I am not a statistician, so feel free to tell me where I am incorrect, but:
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Originally Posted by NewOldGuy
Your advice to always bet odds to the max,
Optimal craps strategy is indeed to take maximum odds (bankroll considerations aside; we're assuming unlimited bankroll, this is an academic question).
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your statement that it is the best bet in the game,
It is indeed the best bet on the craps table. It is not a positive EV bet, but it is the best one available.
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and your repeated implication that this bet is advantageous to the player.
I don't think he implicated it was advantageous; he stated it was neutral - a true odds bet. He implicated that it was MORE advantageous than straight pass line betting. Still not +EV, but better than straight pass line betting.
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Some players might want to increase their variance and their action by putting more money in play just for excitement, and accepting the increased risk that entails. Some might not. But in no case is there any monetary advantage to any player making these bets. Their EV is unchanged, and they will lose the exact same amount of money over time as they would by not making these bets.
Yes, the combined house edge is reduced, as I immediately explained in my first paragraph posted in this thread when I answered the OP's question. But in this case it's an illusion that this helps the player, unless you count the fun factor, and possibly comps/points.
It's the exact same thing as if you are playing some other -EV game and while playing it you decide to put down 5x more units over here on the side with a guy who wants to flip coins for money, so you do both together to give you more stimulation. It has no effect on your winnings over time, but increases your variance and short term risk a lot.
This is where you lose me. "House edge" and EV are the same concept, just phrased differently. If you are reducing the house edge, you are by definition increasing your EV. Not to positive territory, but you improving it. Your coin-flipping example is flawed. If I went to the side bet guy
and got a better payout on my additional 5x units, then yes, I would be increasing my EV.
If you had $1 million to bet at a craps session (or $1 billion or whatever giant number), would you be better off monetarily (not as a %, but actual $) if you made 40,000 $25 pass line bets or 396 (give or take) $25 pass line bets backed by 100x odds (assume you are at the Cannery). -EV in both spots, but the latter will lose you a lot less money. The variance will be MUCH much higher true, but the EV will be higher.