Ace off the top

Any idea the value of a guaranteed ace off the top of a 6d shoe? Assume you aren't shuffle tracking, so you have no idea the content of the pack coming out.

Is it valuable enough to bet outside your planned ramp? If you're a nickel player, do you throw down a black? Thank you!

Assuming the ace goes to your hand, it's worth 51%. If you can get away with it, bet as much as you can.

but I don't know how it is calculated. Personally, I'd be willing to bet half my entire bankroll on it, but I'm sure the math guru's will consider that as an extreme over-bet.

I can't imagine anyone playing with such a small bankroll that a table max bet with a 50%+ advantage would be an overbet. If so, they probably shouldn't be playing at all.

There is some variance here, and the correct Kelly bet is 52% divided by the variance. I think that ended up someplace around 40%. I don�t remember exactly. For some reason, 38% rings a bell.

If you were half-Kelly, you would bet about half that amount.

Suppose you define �unit� so that a Kelly Equivalent Bank is 400 units. Then 40% would be about 160 units. For a nickel player, this would be $800. My guess is that nickel players don�t play at tables which allow $800 bets, so max bet would determine it here.

For a quarter player with a 10K KEB, this would be 4K. Again, most quarter players are not at tables with such high maxes.

This discussion does not consider any longevity issues.

It only considers .. 'Show me the money.'

Would that I get to a station, or place, in life where longevity issues were my biggest concern!

"There is some variance here, and the correct Kelly bet is 52% divided by the variance. I think that ended up someplace around 40%. I don�t remember exactly. For some reason, 38% rings a bell.

If you were half-Kelly, you would bet about half that amount.

Suppose you define �unit� so that a Kelly Equivalent Bank is 400 units. Then 40% would be about 160 units. For a nickel player, this would be $800. My guess is that nickel players don�t play at tables which allow $800 bets, so max bet would determine it here.

For a quarter player with a 10K KEB, this would be 4K. Again, most quarter players are not at tables with such high maxes.

This discussion does not consider any longevity issues. "

Professor, thanks for the 40% rule of thumb on an exposed ace. It's good to know in addition to an exposed ace. What about for an exposed monkey? What is the percentage?

On the 1st base, I frequently get a glance at some quick-draw dealers' exposed cards. There were at least 2 times in which the dealers burnt the exposed cards because of my huge jump bets. In order to milk the dealers slowly, I try really harder not to tip off the dealers with my kamikaze stunts. Oh at one time a dealer warned me that he would burnt the exposed ace if I jumped my bet. So I obeyed & made $37.50. Sometimes you get to go with the flow, right guys?

It's the 10s & JQKs (aka Munkees) exposed by some quick-draw dealers! I'm rolling on the floor laughing my ass off. MB, that's a good one. Hey how's our buddy "Kard" doing? I'm worry for him since he had not returned my calls nor emails.

> What about for an exposed monkey? What is the percentage?

The advantage is around 13%, isn't it?

-Sonny-

"> What about for an exposed monkey? What is the percentage?

The advantage is around 13%, isn't it?

-Sonny- "

Are you inferring that I should bet 13% of my Kelly Equivalent Bank? Say if I were a blackchipper with a 100K KEB, this would be 13K (13%) or table max for an exposed ten, right?

He pretty much got out of gambling a few months ago and has a new project. He may well have enough money to retire right now.

Are you inferring that I should bet 13% of my Kelly Equivalent Bank? Say if I were a blackchipper with a 100K KEB, this would be 13K (13%) or table max for an exposed ten, right?

It would 100K * 13% / 1.3 = 10K.

Plagiarizing from McDowell's Blackjack Ace Prediction, the correct Kelly bet if you know your first card will be an ace is 34% of your bankroll.

This is slightly less than what might be expected because the variance of a hand whose first card is an ace is higher than the variance of a random hand. This is primarily due to the significantly greater chance of receiving a natural, paying 3:2 and thus farther away from the mean outcome.

However, as MathProf and others pointed out, the table maximum and longevity, rather than the Kelly criterion, are probably going to be the limiting factors.

In the linked article below, Grosjean and Mankodi work out the Kelly optimal bet for initial bets when you know you have an ace. First, they work through the optimal strategy for playing your hand in this situation based on the fact you will have a significant fraction of your bankroll on the table. This strategy is risk averse rather than ev maximizing and changes several basic strategy plays. The MacDowell number seems closer to the fractional bet of playing the hand according to basic strategy.

Interesting article--it seems to consider many more playing subtleties than does McDowell's book.

Differences in numbers aside, the main thing is being able to get an ace to your hand in the first place. Whether you bet 42%, 38%, or 34% of your bankroll and whether you modify your playing strategy are relatively minor concerns if you can consistently steer aces into your hand. Not getting kicked out is probably the most significant worry :-)