Tiny theoretical advantage play in baccarat

The BetVoyager casino has a baccarat game where the Player bet pays 1.0282. Six decks are used. The player advantage on the Player bet is 0.00023334. The catch is that the player must pay a 10% commission on any net gambling win per session. There is also a maximum gambling session time of 24 hours, but let's ignore that for the sake or argument. Let's also ignore the practical limitations of making multiple withdrawals of just one unit from an Internet casino. In other words, this is more of a math problem than a practical advantage play.

Maybe somebody can come up with a better strategy, but here is mine: Keep betting the Player until you're up one unit and then cash out. According to my math, it will take on average 1/0.00023334 = 3857.014567 bets to be up one unit. You then withdrawal your 0.9 units and start again. The overall advantage is 0.9/3857.014567 = 0.000210007.

Yes, I know 0.02% is not a practical advantage. The question at hand is can you come up with a better strategy?

What is the smallest unit one can bet? Do they round up fractional units or cents when cashing out?

Quote: DRich

What is the smallest unit one can bet? Do they round up fractional units or cents when cashing out?

I think 10 cents and they round to the nearest penny.

However, for the sake of argument, let's assume there is no minimum bet, unlimited bankroll, and they keep track of the balance as a decimal with unlimited precision.

And whoever voted for colitas, I'm waiting for the answer.

Quote: Wizard

The BetVoyager casino has a baccarat game where the Player bet pays 1.0282. Six decks are used. The player advantage on the Player bet is 0.00023334. The catch is that the player must pay a 10% commission on any net gambling win per session. There is also a maximum gambling session time of 24 hours, but let's ignore that for the sake or argument. Let's also ignore the practical limitations of making multiple withdrawals of just one unit from an Internet casino. In other words, this is more of a math problem than a practical advantage play.

Maybe somebody can come up with a better strategy, but here is mine: Keep betting the Player until you're up one unit and then cash out. According to my math, it will take on average 1/0.00023334 = 3857.014567 bets to be up one unit. You then withdrawal your 0.9 units and start again. The overall advantage is 0.9/3857.014567 = 0.000210007.

Yes, I know 0.02% is not a practical advantage. The question at hand is can you come up with a better strategy?

What is the exact definition of a session? Are you sure about the 24 hours thing? Intuitively it seems like you want to minimize your chances of losing sessions. If sessions could be infinitely long, you would always have winning sessions and just pay a tax on your winnings.

Quote: Wizard

I think 10 cents and they round to the nearest penny.

However, for the sake of argument, let's assume there is no minimum bet, unlimited bankroll, and they keep track of the balance as a decimal with unlimited precision.

And whoever voted for colitas, I'm waiting for the answer.

I didn't vote but my guess is .

Quote: randomperson

What is the exact definition of a session? Are you sure about the 24 hours thing? Intuitively it seems like you want to minimize your chances of losing sessions. If sessions could be infinitely long, you would always have winning sessions and just pay a tax on your winnings.

Yes. You can go to BetVoyager and it is mentioned in the help pages somewhere.

I think your "play as long as possible" strategy is equally as good mine, now that I think about it.

Is it a fresh deck/shoe for every new hand? If player starts off with an edge, no way that's not countable.

Quote: Mission146

Is it a fresh deck/shoe for every new hand?

Yes.

Quote: Wizard

However, for the sake of argument, let's assume there is no minimum bet, unlimited bankroll, and they keep track of the balance as a decimal with unlimited precision.

You have created a utopian world for Capt. Marty Martingale! Certainly with an unlimited bankroll and no maximum bet, the martingale would win units faster than your system. Although, the net win would be higher if one unit equaled infinity :-D.

Quote: surrender88s

You have created a utopian world for Capt. Marty Martingale! Certainly with an unlimited bankroll and no maximum bet, the martingale would win units faster than your system. Although, the net win would be higher if one unit equaled infinity :-D.

If Marty had an unlimited bankroll, then adding more money to it wouldn't increase it.

Yeah, I have a better strategy. Don't waste time or money with this and figure out something better to do.

Since the max gambling session is 24 hours, and you have to play 10% of any win in that session, I would say there's a 100% chance you DON'T have an advantage, even if you have a bot play the game 24/7. Unless they have some system that lets you place billions of wagers in a 24 hour period, there's no advantage to be had here.

Quote: Wizard

I think your "play as long as possible" strategy is equally as good mine, now that I think about it.

One forum member questioned this response behind the scenes, asking suppose you're up a million dollars, how much do you bet on the last bet?

My reply was that there is no last bet, you have to keep playing forever.

I think that does make my original strategy superior as there are defined quitting points.

btw wiz, with a edge that thin, how many hands do you have to play to have a 95% certainty of winning?

The # is probably astronomical.

I think it is the 10% Loss Rebate Game for the casino side.

If you have 1 million bankroll and bet the entire 1 million in one hand and quit regardless of the results, the casino will have advantage.

However, if you bet 1 million hands with bet size of $1, then player will have advantage. Am I missing something ?

Let's re-examine the problem for the case where a "session" is defined as a fixed number of hands N until you must stop. If that number N is small, then you shouldn't even play the game. For example, imagine the N equals 1 case. As N becomes larger, it eventually becomes positive EV to start playing. Your stopping point, to maximize the value of the session, is either when the number of hands are out or when you are at a break even point. Why break even? When you are in positive territory the next bet has a positive EV, even if you were going to stop right after it. Same for when you are in negative territory. At break even, if you were going to stop after the next bet, then its a hugely negative bet to place, because you lose an extra ten percent if you win.

So the solution is to keep playing until you either complete the number of hands in a session or reach break even when the number of remaining hands in the session is small enough so that continuing the session is negative ev.

As in many problems, a finite end point simplifies the analysis significantly. The problem gets more complicated if you can always start a new session whenever you want. My intuition for this problem would be that you would still always want to start over at break even because a break even session with N hands to go is always preferable to a break even session with N-1 hands to go. However, it is now not obvious to me that points other than break even are not also optimal stopping points.

Quote: ssho88

I think it is the 10% Loss Rebate Game for the casino side.

If you have 1 million bankroll and bet the entire 1 million in one hand and quit regardless of the results, the casino will have advantage.

However, if you bet 1 million hands with bet size of $1, then player will have advantage. Am I missing something ?

The value of a loss rebate is heavily dependent on the strategy you employ. In this case, the casino cannot control its strategy which makes this less valuable than a player loss rebate.

That's the reason why I has suggested to play as many hands as possible(to ensure that it's far beyond the loss and win exit point ), then casino will not have advantage.

Let me begin my apologizing to the anonymous forum member that I evidently misquoted, which he complained about behind the scenes.

Quote: Wizard

Let's also ignore the practical limitations of making multiple withdrawals of just one unit from an Internet casino. In other words, this is more of a math problem than a practical advantage play.

It is easy to give me an intellectual beating for ignoring the 24-hour rule in my strategy, but I specifically was trying to ask in the OP what the strategy should be if there were no forced stopping point, as you can see in the quote above.

I fully agree that with the 24-hour rule one must consider the clock.