I'm not interested in cheating - but I *was* trying to imagine a scenario where we could leverage our 4X bet - the thinking was since the the 4X bet is the biggest loser *when it loses*, that recouping that with an incremental bet would tip the scales in our favor slightly.

Though in retrospect, it should be obvious that once incremented, we still have to contend with the other instances of 2x/1x/fold.

Max bet limits is the limiting factor in "ruin" - but also prevents incrementing in the event of losing six 4X bets in a row (using an incrementation of 1,2,3,5,7,10).

While it might seem that increment/decrement based on the portion of the wager that we have an advantage with would provide a good money management scheme, we need the large 4X bets to win at the incremented level to overcome those 2x1xfold bets at that same level.

And we're right back to the same old, same old, only with the D'alembert instead of the Martingale. As I said, full points for creativity, but this is the same thread we've had a million times before.

Yea, somehow I was thinking that basing it around the 4X bet would make a difference - it certainly *seems* to in play simulations.

FWIW, the money management system works like this:

(based on a 5 to 50 ante limit):

A 4X loss increments:

5 10 15 25 35 50


A 2X win decrements any ante over 20 by 5 (i.e. 35 becomes 30).

A 4X win decrements 50 to 35. 25 thru 45 are decremented by 10, and 20 thru 20 are decremented by 5.

A 4X loss will re- increment middle points, such as 20 to 30, 30 to 40.

The result here is that future wins not only cover previous losses, but also add profit.



The two problems as noted above are:

1) The house max limit prevents increasing beyond 50 (or 10x the minimum ante), which prevents larger increases to cover losses at the highest levels.

2) You could increment to the 10 level, and then have a long series of weak hands before a single 4X win.


The advantage of this money management system is that when the game is running such that the antes are staying under 35 of so, the chips rack up damn quick.

But when you jump up and hit the 50 mark, things get "sticky".

For the pure money management and extending your "play time" in this game, which is certainly fun, a money management technique might be to drop back to the start once you have a 4X loss at the highest level.


While it is undoubtedly true that even with this money management system, you can't get a "real" edge - there are a couple of benefits - one is that your ante bets tend to be larger on average and so you should likely be better rated for comps.

As long as the pit boss doesn't "set and forget" your bet size maybe. To get better comps, it's probably best that you come out swinging. They will take an initial read of your bet size, and if they are too busy, they may not adjust that number as frequently as they should. The last thing you would want is the pit boss to set your average bet to the minimum with this system.

Also another problem with this system is...this game swingy as hell to begin with. For example, playing $5/ante has a higher SD than live $1/$2NL with an SD of $247/100 hands. If you are plopping down $200 on a 4X bet, then you really should move to blackjack or poker, imo.

Well I was thinking I'd actually *start at the 10 or 15 level - drop down on 4X wins, etc.

I guess I'll rely on "gambler's feel" to get that edge, LOLOLOL