Hypothetical Heads Up Gambling Situation - Page 4

jay_shark · #31 10-27-2006, 02:40 PM

Great question Nicho .

Here is a follow-up question . What range of hands should the opponent be calling the all in with ?

If he knows player A's optimal shoving range , then player B should know the optimal calling range . This is a classic game theory problem .

Nichomacheo · #32 10-27-2006, 03:16 PM

You mean if he had the option to call or fold? It would complete change the problem because then I wouldnt have to call with a random hand. Very hard problem without a doubt.

jay_shark · #33 10-27-2006, 06:03 PM

I verified that my conjecture is true for all n .

Pretty cool .

Nichomacheo · #34 10-27-2006, 06:22 PM

<font color="blue">Question 2. Now the person offering the bet is allowed to fold once, except for the tenth hand. Now hat is the optimal strategy for both players?</font>

Keep in mind, once the fold is used, the person offering cannot fold again and must call the opponent's next push.

roommate · #35 10-27-2006, 06:32 PM

Now this is poker... no longer is it just odds... both players can think on many levels...

the pushing player can push his first decent hand in hopes that the offering player will use his fold early... so that later on with a better hand the pusher can 'force' the deal.

and obv since the offering player knows that the pusher is thinking this way would be correct to loosen his standards against that first push

but if the pusher knows his opponent is a saavy multi level thinker he will be sure to push the first time not to force the fold but rather trap him into calling

of course it follows that the offering player would be better to fold anyways just in case the pushing player realizes that his pushing will be called loosely and pushes with the goods

but, if the pushing player knows that he will fold for the aforementioned reasons he is best off pushing the first hand no matter what (blind) so that the second player is forced to a decision for all of his chips (secret of poker according to mike) and he can later appropriately push with a better hand if the offering player folds.

~rob

jay_shark · #36 10-27-2006, 06:34 PM

The first player should still shove with the range of hands as before . The caller has to be aware of the optimal shoving range by player A . If player A shoves on the first hand , then B knows he's shoving with the top ninth of all hands . B will only call if his hand is better than 50 % against the shovers all in range .

ie , ace king wins 53 % of the time against the top 9th percentile of hands . Therefore ace king must be included in the calling range for the first shove . It turns out player B should call with AK and 10+ .

You keep on working this out for the 2nd, 3rd ,4th hand etc

I realized after that I answered a slightly different problem .

ok a random hand against Player A's first shove wins 30 % of the time . That means if player B's first hand does better than 30 % , then he should call the all in .

roommate · #37 10-27-2006, 06:43 PM

Disagree jay...
knowing that the offering player is unlikely to have AK and TT+ (or whatever) he should push to eliminate his fold.

~Rob

jay_shark · #38 10-27-2006, 06:46 PM

lol Rob

roommate · #39 10-27-2006, 07:06 PM

jay... i'm serious... your read on your opponent SHOULD affect your play...

bluffing is a possibility... and correct to consider

~rob

Nichomacheo · #40 10-27-2006, 07:08 PM

I think this is a very different problem Jay. Like Rob said, you now have to consider that the pusher is trying to make you lose your fold because its higher EV later when the caller doesnt have this option.

As Rob said, knowing that your opponent might push with air here will change the dynamics a lot.